Hot Bottom Wall Research Articles

Role of curvature of walls (concave/convex) for intensification of thermal processing with optimal exergy loss during natural convection of fluids

Based on its potential to develop more sustainable and energy efficient systems, process intensification is on increasing importance in various processing industries. The process intensification vs efficiency is carried out for natural convection in square enclosure and curved (concave/convex) wall enclosures via heatlines and entropy generation analysis for the development of sustainable process equipment design. As the selection of an optimal cavity is the main objective for the increase in efficiency, a comparative study has been carried out among the enclosures with equal dimensionless area (= unity) and equal heater length (= 1 unit). Two heating strategies are considered such as (a) case 1: hot bottom wall (b) case 2: hot left wall. Numerical simulations have been carried out for various values of Prandtl (Pr) and Rayleigh (Ra) numbers. Heatline trajectories illustrate that convex cavities with case 1 or case 2 may be chosen based on higher thermal mixing for various Ra. On the other hand, based on higher entropy savings with higher wall heat transfer rates, concave cavities with case 1 or case 2 are preferred. Overall, economic design of the cavity must consider the enhanced thermal mixing vs savings of entropy generation or exergy loss.

Analytical study of Al2O3-Cu/water micropolar hybrid nanofluid in a porous channel with expanding/contracting walls in the presence of magnetic field

Forced convection fluid flow and heat transfer is investigated in a porous channel with expanding or contracting walls with which is filled Al2O3-Cu/water micropolar hybrid nanofluid in the presence of magnetic field. In order to solve the governing equations analytically, the least square method is employed. The hot bottom wall is cooled by the coolant fluid which is injected into the channel from the top wall. The range of nanoparticles volume fraction (90% Al2O3 and 10% Cu by volume) is between 0% and 2%. The effects of consequential parameters such as Reynolds number, Hartmann number, micro rotation factor and nanoparticles volume fraction on velocity and temperature profiles are examined. The results show that with increasing Reynolds number, the values of temperature and micro rotation profiles decrease. Furthermore, when the hybrid nanofluid is used compared to common nanofluid, the heat transfer coefficient will increase significantly. It is also observed that when the Hartmann number increases, Nusselt number increases, too.

Numerical simulation of MHD mixed convection in alumina–water nanofluid filled square porous cavity using KKL model: Effects of non-linear thermal radiation and inclined magnetic field

This study examines the influence of non-linear thermal radiation and inclined magnetic field on mixed convection in a square porous cavity. Here, the cavity is saturated with alumina–water nanofluid. Darcy-Brinkman-Forchheimer-extended model has been adopted to formulate governing differential equations. After transforming equations to dimensionless form, these are solved by utilizing weighted residual Galerkin finite element method. Latest Koo-Kleinstreuer-Lee (KKL) model is employed for the evaluation of effective thermal conductivity and dynamic viscosity of nanofluid. Effect of pertinent parameters in specific ranges such as Richardson number (0.01 ≤ Ri ≤ 100), radiation parameter (0 ≤ Rd ≤ 5), temperature ratio parameter (1.1 ≤ Nr ≤ 1.4), inclined magnetic field parameter (0°≤ γ ≤ 90°), Darcy number (10−6 ≤ Da ≤ 10−3), porosity parameter (0.2 ≤ ϵ ≤ 0.8) and volume fraction of solid particles (0 ≤ ϕ ≤ 0.04) has been studied and presented in the form of streamlines, isotherms and plots. Moreover, kinetic energy and average temperature have also been taken into account for better understanding the flow philosophy. It is found that radiation parameter, temperature ratio parameter, Darcy number and porosity parameter augment heat transfer, kinetic energy and average temperature while inclined magnetic field parameter in selected aforementioned range declines heat transfer due to hot bottom wall.

Mixed convection heat transfer of turbulent flow in a three-dimensional lid-driven cavity with a rotating cylinder

A numerical study has been carried out to investigate the combined forced and natural convection heat transfer in a differentially heated 3D obstructed cavity with a thermally insulated rotating circular cylinder. The cavity has a hot stationary bottom wall and a cold top lid-driven wall, and all the other walls completing the domain are motionless and adiabatic. The simulations are performed for different Reynolds numbers, Re=5000, 10,000, 15,000 and 30,000, and for dimensionless rotational speeds of the cylinder, 0≤Ω≤10. The performance of two turbulence methods, Large Eddy Simulation (LES) and Unsteady Reynolds-Averaged Navier-Stokes (URANS), has been evaluated in this research. The flow and thermal fields are studied through flow vectors, isotherm contours and iso-surfaces temperature, as well as through the average Nusselt number (Nuav) and velocity components. The results demonstrate clearly that the flow patterns and the thermal fields are influenced strongly by increasing either the rotating cylinder speed or the Reynolds number. Furthermore, both LES and URANS solutions can capture the essential feature of the primary eddies in the cavity. But this study has shown convincing evidence that only the LES method can predict the structure details of the secondary eddies that have profound effects on the heat transfer behaviour within the enclosure.

Role of thermal and flow characteristics on entropy generation during natural convection in porous enclosures with curved walls subjected to Rayleigh-Bénard heating

The comprehensive analysis of natural convection within various enclosures with the concave and convex horizontal walls involving the classical Rayleigh-Bénard heating (hot bottom wall, cold top wall and adiabatic side walls) is carried out via the entropy generation approach. Galerkin finite element method is employed to obtain the solutions in terms of the isotherms (θ), streamlines (ψ), entropy generation (Sθ,Sψ and Stotal) and average heat transfer rates (Nut‾) for a selected range of Darcy numbers (10-5⩽Dam⩽10-2), Prandtl numbers (Prm=0.015 and 7.2) at Rayleigh number, Ram=106 with various test cases with different wall curvatures (concave and convex). The magnitudes and spatial locations of local entropy generation due to heat transfer and fluid friction are studied for various thermal and geometrical parameters. The active zones with larger Sθ are found along near core region and middle portions of the curved walls with less and moderate concavities whereas, those are found only near the middle portions of the curved walls with the high concavity at the low Dam involving all Prm. In the convex domain, the active zones with larger Sθ are seen near the corner regions for the low Dam at all Prm. The zones prone to the entropy generation with the high Sθ are seen along the mid-horizontal axis of the cavity involving all the concave and convex domains at the high Dam and all Prm. Also, the left and right portions of the curved walls act as the active zones with the high Sθ for the concave domains at the high Dam and all Prm. The larger values of Sψ are seen near all the solid walls (at all Dam) and at the interior zone (at the high Dam) for all Prm involving all concave and convex cases. Based on the comparison of all the concave and convex cases, the concave case with the high wall concavity may be preferred over the specific concave cases (with the less and moderate wall concavities) and all the convex cases due to the larger Nut‾ and less Stotal values for the entire range of Dam and Prm.

Investigations on the effect of non-uniform temperature on fluid flow and heat transfer in a trapezoidal cavity filled with porous media

Simulations were carried out for natural convection in a trapezoidal cavity filled with porous media to investigate the effect of uniformly and non-uniformly heated bottom wall using finite element computational procedure. The enclosure used for flow and heat transfer analysis has hot bottom wall, constant temperature cold top wall and adiabatic side walls. The bottom wall is subjected to uniform/linear/sinusoidally varying temperatures. Results are presented in the form of stream lines, isotherms, heatline plots, local and average Nusselt numbers. Heatline visualization technique is a useful method that gives information on heat transport from the heated to cold region inside the porous trapezoidal enclosure with varying temperature boundary conditions. Nusselt numbers are computed for Darcy-modified Rayleigh numbers or Rayleigh number (Ra) ranging from 100 to 2000 for an aspect ratio (H/L) of 0.5. It is observed from this study that the uniform temperature at the bottom wall of the enclosure gives higher Nusselt number as compared to the linear and sinusoidally varying temperature cases. The average Nusselt numbers increases monotonically with Rayleigh number for bottom wall and top walls. The power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regions.

Free convection in a porous wavy cavity filled with a nanofluid using Buongiorno's mathematical model with thermal dispersion effect

A numerical study of natural convection inside a porous wavy cavity filled with a nanofluid under the effect of thermal dispersion has been carried out using the Forchheimer–Buongiorno approach. The left boundary of the cavity is a wavy isothermal wall while the rest are flat isothermal walls. All boundaries are assumed to be impermeable to the base fluid and nanoparticles. The governing equations formulated in dimensionless stream function, temperature and nanoparticle volume fraction variables have been solved using implicit finite difference schemes of the second order accuracy. The effects of the Rayleigh number, undulation number, thermal dispersion parameter and flow inertia parameter on the average Nusselt number along the hot bottom wall, as well as on the streamlines, isotherms and isoconcentrations have been analyzed. It has been revealed the heat transfer enhancement with Rayleigh number, undulation number and dispersion parameter. While convective flow is attenuated with a growth of undulation number, dispersion parameter and flow inertia parameter. More essential homogenization of nanoparticles distribution inside the cavity occurs with an increase in Rayleigh number and a decrease in undulation number.

Analysis of thermal management on processing of fluids within rhombic cavities: Heatlines vs. entropy generation

The present work involves the detailed heat flow visualization with the distribution of the entropy generation in order to estimate the energy efficiency of rhombic cavities with various angles of inclination (φ=45∘,60∘ and 75°) for different areas (A=0.5,1 and 1.5) with Ra=103−105 for Pr=0.015 and 1000. The cavities involve isothermally hot bottom wall in the presence of cold side and top walls. Results have been presented in the form of isotherms (θ), streamlines (ψ), heatlines (Π), entropy generation due to heat transfer (Sθ) and fluid friction (Sψ). Results have also been compared with the square cavity (φ=90∘) in terms of the total entropy generation (Stotal), average Bejan number (Beav) and average heat transfer rate (Nub¯ and Nul¯). The numerical studies clearly demonstrate that, the square enclosure may not be the optimal choice based on the lesser heat transfer rate and higher entropy generation. Overall, the rhombic cavities with φ=45∘ at A=0.5 may be concluded as the optimal design for the efficient thermal processing based on the higher heat transfer rate and lower entropy generation.

Mesoscale simulation of Marangoni convection about a vapor bubble in a liquid with temperature gradients under microgravity conditions

Marangoni convection around a 2-D vapor bubble in a liquid, subjected to an imposed negative temperature gradient in the vertical direction under microgravity conditions, is simulated with a newly developed lattice Boltzmann liquid/vapor phase-change method. It is shown that a floating bubble, initially at the center of a confined space, moves gradually toward the hot wall under zero gravity condition because of Marangoni convection. With the increase of the Marangoni number, Marangoni convection along the liquid–vapor interface appears to be more and more significant. Under microgravity conditions, a sessile bubble attached on a hot bottom wall facing upward at low superheats, the high velocity region on the liquid/vapor interface moves from the triple-contact line region upward as the wettability of the solid surface changes from hydrophobic to hydrophilic. It is shown that the average Nusselt number of such a sessile vapor bubble under microgravity conditions is larger or smaller than those under zero gravity condition, depending on whether the Marangoni convection is in a direction parallel to or opposite to the direction of the gravity.

Analysis of entropy generation for mixed convection within porous square cavities: Effects of various moving walls

ABSTRACTThe aim of the present investigation is to analyze the effect of the motion of horizontal (cases 1a–1d) and vertical walls (case 2a–2c) on the entropy generation and heat transfer in a porous square cavity during mixed convection. The cavity is subject to the thermal boundary conditions such as the hot bottom wall, cold side walls, and thermally insulated top wall. Analysis has been done for various fluids with Prandtl number, Prm = 0.026–7.2, Grashof number, Gr = 105, Reynolds number, Re = 10–100, and Darcy number, Dam = 10−4–10−2. Numerical results are presented using streamfunction (ψ), local entropy generation due to fluid friction (Sψ), isotherms (θ), and local entropy generation due to heat-transfer (Sθ) contours. In addition, the total entropy generation (Stotal), average Bejan number (Beav), and overall heat-transfer rate at the hot bottom wall are analyzed and discussed.

Finite element simulations on heatline trajectories for mixed convection in porous square enclosures: Effects of various moving walls

Finite element simulation of the mixed convection within porous square cavities for Darcy–Brinkman–Forchheimer model has been carried out in the present work. The penalty optimization based Galerkin finite element method is used to solve the partial differential equations of heat and fluid flow. Bejan’s heatline concept has been employed to visualize the heat flow within the closed cavities based on the motion of the horizontal wall(s) (cases 1a–1d) or vertical wall(s) (cases 2a–2c) involving isothermally hot bottom wall, cold side walls and insulated top wall for various fluids with Prandtl number, Prm=0.026, 0.7 and 7.2, Reynolds number, Re=10–100 and Grashof number, Gr=103–105. The higher permeability at Dam≥10−3 leads to the enhanced buoyancy convection for all the cases. Although the direction of the motion of wall(s) significantly influences the fluid flow field within the enclosure, due to the decoupling between the fluid and thermal fields at the low Pem (Pem=0.26 and 2.6), conductive heat transfer occurs as seen from the end-to-end heatlines. It is also found that the overall heat transfer rates at the bottom wall (Nub¯) are identical for the cases 1a–1d and cases 2a–2c at Prm=0.026, irrespective of Gr and Re at Dam=10−2. At Prm=0.7 and 7.2, the convection dominant heat transfer occurs for all the cases for Gr=105, Re=10 and 100 and Dam=10−2. The strong convective circulation cells are observed at Prm=0.7 and 7.2 for all the cases. The plume shaped isotherms are also observed along the centerline at Prm=7.2, Re=10, Gr=105 and Dam=10−2 for all the cases. At Prm=7.2, Gr=105, Dam=10−2 and Re=100, the multiple convective heatline cells are observed for the cases 1a–1d. It is observed that, the strengths of fluid and heat circulation cells are less at Re=100 compared to Re=10 for all the cases due to weak buoyancy force at the high Re. In order to achieve the high heat transfer rate at the bottom wall (Nub¯) for the mixed convection involving various moving walls, case 2b (a case of the vertically moving wall) is preferred at Prm=0.7, Re=100, Gr=105 and Dam=10−2. At the high Prm (Prm=7.2, Re=100, Gr=105 and Dam=10−2), case 2a (a case of the vertically moving wall) is preferred based on the maximum heat transfer rate at the bottom wall (Nub¯).

Analysis of Entropy Generation During Mixed Convection in Porous Square Cavities: Effect of Thermal Boundary Conditions

Computational studies on entropy generation during laminar mixed convection in porous square enclosures have been carried out based on Darcy–Brinkman–Forchheimer model using the penalty finite element method. Finite element simulations are performed for the isothermally hot bottom wall, adiabatic top wall, and isothermally cold side walls (case 1) or linearly heated side walls (case 2) or linearly heated left wall with isothermally cold right wall (case 3) for a wide range of modified Darcy numbers (10−5 ≤ Dam ≤ 10−2), Grashof numbers (Gr = 103 − 105), and modified Prandtl numbers (Prm = 0.026 and 7.2). Further, the effects of Dam on the total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number are discussed. It is found that Re = 100 is preferred over Re = 1 based on larger heat transfer rate with minimum entropy generation for Prm = 0.026 and 7.2, 10−5 ≤ Dam ≤ 10−2 at Gr = 105 for all the cases.

Analysis of Entropy Generation for Mixed Convection in a Square Cavity for Various Thermal Boundary Conditions

Finite element simulations were carried out to analyze entropy generation during mixed convection inside square enclosures with an isothermally hot bottom wall, adiabatic top wall, and isothermally cold side walls (case 1) or linearly heated side walls (case 2), or linearly heated left wall with isothermally cold right wall (case 3) for Pr = 0.015–7.2, Re = 1–100, and Gr = 103–105. Local entropy maps are studied in detail, and the dominance of thermal (Sθ,l) and frictional (Sψ,l) irreversibility is studied using Bejan number maps. In addition, variation in total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number at the bottom wall with Gr are analyzed to correlate irreversibility and the overall heat transfer rate of the system or process. It is found that, for Pr = 0.015 and 7.2, Re = 100 may be the optimal level for higher convective heat transport with minimum entropy generation in all the cases for Gr = 103–105.

Role of various moving walls on energy transfer rates via heat flow visualization during mixed convection in square cavities

Mixed convection in closed cavities are important for various processing industries especially those associated with conservation of energy. Finite element based simulations are carried out for two cases based on the motion of the horizontal wall(s) (cases 1a–1d) or vertical wall(s) (cases 2a–2c). Heat flow distribution within the cavity enclosed by isothermally hot bottom wall, cold side walls and insulated top wall is analyzed for various fluids with Prandtl number, Pr = 0.026 and 7.2, Reynolds number, Re = 10–100 and Grashof number, Gr = 103–105. The direction of motion of wall(s) plays a significant role on the fluid flow field at Pr = 0.026, Gr = 103 and Re = 10 due to dominant forced convection for both horizontally (cases 1a–1d) or vertically (cases 2a–2c) moving wall(s). At Pr = 7.2, Gr = 105 and Re = 100, multiple convective heatline cells are observed for cases 1a–1d. It is found that, the strength of fluid or heatline circulation cells is less at Re = 100 compared to Re = 10 for cases 2a–2c due to weak buoyancy force at high Re. Energy transfer rates are assessed via local and average Nusselt numbers for cases 1a–1d and 2a–2c.

Numerical investigation of natural convection heat transfer in a symmetrically cooled square cavity with a thin fin on its bottom wall

In the present paper, natural convection fluid flow and heat transfer in a square cavity heated from below and cooled from sides and the ceiling with a thin fin attached to its hot bottom wall is investigated numerically. The right and the left walls of the cavity, as well as its horizontal top wall are maintained at a constant temperature Tc, while the bottom wall is kept at a constant temperature Th ,with Th > Tc. The governing equations are solved numerically using the finite volume method and the couple between the velocity and pressure fields is done using the SIMPLER algorithm. A parametric study is performed and the effects of the Rayleigh number and the length of the fin on the flow pattern and heat transfer inside the cavity are investigated. Two competing mechanisms that are responsible for the flow and thermal modifications are observed. One is the resistance effect of the fin due to the friction losses which directly depends on the length of the fin, whereas the other is due to the extra heating of the fluid that is offered by the fin. It is shown that for high Rayleigh numbers, placing a hot fin at the middle of the bottom wall has more remarkable effect on the flow field and heat transfer inside the cavity.

Role of entropy generation on thermal management due to thermal convection in porous trapezoidal enclosures with isothermal and non-isothermal heating of wall

One of the important objectives of thermal systems engineering is to analyze the utilization of thermal energy in an efficient manner. Analysis on entropy generation may give an insight about thermal efficiency of various thermal systems. Entropy generation analysis during natural convection in a porous trapezoidal structures of various inclination angles (φ) with isothermal (case 1) and non-isothermal (case 2) hot bottom wall has been performed. Simulations have been done to obtain solutions in terms of isotherms (θ), streamfunction (ψ) and entropy generation maps (Sθ and Sψ) for various ranges of modified Darcy number (Da), Prandtl number (Pr) at modified Rayleigh number, Ra=106. It is observed that Sθ,max occurs near bottom corners for case 1 whereas that occurs near middle part of the left and right portions of the bottom wall for case 2. The entropy production due to fluid flow irreversibilities (Sψ,max) occurs either at the top wall, or side walls or along the interface between two counter-rotating cells. It is found that, square cavities may be the optimal geometry in comparison to trapezoidal cavities for both cases. Also, trapezoidal cavities with φ=60° may be the alternative optimal design in comparison with φ=45° for all Pr fluids.

Mixed convection and role of multiple solutions in lid-driven trapezoidal enclosures

This paper analyzes probable steady state flow structures and temperature patterns that may evolve during mixed convection within a lid-driven trapezoidal enclosure with cold top wall and hot bottom wall as the speed of moving lid varies with respect to the intensity of imposed temperature gradients. In this regard, a Grashof (Gr)–Reynolds (Re)–Prandtl (Pr) number formulation has been used to induce varying contributions from moving lid compared to that from imposed thermal gradients, where Grashof number has been varied from 103 to 105 at Re=1 and 100 for three different fluids of Pr=0.015, 0.7 and 10. Simulations have been performed for two different scenarios of isothermal (case 1) and non-isothermal (case 2) bottom wall with inclination angle of the side wall being kept at 45o. It has been found that non-isothermal bottom wall (case 2) leads to multiple steady states in either natural convection dominated regime (Gr/Re2≫1) or mixed convection regime (Gr/Re2∼O(1)) in convection dominated heat transport regime (Pr×Re≳1). Number of steady states are observed to be more in natural convection dominated regime at Re=1. The flow structures of various steady states are found to be crucial to achieve higher heat transfer rates for non-isothermal bottom wall.

Heat flow visualization analysis on natural convection in rhombic enclosures with isothermal hot side or bottom wall

The heat flow visualization method based on heatfunction has been adopted to analyze natural convection via differential heating (case 1) and Rayleigh–Benard convection (case 2) in fluid filled (Prandtl number, Pr=0.015–1000) rhombic enclosures with various inclination angles, φ, using the Galerkin finite element method for the range of Rayleigh number, Ra=103–105. An accurate prediction of the flow structure and heat distribution in such configurations is of great importance due to various engineering applications such as solar energy systems, cooling of electronic devices, combustion, etc. The strength of fluid and heat flow increases with φ and Ra due to an enhanced convection effect and the maximum magnitude of streamfunction (ψmax) and heatfunction (Πmax) is observed at φ=90° in both cases. Conduction based static fluid solutions are also found at φ=90° associated with convection based dynamic fluid solutions in case 2 for all Pr. Heating strategies are compared via heatlines and also based on local (Nu) and average Nusselt numbers (Nu¯). It is also shown that φ=30° shows higher Nu¯ in case 2 compared to case 1, whereas φ=90° shows higher Nu¯ in case 1 compared to case 2 for all Pr. There exists a critical rhombic angle (φ=50°) such that differential heating may be the profound heating situation at φ≥50° for materials involving Pr=1000. Also, the rhombic cavity may be an alternative geometrical design in convective thermal processing of fluids with vertical thermal gradient (case 2) as it establishes only convection based dynamic solutions for all possible angles (φ<90°).

Heatline based thermal management for natural convection in porous rhombic enclosures with isothermal hot side or bottom wall

An accurate prediction of the flow structure and heat distribution in rhombic configurations are of greater importance due to its significant engineering i.e. cooling of electronics devices as well as natural applications i.e. geothermal extraction. Heatline method is used to analyze natural convection in porous rhombic enclosures with various inclination angles, φ for differential (case 1) and Rayleigh–Benard heating situations (case 2). Increase in φ(φ=90°) results in pure conduction dominant heat transfer with stagnant fluid condition for φ=90° at Da=10−5 and a slight perturbation of φ at higher Da (Da⩾4×10−5) leads to convection based dynamic solution for φ=90° in case 2 irrespective of Pr. At Da=10−3, strength of fluid and heat flow increase with φ due to enhanced convection effect and φ=90° shows maximum magnitude of streamfunction (ψmax) and heatfunction (Πmax) values in both cases except convection based solution at φ=90° for Pr=7.2. Both cases are compared based on local (Nu) and average Nusselt numbers (Nu¯) and those are adequately explained based on heatlines. Also, Nu¯ increases with Da in both cases except convection based solution at φ=90° for Pr=7.2. Overall, Nu¯ is higher for case 2 at φ⩽45° whereas case 1 shows larger Nu¯ for φ⩾45° irrespective of Pr at Da=10−3. Hence, φ=45° is the critical rhombic angle which demarcates the heating strategies of case 1 and case 2 to achieve higher heat transfer rates (Nu¯) in various applications.

Analysis of heatlines during natural convection within porous square enclosures: Effects of thermal aspect ratio and thermal boundary conditions

Numerical investigation of natural convection within porous square enclosures has been performed for various thermal boundary conditions based on thermal aspect ratio on bottom and side walls. Penalty finite element analysis with bi-quadratic elements is used to solve the governing equations. The numerical solutions are studied in terms of streamlines, isotherms, heatlines, local and average Nusselt numbers for a wide range of parameters Da(10−5–101), Pr(0.015–1000) and Ra(Ra=103–105). At low Darcy number (Da=10−5), heatlines are perpendicular to the isotherms indicating conduction dominant heat transfer. As Da increases to 10−3, convection is initiated and the thermal mixing has been observed at the central regime for all As. At low Prandtl number (Pr=0.015) with high Darcy number (Da=10−2 and Da=101), multiple circulations are observed in streamlines and heatlines and they suppressed for higher Prandtl number (Pr=1000). Isotherms are highly compressed along bottom wall at higher Prandtl numbers (Pr=0.7 and 1000) at A=0.1 and 0.5. Temperature gradient is found to be high at the center of the bottom wall for A=0.1 due to dense heatlines at that zone and that decreases as A increases from 0.1 to 0.9, irrespective of Pr, Da. Also, the temperature gradient is smaller at the top portion of side walls for A=0.1 due to sparse heatlines along those zones and that is high for A=0.9 due to dense heatlines. Distribution of heatlines illustrate that significant heat transport occurs from hot bottom wall to the top portion side walls at higher Darcy number (Da=101). It is found that Nub attains maximum at X=0.5 and minimum at corners for Da=10−5, whereas that exhibits sinusoidal variation for Da=10−3 and Da=101 irrespective of Pr and A. It is also found that Nul follows wavy pattern at low Prandtl number (Pr=0.015) with higher Darcy number (Da=101) irrespective of A due to larger gradients of heatfunctions at several locations of left wall. The average Nusselt number show that the overall heat transfer rate is high at A=0.1 compared to that of A=0.5 and A=0.9 irrespective of Da and Pr due to larger gradients of heatfunctions at A=0.1.