A numerical study on heat distribution and thermal mixing during steady laminar natural convective flow within fluid-saturated porous square cavities has been carried out based on Bejan's heatlines. Three different cases have been considered: (1) uniformly heated bottom wall, (2) discrete heat sources on walls, and (3) uniformly heated left and bottom walls. Studies illustrate that enhanced thermal mixing occurs at higher Da. It is also found that distributed heating enhances heat distribution and thermal mixing compared to uniform heating case. Overall, heatline approach has been found to be a very useful numerical tool to analyze heating strategies in porous media.

Tanmay Basak

Department Of Chemical Engineering

Satyajit Roy

Department of Mathematics

Ram Satish Kaluri

Porous materials

BOTTOM WALLS

DISCRETE HEAT SOURCES

HEAT DISTRIBUTIONS

Heat flows

HEATING STRATEGIES

NATURAL CONVECTIVE FLOWS

Numerical studies

Numerical tools

NUMERICAL VISUALIZATIONS

POROUS MEDIAS

SQUARE CAVITIES

THERMAL MIXING

Uniform heating

heating

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Bejan's Heatlines and Numerical Visualization of Heat Flow and Thermal Mixing in Various Differentially Heated Porous Square Cavities

Numerical Heat Transfer; Part A: Applications

The conventional method of differential heating within an enclosure may result in the inadequate thermal mixing and that may further lead to the poor thermal management. In order to enhance the overall thermal mixing, the discrete heating strategy may be considered as an effective alternative. In the current work, natural convection studies have been carried out within discretely heated porous square and triangular (type 1 and type 2) enclosures during natural convection. Overall, five different discrete heating strategies (cases 1–4: symmetric heating, case 5: asymmetric heating) have been considered for the present work. The heatline method has been implemented to visualize the heat flow pattern within the cavities for a wide range of parameters (Prm=0.015–7.2,Dam=10-5–10-2,Ram=106). In order to solve the governing equations and Poisson equations for streamfunction and heatfunction, the Galerkin finite element method has been used. At Dam=10-4, computational results clearly indicate the onset of convection whereas enhanced convection is found to occur at Dam=10-2 based on the presence of intense fluid and heatline cells. The intensity of heat flow is observed to be higher for the asymmetric distributed heating strategy compared to the symmetric distributed heating configurations. Heatlines depict the role of hot regime along the side walls and they are also useful in explaining the variations of the local and average Nusselt numbers for the various cases. Common to all the cases, the average heat transfer rate within the triangular- type 1 enclosure is higher compared to the square and triangular-type 2 enclosures irrespective of Dam and Prm. The extent of the thermal mixing in each case has been quantified using the cup-mixing temperature which has been evaluated at higher and lower Dam in order to establish the effect of porosity. It is concluded that the thermal mixing is more effective within the square and triangular-type 2 enclosures at both Dam=10-4 and 10-2. The cases 2 and 5 were inferred to be the optimal discrete heating strategies. © 2017 Elsevier Ltd

International Journal of Heat and Mass Transfer

Role of discrete heating on the efficient thermal management within porous square and triangular enclosures via heatline approach

A detailed study on natural convection heat transfer within porous trapezoidal enclosures has been carried out for two different cases. The effect of linearly heated side walls on flow pattern is investigated in case 1; whereas, the effect of linearly heated left wall and cold right wall is studied in case 2. In both cases, the bottom wall of the cavity is uniformly heated and the upper wall is adiabatic. The results are analyzed for a wide range of parameters such as Rayleigh number, Ra(103Ra106), Prandtl number, Pr(0.015 Pr988.24), and Darcy number, Da(105Da10 3). © 2013 Taylor and Francis Group, LLC.

Heatlines for visualization of heat transport for natural convection within porous trapezoidal enclosures with various wall heating

Analysis of natural convection in porous right angled triangular enclosures with a concave/ convex hypotenuse has been carried out using the Bejan's heatlines approach. A generalized non-Darcy model without Forchheimer term is employed for fluid flow in a porous matrix and the governing equations are solved by the Galerkin finite element method. The cavity is subjected to a thermal boundary condition of an isothermal cold left wall, isothermal hot curved right wall, and adiabatic bottom wall. Due to intense closed loop heatlines, thermal mixing is higher in convex cases compared to the concave case for all parameters. Average heat transfer rate is found to be largest in the concave hypotenuse case. Copyright © Taylor & Francis Group, LLC.

Analysis of convective heat flow visualization within porous right angled triangular enclosures with a concave/convex hypotenuse

A Brinkman extended Darcy model has been used to study the effect of spatial nonuniformity of wall temperatures on the multiplicity of steady convective flows within a square porous enclosure saturated with low Prandtl fluid (Pr = 0.026). The convection is assumed to be driven by the hotter bottom wall in conjunction with colder side walls, where bottom-side wall junctions maintain continuity of temperature to represent a more realistic situation. This configuration enforces nonuniformity on either bottom wall or side walls or both bottom and side wall temperatures. The degree of nonuniformity of wall temperatures are varied parametrically in terms of thermal aspect ratio (Θ) to simulate various possible scenarios of nonuniform bottom/side wall temperatures and steady solution branches are traced in the parameter space of Θ to investigate the variation of multiplicity of the flows. A perturbation technique has been used to initiate the steady solution branches, which are then traced by numerical continuation scheme. A penalty finite element approximation in conjunction with Newton-Raphson method and parameter continuation scheme has been used to construct the bifurcation diagrams of various steady branches. This work reveals three steady symmetric branches and four steady asymmetric branches with exhibition of symmetry breaking bifurcation. This work also shows that the nonuniformity of wall temperatures play a crucial role for the existence of multiple solutions as well as the multiplicity of convective flows. © 2012 Elsevier Ltd. All rights reserved.

On multiple steady states for natural convection (low Prandtl number fluid) within porous square enclosures: Effect of nonuniformity of wall temperatures

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 = 103-10 5). 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. © 2012 Elsevier Ltd. All rights reserved.

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

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 106, Darcy number Da, 10-5 ≤ Da ≤ 10-3, and Prandtl number Pr, 0.71 ≤ Pr ≤ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ≤ 10 -5 irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ≥ 10-4. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented. © 2005 Elsevier Ltd. All rights reserved.

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

The double-diffusive natural convective flow within a rectangular enclosure has been studied using a generalized porous medium approach. The results have been validated with the help of theoretical heat transfer results available for various porous medium flow models and also with the experimental results for double-diffusive convection in a fluid-filled rectangular cavity. The present generalized model covers the entire range from Darcy flow to free fluid flow. Numerical predictions by the model indicate that the flow pattern as well as the heat and mass transfer are profoundly influenced by the buoyancy ratio. Also non-Darcy effects on flow, heat, and mass transfer become significant when the Rayleigh or Darcy numbers are large. The Sherwood and Nusselt numbers become sensitive to bed porosity variation in the non-Darcy regime. © 1996, Taylor & Francis Group, LLC. All rights reserved.

Double-diffusive natural convection in an enclosure filled with fluid-saturated porous medium: A generalized non-darcy approach

Convection Heat Transfer

International Journal of Thermal Sciences

Natural convection in a porous enclosure with a partial heating and salting element

Applied Mathematics and Mechanics

Entropy generation analysis of thermally developing forced convection in fluid-saturated porous medium

Journal	Numerical Heat Transfer; Part A: Applications
ISSN	10407782
Open Access	No