Numerical analysis of the longitudinal size of the partition on natural convection heat transfer and fluid flow within a differentially heated porous enclosure

The article deals with the effect of longitudinal size and shape partition embedded within a differentially heated porous enclosure. The objective is to curtail the heat transfer rate across such porous enclosures by means of partitions embedded within. The partition shapes under consideration are straight vertical left-inclined, right-inclined, L-shaped, wavy, corrugated, and square-wave. It is sought to find the most effective combination of partition length and shape that could serve the required objective. Also, many times, due to the constructional constraints of the porous enclosure or cavity, using full-length partitions may not be feasible. In this regard, it is also sought to find the partition length that is to be maintained for achieving a significant reduction in heat transfer without much compromise. The results of the current study are useful for thermal design engineers particularly in the field of thermal insulation, solar heating application, and packed bed energy storage systems where the major challenge is to reduce the heat transfer across the system. The parameters under consideration are the longitudinal length L and Rayleigh number Ra. All the partitions under study are evaluated for bottom-wall and top-wall attached conditions. Some of the notable findings are that for smaller-sized partitions (B < 0.5), L-shaped partitions are most effective in controlling the convection heat transfer rate across the enclosure while for larger-sized partitions (L > 0.5), square-wave-shaped partitions should be preferred for effective reduction in the rate of convection heat transfer.     

Non—Darcian and Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

Natural convection heat transfer in a horizontal enclosure filled with anisotropic porous media,being isothermally heated at bettom and cooled at top while the vertical walls being adiabatic,is numerically studied by applying the Brinkman model-a modified form of Darcy model giving consideratioin to the viscous effect.The results show that:(1)a larger permeability ratio(K^*) causes a lower flow intensity in the enclosure and a smaller Nusselt number,all Nusselt numbers approach unity in the limit of K^*→∞;a larger thermal conductivity ratio(λ^*) causes a stranger distortion of isotherms in the enclosure and a higher flow velocity near the walls,all the Nusselt numbers approach unity in the limit of λ^*-→0,the permeability and thermal conductivity ratios generally have opposing effects on the Nusselt number.(2) an increasing Darcy number decreases the flow intensity and heat tansfer rates,which is more significant at a lower permeability ratio.In particular,with K^*≤0.25,the Nusselt number for Da=10^-3 would differ from that of Darcy flow up to an amount of 30%,an analysis neglecting the non-Darican effect will inevitably be of considerable error.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Inhomogeneous flow model of natural convection,entropy generation,and heatlines visualization in wavy I-shaped enclosure with rectangular heater

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 $$, Buoyancy ratio number $$, Lewis number $$, heater length $$. The results indicate that the influence of Lewis number on heat transfer bettering is stronger at high Rayleigh number $$ while its impact is negligible at a lower value of Rayleigh number (conduction mode). In addition, the total entropy generation gets its highest value at Lewis number $$. 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 $$ while increasing the heater height to $$ 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 $$ into $$, total entropy generation increases by $$ at $$ while it increases by $$ at $$.     

Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium

A theoretical study of buoyancy-driven flow and heat transfer in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium heated and cooled from inclined walls has been performed in this paper. The governing non-dimensional equations were solved numerically using a finite-difference method. The effective governing parameters are: the orientation or inclination angle of the trapezoidal enclosure , which varies between 0° and 180°, the Rayleigh number Ra, which varies between 100 and 1000, the side wall inclination angle θ_s and the aspect ratio A. The side wall inclination parameter θ_s is chosen as 67°, 72° and 81° and the calculations are tested for two different values of A=0.5 and 1.0. Streamlines, isotherms, Nusselt number and flow strength are presented for these values of the governing parameters. The obtained results show that inclination angle is more influential on heat transfer and flow strength than that of the side wall inclination angle θ_s. It is also found that a Bénard regime occurs around =90°, which depends on the inclination of the side wall, Rayleigh number and aspect ratio.     

Double-diffusive natural convection in a porous medium under constant heat and mass fluxes

Double-diffusive natural convection in a rectangular fluid-saturated porous medium has been studied analytically and numerically. The analysis reveals that there is a range of buoyancy ratios N in which one obtains two types of solutions or oscillating convection. In the case of 0.4 < N < 1.0, there exist two analytical solutions when R_c = 100 and Le = 30. In that case, two solutions, temperature-dominated and concentration-dominated solutions, are calculated when the aspect ratio is small. It is found that the oscillation is due to a temporal formation of a two-roll flow pattern in the cavity when the aspect ratio is sufficiently large. The oscillation of time-dependent Nusselt number and flow patterns are shown. © 1999 Scripta Technica, Heat Trans Asian Res, 28(4): 255–265, 1999     

Non-darcy free convection inside a wavy enclosure

Buoyancy induced flow and thermal fields characteristics inside a porous wavy walled enclosure have been numerically solved and analyzed. The enclosure consists of two isothermal wavy walls. The two parallel straight walls at the top and the bottom are flat and kept adiabatic. Governing equations are discretized using the Finite Element Method. Simulation was carried out for a range of surface waviness ratios, a = 0–0.5; aspect ratio, A = 2; inverse Darcy number, Da = 0.01–∞; and Rayleigh numbers, Ra = 10°–10⁷ for a fluid having Prandtl number equal to 1.0. Results are presented in the form of streamlines and isothermal lines for different values of surface waviness and porosity.     

Two-dimensional natural convection in a porous triangular enclosure with a square body

A two-dimensional numerical solution for steady-state buoyancy induced convection in a right-triangular enclosure with a square body is obtained using finite difference technique. The solid body is located far from the origin with the distance of 0.3 in both directions. It is considered that the temperature of the bottom wall of triangular enclosure is higher than that of inclined wall while the vertical wall is insulated. To obtain the effects of the presence of a square body on heat transfer and fluid flow inside the enclosure, four different temperature boundary conditions were applied for the body as heated, cooled, neutral and adiabatic at different Ra numbers. It is observed that fluid flow and temperature fields strongly depend on thermal boundary conditions of the body.     

Multiobjective optimization of free convection through a nonuniform cabinet filled with porous media

In the current study, multiobjective optimization and numerical simulation were used to evaluate free convection through a nonuniform cabinet, which has several technical applications, such as cooling techniques, solar air collectors, and heat sinks. The new aspect of the current study is to compute the maximum free convection within an irregular L-shaped cavity filled with porous media using both computational analysis and response surface methodology (RSM). Moreover, the impacts of constant coefficients, such as aspect ratios of the horizontal (AR_h), vertical (AR_v), and Darcy numbers (Da) on the Nusselt number (Nu_ave), Nusselt number maximization (NNM), the temperature of the surface (Ts), and entropy (S) are studied and discussed to evaluate their effect on the thermal performance. The results showed that when Da, AR_h, and AR_v increase, Nu_ave improves while the Ts and S decline and the largest desirability is achieved at AR_h = 0.9, AR_v = 0.9, and Da = 10⁻¹. Additionally, when compared with the subpar design data, the largest gain in NNM was 26.7 times, while the biggest decreases in surface temperature and entropy were 59% and 97%, respectively. As a result, the combination of the numerical simulation and RSM study produces a novel strategy and insightful suggestions for the ideal cooling L-shaped cabinet design.     

Conjugate natural convection in a fluid-saturated porous enclosure with two solid vertical partitions

Conjugate natural convection in a fluid-saturated square porous enclosure with two solid vertical partitions of finite and equal thickness equispaced from center of enclosure is investigated in this paper. The primary objective is to attenuate the Nusselt number (Nu) and hence the heat transfer rate across a differentially heated enclosure. Darcy's model is considered. Numerical computation is performed using successive accelerated replacement and explicit scheme. Partition ratio, partition length, thermal conductivity ratio, and modified Rayleigh number are the parameters under study. Fluid flow is analyzed by observing transient changes of streamlines and isotherms for partition length 0.3-1, thermal conductivity ratio 0.5-2, partition ratio 0.1-0.3 and modified Rayleigh number 100 and 1000 where partition ratio is the ratio of distance between center of enclosure and either of the partition center to the total length of the enclosure; while Nusselt number is calculated to estimate the heat transfer rate for each configuration. It is found that, employing a solid partition within the enclosure most definitely reduces the Nusselt number. The drop in Nusselt number is more for partition length 0-0.6 after which it does show a drop in Nu but only very subtle. Further, Nu is the least for partition ratio 0.2. Also, Nusselt number is proportional to thermal conductivity ratio which is the ratio of thermal conductivity of solid to porous medium.     

Experimental study of natural convection heat transfer in a semicircular enclosure

An experimental study of natural convection heat transfer in a differentially heated semicircular enclosure was carried out. The flat surface was heated and the radial surface was cooled isothermally. The effects of angle of enclosure inclination on the heat transfer across semicircular regions of several radii were measured for Rayleigh numbers Ra_R ranging from 6.72 × 10⁶ to 2.33 × 10⁸, using water as the working fluid. The angle of inclination varied from −90 degrees to 90 degrees with radii R of 50, 40, and 30 mm. The flow patterns were sketched from the results of a visualization experiment using aluminum powder. The temperature measurements in the enclosure were carried out using liquid crystals and thermocouples. The results indicate that different flow patterns were encountered as the angle of inclination varied, and the heat transfer rate was largely dependent on the flow pattern. In particular, enhanced heat transfer rates can be obtained when plume-like flow occurs along both hot and cold walls in the case of an upward-facing hot wall. Heat transfer for the inclined enclosure can be predicted using the equation for a vertical enclosure presented in this paper. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 131–142, 1997     

Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall

Numerical investigations of steady natural convection flow through a fluid-saturated porous medium in a rectangular enclosure with a sinusoidal varying temperature profile on the bottom wall were conducted. All the walls of the enclosure are insulated except the bottom wall which is partially heated and cooled. The governing equations were written under the assumption of Darcy-law and then solved numerically using finite difference method. The problem is analyzed for different values of the Rayleigh number Ra in the range 10 ≤ Ra ≤ 1000, aspect ratio parameter AR in the range 0.25 ≤ AR ≤1.0 and amplitude λ of the sinusoidal temperature function in the range 0.25 ≤ λ ≤ 1.0. It was found that heat transfer increases with increasing of amplitude λ and decreases with increasing aspect ratio AR. Multiple cells were observed in the cavity for all values of the parameters considered.     

MHD natural convection inside an inclined trapezoidal porous enclosure with internal heat generation or absorption subjected to isoflux heating

A steady laminar two‐dimensional magneto‐hydrodynamic natural convection flow in an inclined trapezoidal enclosure filled with a fluid‐saturated porous medium is investigated numerically using a finite difference method. The left and right vertical sidewalls of the trapezoidal enclosure are maintained at a cold temperature. The horizontal top wall is considered adiabatic while the bottom wall is subjected to isoflux heating. A volumetric internal heat generation or absorption is embedded inside the trapezoidal enclosure while an external magnetic field is applied on the left sidewall of the enclosure. In the current work, the following parametric ranges of the non‐dimensional groups are used: Hartmann number is varied as , Darcy number is taken as , 10^?4, and 8 × 10^?5, Rayleigh number is varied as , Prandtl number is considered constant at Pr = 0.7, the dimensionless internal heat generation or absorption parameter is varied as Δ = ?0.2, 0, 1, and 2.0, while the trapezoidal enclosure inclination angle is varied as . The results indicated a strong flow circulation occurs when the Darcy and the Rayleigh numbers are high. In addition, it is found that the Hartmann number, internal heat generation or absorption parameter and inclination angle have an important role on the flow and thermal characteristics. It is also found that when the enclosure inclination angle and Hartmann number increase the average Nusselt number along the hot bottom wall decreases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21013     

Natural convection in porous triangular enclosure with a centered conducting body

A numerical work was performed to examine the heat transfer and fluid flow due to natural convection in a porous triangular enclosure with a centered conducting body. The center of the body was located onto the gravity center of the right-angle triangular cavity. The Darcy law model was used to write the governing equations and they were solved using a finite difference method. Results are presented by streamlines, isotherms, mean and local Nusselt numbers for the different parameters such as the Rayleigh number, thermal conductivity ratio, and height and width of the body. It was observed that both height and width of the body and thermal conductivity ratio play an important role on heat and fluid flow inside the cavity.     

Natural convection and its fractal for liquid freezing in a vertical cavity filled with porous medium

The numerical simulation for a freezing liquid-saturated porous media in a vertical cylindrical cavity under the third kind of thermal boundary condition is reported in this paper. It shows that the effect of natural convection in the liquid phase decreases the freezing layer thickness and the freezing front has a wave shape instead of a stable plane, with one or more pair of eddy cells. This indicates a fractal existence. © 1999 Scripta Technica, Heat Trans Asian Res, 28(3): 165–171, 1999     

Natural convection heat transfer in a circular enclosure

Natural convection heat transfer in a circular enclosure, one half of which was heated and the other half of which was cooled, was investigated experimentally, focusing on the effect of the inclination angle. The experiments were carried out with water. Flow and temperature field were visualized by using the aluminum and liquid-crystal suspension method. The results show that with downward heating the heat transfer coefficient increased as the inclination angle of the boundary between the heating wall and the cooling wall approached the vertical. But with upward heating, the heat transfer coefficient showed minimal change, exhibiting a small peak value when the inclination angle was γ ˜ –45°. The heat transfer coefficient of a flat circular enclosure was estimated from the circular enclosure's heat transfer coefficient. These results can be explained by the obtained flow and temperature fields. © 1999 Scripta Technica, Heat Trans Asian Res, 28(2): 152–163, 1999     

Experimental study on transient natural convection in a cube enclosure with an isolated vertical cyclically heated plate

INTRODUCTIONNaturalconvectioninsideenclosuresisatopicofconsiderablecurrentinterestandimportance.Ofparticularinterestarethetransientcoolingproblemsinenclosureswithinternalisolatedheatedbodies,inwhichnaturalconvectionisoftenthedominantheattransfermecha...     

Finite element simulation of magnetoconvection inside a sinusoidal corrugated enclosure with discrete isoflux heating from below

A numerical investigation of the steady magnetoconvection in a sinusoidal corrugated enclosure has been performed. In this analysis, two vertical sinusoidal corrugated walls are maintained at a constant low temperature whereas a constant heat flux source whose length is varied from 20 to 80% of the reference length of the enclosure is discretely embedded at the bottom wall. The Penalty finite element method has been used to solve the governing Navier–Stokes and energy conservation equation of the fluid medium in the enclosure in order to investigate the effect of discrete heat source sizes on heat transfer for different values of Grashof number and Hartmann number. The values of the governing parameters are the Grashof number Gr (10³ to 10⁶), Hartmann number Ha (0 to 100) and Prandtl number Pr (0.71). The present numerical approach is found to be consistent and the solution is obtained in terms of stream functions and isotherm contours.