بحوث سكوبس — عمار عبد الكاظم فتحي

Through a numerical study, the thermo-hydraulic behavior of a solar air heater with quarter petal shaped ribs on its absorber plate is examined including a comparative evaluation of three unique rib configurations. The continuity, momentum (Reynolds-Averaged Navier-Stokes) and energy equations of steady, incompressible, turbulent flow are solved. Renormalization Group (RNG) k -ε turbulence model was chosen to solve the turbulent flow phenomena. The thermal performance has been studied under varying design parameters: relative roughness pitch (7.14 ≤ P/e ≤ 17.86), Reynolds number (4000 ≤ Re ≤ 20,000), while the relative roughness height was kept constant at e/Dh = 0.042. The key performance indicators of the SAH performance are measured against the Nusselt number (Nu), the friction factor ( f ), the thermal-hydraulic performance factor (TPF) and observation of critical flow features. Results indicated that the configuration of the quarter petal shaped ribs has a decisive impact on the heat transfer and the friction factor features, and its performance becomes very sensitive to the variation in P/e and Re. With the artificially rough SAH, the optimal configuration achieved a TPF of 2.155, which corresponded to a 115.5 % thermal performance enhancement. Correlations for Nu and f as functions of the Reynolds number and relative roughness pitch were obtained by non-linear regression analysis. © 2025 Elsevier Masson SAS.

A CFD interpretation is presented to analyze the double-diffusive natural convection along with the entropy generation inside inclined E-shaped enclosure with wavy wall under the influence of magnetic field. The existence of inner heated circular body had been included in this study that it solved numerically using finite element formulation. The enclosure wavy wall is kept at the same hot temperature of the inner heated body while the vertical wall of the enclosure is kept at cold temperature and the rest of the horizontal walls are thermally insulated. The enclosure had been filled by electrically conducting fluid with Prandtl number of Pr=0.024. Additionally, Hartmann number and Darcy number kept constant at as Ha=20Da=10−5. The studied parameters are the inclination of the magnetic field that varied as γ=0°15°30°45°60°75°and90°. Additionally, the enclosure its self is orientated as λ=0°45°90°135°180°225°270°315°and360°. The Rayleigh number are varied as Ra=103−106. The buoyancy ratio had been varied as N=0246810and Lewis number is varied as Le=1−10. Additionally, the inner circular body is varied −0.3≤δ≤+0.3. The results show that applied the magnetic field in the vertical direction γ=90° helped in enhancing the heat transfer and lower entropy generation while at γ=0° helped in better mass transfer. Additionally, in spite inclining the enclosure at λ=270° contributed in lower entropy generation but it led to lower heat and mass transfer rate. At zero buoyancy ratio number N=0, there is no impact of Lewis number on heat transfer rate. However, when buoyancy ratio number into N=10, it is noted that increasing Lewis number from Le=1 into Le=10, leads to decreases Nu by 52.17 %. Similar behavior is noted for the entropy generation while Sherwood number increases with the increasing of Lewis number regardless the value of buoyancy ratio number. Lastly, the position of the inner body and its role in heat and mass transfer is highly impacted by the Rayleigh number. It is obtained that at low Ra, the best position for heat transfer is at δ=−0.2 while at high Ra, the best position is at δ=−0.3. Additionally, at high Ra, the entropy generation decreases as the inner body moved in the positive direction. © 2025

The present work numerically demonstrates the uniform magnetohydrodynamics Newtonian, laminar natural convection in elliptical cold enclosure with inner hot circular body considering the influence of its vertical movement on the fluid flow and heat transfer. The gap area between the elliptical enclosure and the inner body had been filled by the Al2O3-water nanofluid in the upper layer, whereas lower layer has been filled by the porous medium that has been saturated by an identical nanofluid. The local thermal equilibrium model had been implemented to model the nanofluid and porous media. Additionally, Darcy–Brinkman model considered in the representation of the porous media. The three governing equations of heat and fluid flow like energy and momentum of fluid, in addition to the continuity equation, had been solved numerically utilising finite element formulation. The parameters under investigation are the Rayleigh number value (Formula presented.), Darcy number (Formula presented.), and Hartmann number (Formula presented.). Additionally, two geometrical parameters had been selected, which are the three different locations of inner cylinder (top, middle, bottom), as well as the four different values of the enclosure’s orientation angle (Formula presented.). The results have been presented to reflect the influence of the abovementioned parameters on isotherms and streamlines, besides Nusselt’s number. It has been proved that to improve the heat transfer rate, it is better to locate inner body in bottom region. The Nusselt number increases by 17.44% when it is moved from the top to the bottom. Additionally, the Nusselt number along the elliptical enclosure attached to the nanofluid layer when rotating the elliptical body from (Formula presented.) into (Formula presented.) leads to lower the Nusselt number by 32.3372%. This result is exactly inverse considering Nusselt number along nanofluid–porous layer which proved that increasing the orientation angle from (Formula presented.) to (Formula presented.) contributed to enhancing Nusselt number by 24.7009%. © 2024 Engineers Australia.

Background: Free convective heat transfer and irreversibility characteristics in a square-shaped cavity filled with multiple layers of nanofluid (SWCNT-water) and nano-porous media are studied for use in solar power plants. The application is within the concentrating solar dish collectors where the reflected absorbed thermal radiation reflected on the receiver (enclosure). Methods: This study is done numerically for various dimensionless parameters, including Darcy number (10–5 ≤Da ≤10–1), the porosity of the porous layer (0 ≤ ε ≤ 0.8), Rayleigh number (103 ≤ Ra ≤ 106), and the nanoparticle volume fraction (0 ≤ φ ≤0.06). Different cases depending on the distribution of the nanofluid and nano-porous layers inside the cavity are studied. The number of porous layers and their distribution within the cavity have a remarkable impact on the rates of fluid flow and heat transfer. Significant findings: The novelty point in the current study is that it is the first theoretical study that includes the study of natural convection through the stream function, isotherms and the entropy effect in a square enclosure that contains layers of porous and nanofluid, and these layers are longitudinal and transverse. The flow intensity drops as the porosity gets closer to 0.63, especially at the interface between the nanofluid and nano-porous. Moreover, Ra = 106 causes an increase in natural convection, which causes the Nu‾ to rise until permeability, ε = 0.4. The Nu‾ starts to fall as the porosity rises after this permeability value (ε = 0.4). © 2025 Taiwan Institute of Chemical Engineers

A finite element-based numerical study is conducted on MHD double-diffusive natural convection and entropy generation in an inclined, corrugated porous enclosure with a star-shaped inner body. The role of various parameters had been selected such as enclosure's angle Φ=0°15°30°45° along with various Rayleigh number104≤Ra≤106, buoyancy ratio N=0246810 and Lewis number Le=0.1,110 while Hartmann and Darcy numbers had been kept constant at Ha=20Da=0.001. The role of corrugated length had been tested as well with rangingL=0.10.150.2. The results had been presented in terms of streamlines, isotherms with four different types of entropy due to fluid friction, heat transfer, double diffusive and magnetic field. Additionally, the variation of Nusselt number, Sherwood number and Bejan number had been studied as well. The major results show a small decrease in heat transfer, approximately 2.5%, with the increment of the enclosure's angle from Φ=0° to Φ=45°. The mass transfer decreased by 8. under the same enclosure angles values. It is important to note that entropy generation decreases by 10 with an increase in the enclosure's angle. The analysis also revealed that a longer corrugated length improved heat and mass transfer performance; however, this enhancement was accompanied by a rise in entropy generation. Lastly, the Bejan number is reduced as the corrugated length increases. © 2025 Elsevier Ltd

Domestic stack is considered to investigate the double-diffusive laminar natural convection. The working fluid is a gaseous mixture that has similar physical properties to carbon dioxide. Knowing the patterns of gaseous mixture distribution and determining the carbon deposit regions can help in carbon capture problems. The present study uses the finite element method to numerically examine the double ratio-diffusive physical phenomena in a rectangular-trapezoidal enclosure and to simulate the stack under a wide range of dimensionless parameters, such as buoyancy ratio (Formula presented.), Lewis number (Formula presented.), and Rayleigh number (Formula presented.) for different aspect ratios. Nine different cases of the geometrical ratio are selected to cover most possible design configurations. The results indicate that increasing the Lewis number leads to augmented solutal transport but reduces heat transfer. However, both heat and mass transfer are observed by increasing the buoyancy ratio. It is worth mentioning that increasing the ratio of upper side length to base length (Formula presented.) from (Formula presented.) to (Formula presented.) leads to a significant increase in mass transfer by 75% and heat transfer enhancement ratio by around 50%. © 2023 Wiley Periodicals LLC.

The present work examines numerically the natural convection along with the entropy generation within H-shaped enclosure with wavy walls filled by (Ag-MgO/water) hybrid nanofluid considering inner bodies and under the influence of horizontal magnetic field and thermal radiation using finite element scheme. The inner bodies of the circular shapes are kept at a hot temperature, while the two-sided wavy walls are kept at a cold temperature. The rest of the enclosure’s walls are thermally insulated. The influence of many parameters had been examined such as Rayleigh number (103≤Ra≤105), Hartmann number 0≤Ha≤60 vertical location of inners bodies 0.2≤δ≤0.8, distance between inner bodies 0.3≤E≤0.9, height of the enclosure walls 0.2≤B≤0.8 and width of the enclosure wall 0.1≤A≤0.9 in addition to the radiation parameter 0≤Rd≤3 on fluid flow, heat transfer and entropy generation. The results of this study had been presented in terms of streamlines, isotherms, entropy generation, Nusselt and Bejan number. The results showed that the Nusselt number will be at its lowest value when the vertical location of the inner bodies is δ=0.8 and the influence of Hartmann number will be negligible at this value. Also, at high Rayleigh number Ra=105 increasing the distance between the inner bodies from E=0.3 into E=0.9 leads to increasing Nu by 76%. However, increasing the height of the enclosure’s walls from B=0.2 into B=0.8 leads to enhancing Nu by 0.02%. However, increasing width of the enclosure wall from A=0.1 into A=0.9 leads to an obvious reduction in Nusselt number by 20%. Additionally, it had been obtained that increasing the vertical location of the inner bodies, the distance between them and the width of the enclosure and reduction of the height of the enclosure’s wall lead to increasing Bejan number. Stronger magnetic fields enhance conductive heat transfer; increasing the Bejan number which represents irreversibility as noted at increasing Hartmann number from Ha=0 into Ha=60 leads to increasing Bejan number by 79%. © Akadémiai Kiadó, Budapest, Hungary 2024.

The present work focuses on investigating magnetohydrodynamic (MHD) natural convection in a complex I-shaped enclosure with corrugated walls, filled with nanofluid and porous media layers. This study analyzes various parameters' effects on heat transfer and fluid flow. The enclosure's left and right walls maintain low temperatures, while the other walls are insulated. The inner corrugated cylinder experiences high temperatures. The study examines the impact of Rayleigh number (Ra), Hartman number (Ha), nanofluid volume fraction (ϕ), Darcy number (Da), MHD inclination angle (γ), position of the corrugated cylinder (δ) and number of undulations (N) on isotherms, streamlines, velocity profiles and average Nusselt number variations. The results show that higher Ra values increase the average Nusselt number while increasing Da enhances it by 65%. Magnetic source inclination greatly affects heat transfer, with Nusselt at γ = 90° being 15.34 compared to 10.234 at γ = 0°. The study concludes that optimal heat transfer occurs at γ = 90°, Ra = 106, Da = 10−3, Ha = 30 and N = 2. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

The current study investigates the influence of MHD on the natural heat transfer considering the irreversibility in a complex-shaped cavity with the existence of inner roundish heater with four attached fins utilizing finite element formulation. Three different cases are considered to figure out the major characteristics of temperature, stream function and total generated entropy, Nusselt number in addition to Bejan number. Concentrated attention is directed to the enclosure geometry modifications and the varied length of attached fins and their impacts. The parameters of study are ranged as follows; Rayleigh number 103≤Ra≤106, Hartmann number 0≤Ha≤60, fins’ length 0.1≤H≤0.3. The novelty of the present work is on studying all of these parameters in the complex enclosure considering three different cases of the shape of the outer walls so that the star-shaped enclosure is classified as case 1. With increasing the length that separated between the outer arc of the star enclosure, the octagonal-shaped enclosure will appear as denoted in case 2 and 3. It had been seen that at low Rayleigh number Ra=104, case one is the best choice in heat transfer bettering while it is the lowest case at high Rayleigh number Ra=106. Additionally, the influence of Hartmann number on the total entropy generation reduction percentage for case three is 63.57% while it is 51.11% for case two while Hartmann number had negligible impact of entropy generation reduction for case one. Lastly, the highest Bejan number is at fin length H=0.3 is recorded for case one. © Akadémiai Kiadó, Budapest, Hungary 2023.

Nanofluids have garnered significant interest as a potential solution to address overheating challenges across diverse industries. Researchers are actively exploring different types of nanofluids to mitigate these issues. In this study, a numerical analysis was conducted using ANSYS software to examine the fluid flow and heat transfer characteristics of nanofluids (ranging from 0 to 4 volume fractions) in a corrugated wavy channel within the turbulent range. Various nanoparticles, including Al2O3, CuO, SiO2, and ZnO, were employed and dispersed in different base fluids such as ethylene glycol, glycerin, and water. The particle size of the nanoparticles ranged from 20 to 70 nm. The results revealed that SiO2/water-based nanofluids provide better heat transfer than all the water-based nanofluids. The maximum average Nusselt number and pressure drop of 200 and 115 Pa, respectively, were observed for SiO2 nanofluid (volume fraction of 0.04) with a particle size of 20 nm. Highlights Al2O3, CuO, SiO2 and ZnO considered in this work. Corrugated plates with three different corrugated angles of 20° to 60° are tested. Eexperiments are performed for different heat flux in turbulent range. Maximum heat transfer obtained for SiO2/water nanofluid. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

The present investigation is on examination of the natural convection and entropy generation considering the heatlines visualization of nanofluid I-shaped enclosure with two corrugated walls considering inner rectangular heater of three different heights. The influence of Brownian motion along with thermophoresis had been implemented using Inhomogeneous two-phase model of nanofluid. The governing equations were solved numerically using COMSOL software. Influence of Rayleigh number (Formula presented.), Buoyancy ratio number (Formula presented.), Lewis number (Formula presented.), heater length (Formula presented.). The results indicate that the influence of Lewis number on heat transfer bettering is stronger at high Rayleigh number (Formula presented.) while its impact is negligible at a lower value of Rayleigh number (conduction mode). In addition, the total entropy generation gets its highest value at Lewis number (Formula presented.). Bejan number, fluid flow strength and heat rate increase as the rectangular heater height increases. Also, higher heat transfer augmentation is taken when the heater height is (Formula presented.) while increasing the heater height to (Formula presented.) leads to more total entropy generation. The impact of heater height on total entropy generation is highly affected by Rayleigh number as increasing the heater height from (Formula presented.) into (Formula presented.), total entropy generation increases by (Formula presented.) at (Formula presented.) while it increases by (Formula presented.) at (Formula presented.). © 2024 Wiley Periodicals LLC.

In magnetohydrodynamics (MHD) flowing and mass transfer, 2-D unsteady non-Newtonian liquid flow across the stretched surface with a surface temperature had been examined numerically. Casson fluid model was utilized for the full description of the non-Newtonian fluid. Similarity transformation had been considered for transforming the dimensionless heat and fluid flow basic partial differential equations into simple ordinary equations. After that, the bvp4c MATLAB solver utilizes numerical methods to resolve the altered equations. We study and discuss in depth the flowing and heating attributes under various parameters, including the magnetic, Casson, and unsteadiness parameters, Schmidt number, and Prandtl number. It has been proven numerically that the velocity of the fluid first reduces when temperature and unsteadiness parameters increase, which significantly negatively impacts concentration. The velocity field is suppressed when the Casson parameter’s values are increased. But when with the increment of the Casson variable, then, the concentration and temperature go up. The velocity field is suppressed as the magnetic parameter’s values increase. But with the rise in the magnetic parameter, there will be an improvement in both the temperature and concentration. © 2023 Taylor & Francis Group, LLC.

The present work investigates the mixed convection of nano-encapsulated phase change material (NEPCM) inside a trapezoidal-wavy cavity subjected to a magnetic field. The mixed convection results from the movement of the upper lid of the cavity and the temperature difference between the inclined cold side walls and the hot bottom wavy wall. The main goal of this study is to address the impact of wall waviness and the magnetic field on mixed convection on a disclosure filled with NEPCM. The governing equations representing the investigated case were solved by Galerkin finite element method (GFEM). The influences of lid velocity (Re = 1-1000), bottom wall undulation number (N = 1-4), and magnetic field strength (Hartmann number (Ha) = 0-100) on the thermal behavior and the flow patterns were examined and reported. The results revealed that the mean Nusselt number is directly proportional to the lid velocity (Re), whereas it is reverse proportional to the bottom wavy undulation number (N) and the magnetic field strength (Ha). The higher values of Re (e.g., Re = 1000) could lead to a 300% enhancement in local Nu values compared to those of lower Re values (e.g., Re = 1). At Re = 1000, increasing Ha from 0 to 100 and N from 1 to 4 reduced the mean Nusselt number by 53% and 30%, respectively. According to the findings of the present study, it is recommended that heat transfer augmentation should eliminate both the waviness of the bottom wall and the magnetic field since they hinder the free and mixed convection flow. © 2023 The Authors.

The present work examines experimentally the natural convection heat transfer within a three-dimensional novel I-shaped enclosure with wavy-walled and inner circular pipe. The left layer is filled by Al2O3–water nanofluid while the right layer is filled with nanofluid/porous medium. The nanofluid thermophysical properties had been measured experimentally. The thermal conductivity had been measured utilizing hot-wire approach, viscometer is used to measure the nanofluid viscosity, and densitometer is used to measure the nanofluid density. It noted that there is a good agreement between the measured nanofluid thermophysical properties and the calculated properties based upon the theoretical models within nanofluid concentrations [0–0.06]. K-type thermocouples had been installed on the left and right walls as well as along the center of the midsection in order to measure the temperature experimentally. Two cores of magnetic field had been installed with magnetic intensity of 20 mT. It had been proved that there is a slight increase in the temperature with the existence of the magnetic field. For example, at 20 mT, the temperature increases into 29.1 °C while the temperature equals to 28.8 °C at the absence of the magnetic field. Additionally, it had been illustrated that increasing the hot side wavy-walled temperature leads to an increase in the temperature difference which increases the temperature level in the nanofluid–porous region and the nanofluid region. © 2023, Akadémiai Kiadó, Budapest, Hungary.

The present work examines numerically the inclined magnetic field on thermogravitional heat transfer in a novel I-shaped enclosure filled partially with nanofluid in the left layers and filled by partially by porous medium saturated by the same nanofluid using finite element method. Three different shapes of inner bodies had been embedded in the enclosure. The enclosure is partially wavy from its vertical walls with four different cases of multi-inner bodies of various shapes such as case 1, 2, 3 and 4 represent circular, square, rhombus and triangular in order to examine their impact on heat transfer and fluid flow. Also, the influence of nanofluid loading, Rayleigh number (10 4≤ Ra≤ 10 6) , Darcy number (10 - 5≤ Da≤ 0.1) , Hartmann number (0 ≤ Ha≤ 60) , MHD angle (0 ∘≤ γ≤ 90 ∘) along with the number (1 ≤ No≤ 3) and position (0.3 ≤ Y≤ 1.3) of inner hot bodies had been examined in terms of streamlines, isotherms and Nusselt number. The results indicate that the number of inner body and its position along with its shape influence on the heat transfer rate. It is obtained that Nusselt number for Case1 > Case3 > Case2 > Case4. Also, movement the inner hot body from bottom to the top leads to an obvious reduction in the Nusselt number. The increasing of magnetic field angle from γ= 0 ∘ into γ= 30 ∘ leads to decreases the heat transfer rate while more increasing of magnetic field angle augments the rate of heat transfer. Finally, increasing the number of inner hot bodies leads to reduce the total Nusselt number. Thus, for better heat transfer augmentation it is recommended to locate the inner hot body at Y= 0.3 and No= 1. © 2022, The Author(s) under exclusive licence to Associação Brasileira de Engenharia Química.

The present study examines the turbulent flow of mixed convection heat transfer enhancement within a rectangular channel considering three different novel shapes of ribs (smooth, scalene, and curved-side triangular). The investigations were conducted experimentally by developing a new test facility, while the numerical computations were carried out using the finite volume method. The experimental work involves constructing of the channel, ribs, and all equipment and measurement instruments. The numerical work is based on ANSYS FLUENT considering the k–ε turbulent model. The results are presented and compared in terms of Nusselt number, friction factor, and performance factors for Reynolds numbers ranging between 3000 and 12,000. By comparing the average values of the numerically obtained Nusselt number with experimental measurements, the data showed a close agreement with a maximum difference of 5%. It also found that scalene triangular ribs (STRs) provide better performance in terms of heat transfer, although introducing a slight increase in friction losses. STRs showed (20%) increase in Nusselt number compared with smooth channel, and 3%–6% increase in Nusselt number compared with curved-side triangular ribs (CTRs). In contrast, CTRs have a lower friction factor value of 5% compared with STRs at a low value of a Reynolds number of 3000. Furthermore, the Nusselt number changes significantly (250% increase) by increasing the value of the Reynolds number from 3000 to 12,000. A thermal performance factor of up to 1.28 was achieved for the STRs at the lowest range of Reynolds' number of 3000. The findings from the present study are of practical importance for industries requiring heat transfer enhancement techniques to improve heat transfer equipment performance. © 2023 Wiley Periodicals LLC.

Due to high affinity and extensive surface area between arsenic and nitrogen in C3N, the two-dimensional C3N monolayer has considerable the potential to effectively adjust the release of gaseous As2O3. By performing density functional theory (DFT) calculations, the adsorption of As2O3 on the surface of C3N monolayer was investigated. The results revealed that site C4N2 on the surface of the C3N monolayer has greater ability than site C6 to strongly adsorb As2O3. Also, the recovery time of the C3N monolayer for As2O3 were about 25.64 s and 5.23 μs at 298 and 400 K, respectively. The results related to the charge transfer (CT), adsorption stability, electronic and geometric structure confirmed that the C3N monolayer was an appropriate choice for adsorption of As2O3. Overall, the C3N monolayer can be considered as one of the most suitable adsorbents that can be used to effectively control gaseous As2O3. © 2023 Elsevier B.V.

The present article presents a detail theoretical study of the hydrodynamics boundary layer generated over a flat plate considering laminar, transition and turbulent regions. The importance of Reynolds number within the boundary layer and how it plays a major role for the heat and fluid flow has been discussed thoroughly this article. The corner stone equations of heat and fluid flow has been presented which they are the three physics laws; mass, energy and momentum of fluid. In the subsequent sections the basic concept of the boundary layer characteristics likes displacement, momentum and energy thickness are discussed. A separate section for deriving momentum integral equation and various relations of drag, rate of growth of each layer have been presented from this equation. In this work authors have focused in the transition region which plays a crucial role in both heat transfer and fluid flow phenomenon and there are limitations in explaining this region and most of the previous published work describes only on the laminar and turbulent region without considering the transition zone. Hence the present work provides a comprehensive analysis for this region. The boundary layer thickness, drag and drag coefficient for the transition zone derived mathematically. © 2023 Author(s).

The present work examines numerically the heat transfer and the buoyancy-driven flow within a U–shaped baffled enclosure filled with a nanofluid-saturated porous medium in the presence of an inclined magnetic field using a finite element scheme. The enclosure bottom wall is heated sinusoidally while the two baffles and the inner walls are maintained at a constant cold temperature. The rest walls of the enclosure are kept adiabatic. The parameters under investigation are Hartmann number (Ha), volume fraction (φ), Darcy number (Da), Rayleigh number (Ra), nanoparticles aspect ratio (AR), and the angle of applied magnetic field (γ). The results are crucial and illustrate that increasing the values of Ra, Da and the nanoparticles volume fraction enhances the heat transfer while the Hartmann number inversely affects the heat transfer augmentation. Moreover, the average Nusselt number (Nuave) increases by increasing the enclosure aspect ratio. For the geometry under consideration and for a better heat transfer rate, it is recommended to choose an AR = 0.6 at Ha = 0 with a 0.1 vol fraction. © 2022

The current article presents a numerical simulation of the nanofluid convection inside a square enclosure with two inner adiabatic circular bodies. Galerkin finite-element analysis was utilized to solve the governing equations under the assumptions of laminar, steady flow conditions considering a homogeneous single-phase approach. The parameters under investigation are Rayleigh number (Ra), solid volume fraction, the horizontal position of the two inner cylinders, and the inclination angle of the enclosure. The results indicate that increasing the Rayleigh number, and the solid volume fraction improves the heat transport rate. It is obtained that at low Ra, there is no significant impact on the enclosure angle, while as the Ra goes up, the heat transfer rate increases gradually. In addition, the best location of the internal bodies is in the middle of the cavity as it exhibits an increase in the flow velocity. To obtain the highest Nusselt number, it is recommended to use an inclination angle of 30 at any value of the Rayleigh number. © 2022, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.

The present work numerically examines natural convection within an I-shaped wavy-walled enclosure with multi-pipes of heat exchangers filled with multi-layers of nanofluid and porous medium saturated with the same nanofluid. The finite element scheme is used to solve governing equations of mass, momentum along with the energy in dimensionless form. The influence of various dimensionless parameters such as Rayleigh number (10 4≤ Ra≤ 10 6) , Darcy number (10 - 5≤ Da≤ 0.1) , Hartmann number (0 ≤ Ha≤ 60) , number of undulations (1 ≤ N≤ 5) , nanofluid volume fraction (0.00 ≤ ϕ≤ 0.06) , porous layer thickness 0.6 ≤ XP≤ 1 and MHD inclination angle (0 ∘≤ γ≤ 90 ∘) is studied to explain their effect on fluid flow and heat transfer that presented in terms of streamlines, isotherms and average Nusselt number. Three different thermal cases of the location of the internal hot pipe are treated. Our results are in a good agreement with previous works. The finding of this study proved that for better heat transfer, it was recommended to use number of undulation N= 1 and that the location of the inner pipe is at the bottom of the enclosure (case 1). Moreover, it was obtained that the increase of Rayleigh number (Ra), Darcy number (Da), inclination angle of MHD and the reduction of the porous layer thickness as well as the reduction of Hartmann number (Ha) leads to an increase in heat transfer. Also, the results indicate that enhancement percentage of Nusselt number is 57.77% for Case 1 in a comparison with Case 3 when the number of undulation is N= 1. Finally, applying the magnetic field in the vertical direction (at γ= 90 ∘) enhances Nusselt number for Case 1 by 53% in a comparison with Case 3. © 2021, Akadémiai Kiadó, Budapest, Hungary.

The current work investigated numerically the natural convection within a square enclosure filled with nanofluid by examining four different types of attached fins (rigid fins, flexible oscillating in the same and opposing directions) and comparing it to the case without fins. The governing equations of heat and fluid flow (mass, energy and momentum) of fluid had been solved using the finite element scheme. The results are validated with the previous studies and presented in terms of streamlines, isotherm and Nusselt number. The influence of Rayleigh number (104 ≤ Ra ≤ 106), dimensionless time (10–4 ≤ τ ≤ 1), thermal conductivity ratios (1 ≤ ks ≤ 1000), the amplitude of the flexible fins (10–2 ≤ A ≤ 0.1) and frequency (0.05 ≤ λ ≤ 0.5) are studied. The governing parameters have been tested based upon their influence on fluid flow and heat transfer for the current study. The results are shown as contours of vortices, velocity, streamlines and isotherms as well as the local and average Nusselt number (Nuave). It is observed that the larger amounts of heat are transmitted by convection at higher thermal conductivity ratios, and the greater the magnitude of the Nusselt number demonstrates the pronounced effect of the fin oscillation. In addition, when the flexible fins oscillated in the same directions, the Nusselt number increased by 18.34% as compared to the case without fins. Furthermore, increasing the flexible fins' amplitude improves the oscillating motion of the fins inside the cavity, which improves fluid flow and heat transmission strength. © 2022, Akadémiai Kiadó, Budapest, Hungary.

The current study focuses on the transient mixed convection within a vented square enclosure with differentially heated vertical walls and a flexible baffle coupled to a circular solid cylinder. In numerical analysis, the COMSOL Multiphysics tool is used to simulate and solve two-dimensional governing equations using the Galerkin finite element approach and the arbitrary Lagrange–Euler (ALE) method, as well as the coupling of structure deflection and fluid flow. This work considered the effects of changing locations of flexible baffles attached to a cylinder on thermal and flow structures. The effect of several parameters, such as Richardson number (10–1 ≤ Ri ≤ 102), Cauchy number (10–12 ≤ Ca ≤ 10–4), and Reynolds numbers, (50 ≤ Re ≤ 250) on convective heat transfer characteristics are investigated for time 0.01 to 10 s. It is observed that changing time steps leads to a continuous change in fluid flow intensity which reflects on the deformation direction of the flexible baffle. The results indicated that the cavity with flexible baffle has the best average Nusselt number compared to cavities with rigid baffle and without baffles, respectively. As Re is raised from 50 to 250, the percentage of the average Nusselt number increased to 40% at Ri = 0.1 and 59% at Ri = 200. © 2022, King Fahd University of Petroleum & Minerals.

The present work examines utilizing CFD simulation of the natural convection within complex enclosure with four different cases of wavy patterns considering the existence of inner heated elliptical body. The influence of inclined magnetic field had been taken into consideration. The space between the inner body and the enclosure had been filled by two layers. The first right layer was filled by nanofluid while the second left layer had been filled by porous medium with the same nanofluid. The influence of various parameters such as number of undulations, the distance between the wavy walls, and the inner elliptical body position for four different cases of wavy walls patterns with and without magnetic field on fluid flow and heat transfer had been drawn in terms of streamlines, isotherms and Nusselt number. The results indicate that in the absence of magnetic field the Case 3 has the highest stream function with a dimensionless value of | Ψ max| = 34.229 which make Case 3 is recommended wavy patterns for bettering the fluid flow strength when the number of undulations kept at (N= 1) and the distance between the wavy walls kept at (B= 0.8). It is important to note that at (B= 0.8) , Case 1 has the lowest strength of the fluid flow while it enhanced by 41.17% when (B= 1.0). On the other hand, increasing the distance between wavy walls from (B= 0.8) into (B= 1.4) enhances Nusselt number by 31.67%. The influence of inner body position had the highest impact of heat transfer rate in a comparison with the other as it helps in improvement of Nusselt number by 67.70% when it moves toward to bottom of the enclosure. Generally, the magnetic field reduces both of the fluid flow intensity and heat transfer for all of the shape of wavy patterns. © 2022, Akadémiai Kiadó, Budapest, Hungary.

The research was conducted to examine the dispersion of pollutants ejected from a chimney a around three-dimensional rectangular building. Regarding the experimental study, the wind tunnel experiment comprises data acquired through the dispersion of continuous source tracer discharges (air seeded with glycerin particles) from a punctual source situated in a regular network of a building-like obstacle, and these data include measurements of mean velocity and turbulence parameters. The relevant data are followed using particle image velocimetry (PIV) to track various instantaneous and mean dynamic characteristics. Concerning the numerical study, the suggested model simulates both the dynamics and the heat transfer flow field using the overall mean three-dimensional Navier-Stokes equations with a Reynolds stress model (RSM) turbulence closure model. The findings of a deep comparison of turbulent flow and dispersion between a full wind tunnel experiment and the model predictions are reported. A high degree of concordance was obtained with the experimental flow and numerical simulation data. The detailed investigation, which included numerical and winds tunnel studies, was performed to evaluate the impact of wind velocity on the pollutant dispersion issued from a chimney around the building in their vicinity. The simulated mean flow results were checked against the respective wind tunnel tests, demonstrating for most flow positions be in good agreement. The results clearly showed how wind velocity influenced the environmental air flows and pollutant dispersal pathways. The results of this study show that the shape of the building and the resulting interaction between the wind structure play a determining factor in the distribution of pollutants around a building, thereby affecting the air quality in the various parts of the building. The work has clearly indicated that sophisticated CFD modeling can yield valuable insights for city planners when changes to the urban landscape are being addressed, so that appropriate design approaches can be checked according to environmental suitability criteria. Copyright © 2022 by ASME

Taking a more complex engineering geometry into account, magnetohydrodynamic natural convection of nanofluid (Cu-water) in a wavy walled enclosure having a circular hot cylinder inside is investigated by employing Galerkin-weighted residual formulation. In order to investigate the flow and heat transfer characteristics from several perspectives and increase the ability of adaptation to various engineering applications, the influences of the Hartmann number, Ha, Rayleigh number, Ra, and nanoparticle concentration are examined in detail. In addition to that, heat generation and heat absorption situations are also considered within the present work, which are simulated by a heat coefficient in a range of −10 ≤ q ≤ +10. The results revealed that increasing Ha has an insignificant effect on Nusselt number, Nu, at low Ra, however, it significantly pulls Nu down up to 33% for higher Ra, because of restricting convection. It is found that the heat coefficient, q, has a remarkable impact on Nu at low Ra, while its significance is diminished when Ra is increased. For q < 0, the heat absorption creates a heat sink, which increases Nu up to 34%, while the heat generation (q > 0) conversely reduces Nu up to 48%. Besides, variation in heat coefficient does not considerably affect the improvement impact of nanoparticles. © 2020 Elsevier Ltd

The previous studies related to the thermal-driven flow within enclosures had been summarized in the present work. Various geometries of enclosures like square, rectangular and triangular had been summarized. Besides, enclosures filled with different fluids had been taken into consideration like traditional and nanofluids as well as porous medium, Newtonian and non-Newtonian fluids and multilayer systems. The governing equations of heat transfer and fluid flows had been presented for different cases. Different numerical models like homogeneous, inhomogeneous and thermal non-equilibrium model, Darcy, Darcy extended–Forchheimer model, etc., had been summarized. The influence of various dimensionless parameters like Rayleigh, Darcy, Bejan and Hartmann number, nanofluid loading, diverse thermal cases of the applied boundary conditions, angle of inclination, the number for undulations, the existence of inner body and many others parameters acting and influencing hardly up on both of the entropy generation and the heat transfer was illustrated. The present review illustrates the physical mechanism behind the buoyancy thermally driven flow in terms of figures of contours as well as the Nusselt numbers profiles. © 2021, King Fahd University of Petroleum & Minerals.

The present work exhaustively examines natural convection in complex enclosure forms such as trapezoidal, rhombic (parallelogrammic), elliptical and wavy geometries, taking into account various numerical methods that have been used in previous studies over the last ten years. Many dimensionless parameters such as a wide range of dimensionless numbers like Rayleigh, Darcy, and Hartmann were treated. The influence of the volume fraction of nanofluids, the thickness of the porous layer, and the number of undulations are studied. The existence of an inner body with different shapes (square, rectangle, triangle, rhombic, elliptical and wavy) was also mentioned. The impact of the position of the inner body and its size were also examined. The results of the previous works are presented in term of streamlines, isotherms, local and mean Nusselt number. It can be seen that there was a real limitation to the existence of the inner body in trapezoidal enclosures. There is also a limitation of the action of the wavy form as an inner body. © 2021 The Physical Society of the Republic of China (Taiwan)

The natural convection of nanofluid flow, which occurs between a sinusoidal-corrugated enclosure and a concentric inner cylinder has been numerically investigated. The two horizontal walls of this enclosure are considered adiabatic and two vertical corrugated walls are held at a constant value of the cold temperature while the inner concentric cylinder is heated isothermally. Different cylinder geometries (i.e, circular, square, rhombus, and triangular) located inside the enclosure are examined to find the best shape for optimum heat transfer. The physical and geometrical parameters influencing heat transfer are Rayleigh number (Ra=103-106), undulation numbers (N=0,1 and 2), aspect ratios (AR=5, 2.5 and 1.67) and two values for the volume fraction (φ=0 and 0.05). The numerical simulation was carried out using Comsol Multiphysics Software (5.3a). Galerkin approach along with the finite element method are used to solve equations of Navier-Stokes and energy with associated boundary conditions. In this study, validations of results between some available literatures and the present study found to be in an excellent agreement. Results indicate that the heat transfer and nanofluid flow characteristics in the sinusoidal-corrugated enclosure is significantly influenced by aspect ratio, undulation number, and Rayleigh number for all cylinder shapes. Thus, with the decrease in the aspect ratio, the intensity of streamlines becomes smaller, whereas, with rice in the Rayleigh number and undulation number, intensity increase is observed. Moreover, as the undulation number increases, the average value of the Nusselt number, including the hot surface of cylinders increases. At high Rayleigh numbers, the undulation number effect on the average value of the Nusselt number is more pronounced. Besides, the research showed that the circular cylinder shape inside the enclosure has the best heat transfer characteristics and flow than the others. © 2021, Global Digital Central. All rights reserved.

Heat transfer by natural convection for a centered inner adiabatic circular cylinder inside a trapezoidal enclosure filled with Ag-water nanofluid superposed saturated porous-nanofluid layer is numerically investigated. The inclined left and right walls of the trapezoidal enclosure are insulated. The bottom wall is partially heated at isotherm hot temperature, while the top wall is maintained at isotherm cold temperature. Finite element technique is used to numerically solve dimensionless Navier-Stoke equations for the nanofluid and porous-nanofluid media between inner adiabatic circular cylinder and trapezoidal enclosure. The numerical results are validated with those of Kim et al. [2008] in terms of streamlines and isotherms to check the accuracy of the present program. The validation illustrates a favorable agreement between the present work and Kim et al. The following parameters are studied: Rayleigh number (103 ≤ Ra ≤ 106), Darcy number (10-1 ≥ Da ≥ 10-5), nanoparticle volume fraction (0 ≤ ϕ ≤ 0.1), and porous layer thickness (0 ≤ Yp ≤ 100%). © Faculty of Mechanical Engineering, Belgrade. All rights reserved.

The present work demonstrates the natural convection of two layers filled the space between inner circular cylinder located within wavy enclosure using finite element scheme. The right layer is filled with Ag nano-fluid while the left layer is filled saturated porous media and the same nanofluid. The governing equations of fluid flow and heat transfer (mass, energy and momentum of the fluid) have been formulated in dimensionless form with related initial and boundary conditions the numerical solution include the subdividing the fluid flow domain to two sets of transport equations. The Darcy-Brinkman model was considered for modeling porous media with nano-fluid. The considered dimensionless parameters are Rayleigh number (106≥Ra≥103), Darcy number (10-1≥Da≥10-5), cylinder's radius (0.4≥R≥0.2), circular cylinder vertical position (+0.2≥δ≥-0.2), the number of undulation (3≥N≥0) and nano-particle volume fraction (0.1≥φ≥0). The nanofluid is combining of Ag solid particle and water as a main fluid. The results were presented according to the stream-lines, isotherms, local and the mean of Nusselt number. The results have demonstrated the increasing in the value of the Rayleigh and Darcy numbers as well as nanofluid volume fraction enhances both fluid flow strength and average of heat transfer. It has been concluded that when the number of undulations N = 1 gives better heat transfers enhancement. It is recommended that for better heat transfer average to move the internal circular cylinder with radius (R = 0.2) vertically downward (δ=-0.2) with undulations' number (N=1). © 2020 International Information and Engineering Technology Association. All rights reserved.

This paper investigates numerically and experimentally heat transfer forced convective two-phase flow (i.e. air and water) over a rectangular ribbed channel with a vertical orientation. Three distinct rib–groove shapes have been examined. Ribs - groove shapes are; Triangle, Trapezoid, and Semi-Trapezoid ribs-groove. The present study has been performed with continuous heat flux through range of water and air superficial inlet velocity values between 0.105 – 0.316m/s, and 0.263 – 1.320 m/s, respectively. Continuity, momentum and energy calculations have been formulated using the Finite Volume Approach (FVM). Results indicate that the triangle rib-groove has the high heat transfer coefficient and lower temperature difference than other cases against a different number of Reynolds. The experimental data has been compared to numerical results for ribs –grooved channel with deviation of about 1.0% - 7.5%. The channel fitted with triangle ribs shows the highest heat transfer, which is about 59% higher than the smooth channel; 56% for trapezoidal rib, and 44% for channel fitted by semi-trapezoidal rib. Finally, the triangle rib-groove gives a better heat transfer improvement value in comparison with trapezoidal and semi trapezoidal rib-groove channel at constant pumping power. © 2020. All Rights Reserved.

The natural convection of heat transfer is presented numerically using a temperature gradient from the hot inner corrugated cylinder. Different inner corrugated numbers located inside a cooled wavy-walled enclosure filled with two layers were simulated. The right layer is filled with Ag nanofluid and the left with a fully saturated porous media with similar nanofluid. The porous media with the nanofluid was modeled using the Darcy–Brinkman model. The main dimensionless equations are solved numerically using the method of Galerkin. This study considered the following dimensionless parameters: the Rayleigh number (106 ≥ Ra ≥ 103), the Darcy number (0.1 ≥ Da ≥ 0.00001), the vertical location (0.2 ≥ H ≥ −0.2), the number of sinusoidal inner cylinders (6 ≥ N ≥ 3), fraction volume of the nanoparticle (0.1 ≥ ⱷ ≥ 0), and porous layer thickness (0.8 ≥ XP ≥ 0.2). Results suggest that to increase the fluid flow strength, the internal sinusoidal cylinder must move upward to increase the fluid flow strength. Increasing the thickness of the porous layer reduces the average heat transfer. Results indicate further that highest fluid flow strength occurs at N = 4 when the inner sinusoidal cylinder moves downward vertically. © 2019 Elsevier Ltd

Numerical investigations are presented for mixed convection problems in a concentric inner sinusoidal cylinder and an outer rotating circular cylinder, which were kept at constant hot and cold temperatures, respectively. The free space between the cylinders and the enclosure walls was filled with a water-Cu nanofluid. The governing equations are formulated for velocity, pressure, and temperature formulation and are modeled in COMSOL5.2a, a partial differential equation solver based on the Galerkin finite element method. The governing parameters considered are the solid volume fraction, [0, 0.02, 0.04, and 0.06], Re (1, 25, 100, 200, and 300), and Ra (less than 104), and the inner cylinder corrugation frequencies varied from (N = 3, 6, and 9). According to the calculations, the Reynolds number, the Rayleigh number, the nanoparticle volume fraction, and the number of corrugations play an important role of forming the stream and isothermal lines, the local and the average Nusselt number inside the annulus enclosure. The average Nusselt number decreases with increasing Reynolds number and the number of corrugations, while it increases as the Rayleigh number and the volume fraction increase. © 2018 Wiley Periodicals, Inc.

Fluid flow and natural convection heat transfer in a parallelogram enclosure with an inner circular cylinder using Cu-water nanofluid are studied numerically. Dimensionless Navier-Stokes and energy equations are solved numerically using finite element method based two-dimensional flow and steady-state conditions. This study evaluates the effect of different concentrations of Cu-water nanofluids (0% to 6%) with different Rayleigh numbers 103 ≤ Ra ≤ 106 under isotherm wall temperatures. The effects of geometrical parameters of the parallelogram enclosure (inclination angle in range of 0 ≤ α≤ 30 and location of inner circular cylinder-0.2 ≤ H ≤ +0.2 on the flow field and heat transfer are examined. The results are presented in terms of streamlines, isotherms, local and average Nusselt number. It is found that the inclination angle has a significant effect on flow pattern and heat transfer and the inclination angle of 30o at a vertical location H=-0.2 gives better fluid flow strength. Moreover, the maximum heat transfer enhancement is obtained when the circular cylinder moves vertically downward up to H=-0.1 and the inclination angle is 30o. The results also indicate that as the Rayleigh number, nanofluid concentration increase, the rate of heat transfer will increase. © 2019, Global Digital Central. All rights reserved.

I demonstrated numerically the natural convective heat transfer between inner heated circular cylinder located within cooled elliptical enclosure filled with copper-water nanofluid with internal heat generation/absorption in the presence of horizontal magnetic field. The dimensionless governing equations are solved numerically using finite element scheme. The considered parameters of this study Rayleigh number (103<Ra<107), Hartmann number (0<Ha<60), nanofluid volume fraction (0<ϕ[symbol]<0.06), heat generation/absorption (-10<q<+10) and the horizontal position of the inner circular cylinder (-0.2≤δ≤+0.2). The results show that increasing Rayleigh number and nanofluid volume fraction increases the fluid flow strength and heat transfer rate. While Hartmann number increasing leads to reduce the Nusselt number. It is obtained also, that absorption of heat augments the heat transfer. Finally, it is found that when the circular cylinder moves into the left side, a better heat transfer will be obtained while it is recommended to move the inner cylinder into right for better fluid flow strength. © 2019 International Information and Engineering Technology Association.

The two-phase fluid flow had many engineering applications like the fluidized bed, combustion, separation and collection of ducts, nuclear waste disposal, etc. which is the motivation for the researchers to investigate this phenomenon. In present investigation an experimental facility was developed to study the two-phase flow behavior inside a rectangular channel with rectangular obstructions with various air/water flow rates. The flow arrangement, air bubble generation along with pressure drop and pressure fluctuations were monitored in the present work. The experimental data was recorded using four pressure transducers and the air-water flow behavior was visualized with a camcorder for air flow rates of 8.3, 16.6, and 25 L/min and different water flow rates of 5, 10, 15 and 20 L/min. The results showed that by increasing the water or air flow rate values, the shape, size and amount of air bubbles in the water change accordingly. Higher water flow rate causes the flow to become highly turbulent and frothy. Furthermore, significant increase in the pressure difference along the channel was observed after increasing the gas and fluid discharge values. © 2019, Mathematical Modelling of Engineering Problems.

This study examined numerically the natural convection heat transfer in enclosure filled with various types of nanofluids with partial active walls. The governing equations of Navier-Stokes and energy have been solved using finite element method. Two cases of thermal active walls are considered for various Rayleigh numbers 10 3 ≤ Ra ≤ 10 6 , nanofluid type like Cu, Al 2 O 3 and TiO 2 and aspect ratio 0.5 ≤ AR ≤ 2. The left sidewall is partially cooled while the right sidewall is partially heated. The other walls and remaining portions are considered adiabatic. Depending upon the location of active zones, various cases can be considered. In this work, we limited into two different cases: top-bottom (case-1) and bottom-top (case-2) active walls. The numerical programme is validated with significant researchers in terms of average Nusselt number to obtain the accuracy of the programme. The results are presented in terms of streamlines, isotherms, local and average Nusselt number. The obtained results indicate that case-1 gives better heat transfer characteristic in a comparison with case-2. Also, Cu gives better heat transfer rate with other two types. It is obtained that as the aspect ratio increases, the mean Nusselt number decreases in both the cases. © 2019 Pushpa Publishing House, Prayagraj, India.

In this work, forced convection heat transfer through a horizontal pipe built-in with/without twisted tape-inserts is numerically studied under a uniform heat flux condition. Water is used as a working fluid. The governing equations are numerically solved in the domain by a finite volume method (FVM) using the Realizable κ-ϵ (RKE) model. The computational results are performed for a range of the Reynolds number (4000≤ Re ≤ 9000), the twisted ratio (4.0 ≤ TR ≤ 6.0), and heat flux (5000 ≤ q ≤ 1000 W/m2). Two type of twisted tape which inserts across a circular pipe (P-TT) and (V-cut) are carried out. The influence of these parameters on the local, average Nusselt Number and the thermal performances were examined and compared with a plain pipe under similar conditions. The results show that the average Nusselt number and friction factor raise as the twisted ratio rise for any value of Reynolds number. Furthermore, thermal performance factor tended to increase with increasing Re and decreasing tape twist ratio. Obviously, the (V-cut) twisted- tape and (P-TT) twisted tape with TR = 4 gave a higher mean thermal performance factor (4.45, and 4.19) than that with TR = 6, respectively. Finally, the present study can offer some useful results to select optimum geometrical parameters for use in shell and tube heat exchangers with a twisted tape inserted based on their specific applications. © 2018 The Authors. Published by Elsevier Ltd.

The conjugate natural convection heat transfer in a partially heated square porous enclosure had been studied numerically. The governing dimensionless equations are solved using COMSOL Multiphysics and Darcy model assumed to be used. The considering dimensionless parameters are modified Rayleigh number, finite wall thickness, thermal conductivity ratio and the heat source length. The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that; the heat transfer can be enhanced by increasing the modified Rayleigh number. When the heat source length increases, the local Nusselt number of fluid phase increases, while, a reverse behavior of the local Nusselt number along the heat source is found. As the Rayleigh number increase, the local Nusselt number for both fluid and solid phase increases, therefore, the heat transfer rate will be enhanced. On the other hand, when the thermal conductivity ratio increase, the local Nusselt number for the fluid phase increases, and the local Nusselt number along the heated wall decreases. © 2018 International Information and Engineering Technology Association. All rights reserved.

A numerical investigation is presented to illustrate the impact of aspect ratio in a conjugate heat transfer enclosure filled with porous media and partially heated from vertical walls. The left and right walls are partially heated and cooled, respectively. The remaining partitions of the vertical walls in addition to the top and bottom walls are considered to be adiabatic. the present work is limited to two different cases: Top-Bottom (case 1) and Bottom-Top (case 2). The dimensionless Navier-Stokes governing equations are solved using the finite element method. The parameters of interest are the modified Rayleigh number 10 ≤ Ra ≤ 103, the finite wall thickness 0.02 ≤ D ≤ 0.5, 0.1 ≤ Kr ≤ 10 and the aspect ratio 0.5 ≤ A ≤ 10. The results are presented in term of streamlines, isotherms and average Nusselt number for fluid phase and along the solid hot wall. The results indicated that the locations of partially active walls have great influence on heat transfer rate. I was shown that Bottom-Top arrangement gives better heat transfer rate compared to that of Top-Bottom. It was also found that by increasing the Rayleigh number, the rate of heat transfer increased. In contrast, increasing the wall thickness and aspect ratio reduced the heat transfer rate. © 2018 Mathematical Modelling of Engineering Problems.

The conjugate natural convection heat transfer in a partially heated porous enclosure had been studied numerically. The governing dimensionless equations are solved using finite element method. Classical Darcy model have been used and the considering dimensionless parameters are modified Rayleigh number (10 ≤ Ra ≤ 103), finite wall thickness (0.02 ≤ D ≤ 0.5), thermal conductivity ratio (0.1 ≤ Kr ≤ 10), and the aspect ratio (0.5 ≤ A≤ 10). The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that heat transfer can be enhanced by increasing the modified Rayleigh number, and thermal conductivity ratio. Wall thickness effects on the heat transfer mechanism had been studied and it is found that; as the Wall thickness increases, the conduction heat transfer mechanism will be dominated. Also, increasing aspect ratio will increase the stream function and reduced the heat transfer rate. © 2018, Global Digital Central. All Rights Reserved.

The present work studies numerically natural convective flow between a circular adiabatic cylinder located in a square porous enclosure using finite element method. Darcy-Forchheimer model is used in solving the dimensionless governing equations including; continuity, energy and momentum of the fluid along with Bousseinesq approximation. The enclosure is heated from bottom and cooled at isothermal temperature for the vertical walls. The top wall and obstacle are assumed adiabatic. The considered parameters are 103 ≤ Ra ≤ 106, 10-5 ≤ Da ≤ 10-3, obstacle vertical location 0.25 ≤ h ≤ 0.75 and cylinder radius 0.1 ≤ D ≤ 0.9 with Pr = 0.7. It is obtained that as the Rayleigh and Darcy numbers increase, both streamlines; Nusselt numbers will increase leading to increase the rate of heat transfer. The results show that the heat transfer rate is significantly dependent on the diameter of the circular cylinder and the location of the cylinder. It is found the maximum heat transfer rate obtained at D=0.1 and when the cylinder moves vertically upward at h=0.3. © 2018, AIDIC Servizi S.r.l.

Natural convection heat transfer in a porous rectangular partially active heated wall is numerically investigated using finite element method. Three different cases of heating and cooling zone had been taken in the consideration along the vertical walls while the others are considered to be adiabatic. The governing equations are obtained by the applying of Darcy Model and Boussinesq approximation. Finite element method is used to solve the dimensionless governing equations with the specified boundary conditions. The investigated parameters in the present study are the modified Rayleigh number (10 •Ra • 103), aspect ratio (0.5 • A• 2), finite wall thickness (0.02 • D•= 0.5) and the thermal conductivity ratio (0.1• Kr • 10). The results are presented in terms of streamlines, isotherms and Nusselt number. The results indicate that as the aspect ratio, finite wall thickness increase, Nusselt number decrease. Also, as the modified Rayleigh number increases, the Nusselt number will increase. Case 1 and 2 gave approximately the same effects of heat transfer rate while case 3 give lower rate of heat transfer rate. © Medwell Journals, 2018.

The present work, the natural convection and the entropy generation of trapezoidal enclosure with an embedded baffle using Cu nanofluids are numerically studied. The governing equations of fluid heat transfer and fluid mechanics like continuty, energy and momentum of the fluid has been solved numerically using the finite element method. The impact of many dimesnionless parameters such as Rayleigh number, three different cases of baffle height (CASE-1, CASE-2, and CASE-3) on streamlines, isotherms, entropy generation, local and the average Nusselt number is presented for Cu nanofluid. The results indicate that as the Rayleigh number goes up, fluid flow strength will increase and heat transfer will enhance. Also, at high Rayleigh number, the entropy generation due to fluid friction will be greater than that due to heat transfer. Finally, it is obtained that CASE-1 gives better heat transfer characterize in a comparison with other cases of baffle height. © 2017 Lavoisier.