Tanmay Basak

The phenomena of natural convection within a trapezoidal enclosure filled with porous matrix for linearly heated vertical wall(s) with various inclination angles φ has been studied numerically. A penalty finite element analysis with bi-quadratic elements is used for solving the Navier-Stokes and energy balance equations. Wide range of parameters such as Rayleigh number, Ra (103 ≤ Ra ≤ 106), Prandtl number, Pr (0.026 ≤ Pr ≤ 1000) and Darcy number, Da (10- 5 ≤ Da ≤ 10- 3) have been used. Numerical results are presented in terms of streamlines, isotherms and Nusselt numbers. It has been found that secondary and tertiary circulations appear at the bottom half of the cavity for φ = 30° and φ = 0° with Pr = 0.026 and 0.7, Da = 10- 3 and Ra = 106 for linearly heated side walls. On the other hand, for linearly heated left wall and cold right wall, multiple circulations occur near the top portion of the cavity. For linearly heated side wall, the local Nusselt number (Nub) shows sinusoidal behavior with distance at high Darcy number for all tilt angles whereas increasing trend in Nus is observed in the upper half of the side wall for all tilt angles. For linearly heated left wall with cold right wall, increasing trend in Nub is observed irrespective to Da and Pr and Nub is even larger for higher Da. Increasing trend is also observed in Nul for all tilt angles for linearly heated left wall. Due to discontinuity in right corner, Nur first decreases and thereafter that increases for Y ≥ 0.2. The average Nusselt number remains constant up to Ra = 106 at low Da for Pr = 0.026 whereas for Pr = 1000 and high Ra, that starts to decrease for bottom wall whereas that starts to increase for side walls due to convection dominant effect at high Da. In general, the average Nusselt number increases with the increase of Da and Ra for higher Da. © 2009 Elsevier Ltd. All rights reserved.

A detailed analysis has been shown to illustrate the influence of various shapes of annular metallic support on microwave heating of 2D cylinders for beef samples. The beef samples are chosen to represent typical food materials with high dielectric loss. A preliminary analysis on microwave heating of samples has been shown via average power within a sample vs cylinder radius diagram in the absence of support and three regimes have been identified such that regimes I (R=0.50cm) and III (R=2cm) denote the local minima in average power and regime II (R=0.67cm) corresponds to a maxima in average power. In addition, regime I corresponds to a spatial maxima in power at the unexposed face, regime II corresponds to maxima in power at both the exposed and unexposed faces and regime III has two maxima at the exposed face and the center of the sample. The influence of support has been illustrated with average power distribution vs aspect ratio (φ) diagram. Three types of cross sections of annular supports such as circular (type I), horizontal square (type II) and inclined square (type III) are considered. It has been observed that the average power is enhanced due to the metallic support for φ≤0.3. Type I support would correspond larger power distributions and heating rates, for regimes I and II whereas for regime III, the square shaped supports correspond to greater heating rates at larger aspect ratios. The location of spatial maxima in power or heating rate is found to be shifted due to metallic support with high aspect ratios. The shape of the support plays important role on localized heating for the samples corresponding to regime III. © 2005 Elsevier Ltd. All rights reserved.

A penalty finite element method based simulation is performed to analyze the influence of various walls thermal boundary conditions on mixed convection lid driven flows in a square cavity filled with porous medium. The relevant parameters in the present study are Darcy number (Da = 10-5 - 10 -3), Grashof number (Gr = 103 - 105), Prandtl number (Pr = 0.7-7.2), and Reynolds number (Re = 1-102). Heatline approach of visualizing heat flow is implemented to gain a complete understanding of complex heat flow patterns. Patterns of heatlines and streamlines are qualitatively similar near the core for convection dominant flow for Da = 10-3. Symmetric distribution in heatlines, similar to streamlines is observed irrespective of Da at higher Gr in natural convection dominant regime corresponding to smaller values of Re. A single circulation cell in heatlines, similar to streamlines is observed at Da = 10-3 for forced convection dominance and heatlines are found to emanate from a large portion on the bottom wall illustrating enhanced heat flow for Re = 100. Multiple circulation cells in heatlines are observed at higher Da and Gr for Pr = 0.7 and 7.2. The heat transfer rates along the walls are illustrated by the local Nusselt number distribution based on gradients of heatfunctions. Wavy distribution in heat transfer rates is observed with Da ≥ 10-4 for non-uniformly heated walls primarily in natural convection dominant regime. In general, exponential variation of average Nusselt numbers with Grashof number is found except the cases where the side walls are linearly heated. Overall, heatlines are found to be a powerful tool to analyze heat transport within the cavity and also a suitable guideline on explaining the Nusselt number variations. © 2011 Elsevier Ltd. All rights reserved.

A comprehensive theoretical analysis has been carried out to study the effect of microwave heating on a first order endothermic reactions. The mathematical model considers detailed description of microwave power absorption along with transport of heat and mass within the reacting domain. The effect of microwave heating on the progress of the endothermic reaction has been analyzed in terms of spatial nonuniformities as well as overall progress of the reaction compared to the case of conventional heating. The analysis is carried out for all possible spectrum of microwave power absorption, which enables us to quantify the effect of microwave heating in terms of percentage savings of reaction time. The detail mathematical model also allows to identify and study the effect of various parameters responsible for describing the interaction between the heat and mass transport in presence of volumetric heating. A systematic and thorough analysis on the effect of these parameters demonstrate an interesting regime, where volumetric heating may not yield better progress than conventional heating. © 2011 Elsevier Ltd.

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.

The present numerical study deals with mixed convection flows within square enclosures filled with porous media. The influence of various thermal boundary conditions on bottom and side walls based on thermal aspect ratio (A) is investigated for a wide range of parameters (1 ≤ Re ≤ 100, 0.015 ≤ Pr ≤ 7.2, 10 -5 ≤ Da ≤ 10 -3 and 10 3 ≤ Gr ≤ 10 5). A penalty finite element method with bi-quadratic elements has been used to investigate the results in terms of streamlines, isotherms and heatlines and average Nusselt numbers. Lid driven effect is dominant at low Darcy number (Da = 10 -5), whereas buoyancy driven effect is dominant at high Darcy numbers (Da = 10 -4 and Da = 10 -3) for Re = 1. Asymmetric pattern is observed in isotherms and heatlines for Re = 100. It is found that thermal gradient is high at the center of the bottom wall for A = 0.1 due to large dense heatlines at that zone and that is low for A = 0.9 irrespective of Re, Pr and Gr. Overall heat transfer rates are higher for A = 0.1 compared to other thermal aspect ratios (A = 0.5, A = 0.9) irrespective of Darcy number, Prandtl number and Reynolds number. © 2012 Elsevier Ltd. All rights reserved.

Natural convection in an enclosure (internal convection) is an important problem due to its significant practical applications. In energy related applications, natural convection plays a dominant role in transport of energy for the proper design of enclosures in order to achieve higher heat transfer rates. This review summarizes the studies on natural convection heat transfer in triangular, trapezoidal, parallelogrammic enclosures and enclosures with curved and wavy walls filled with fluid or porous media. In addition, this review also summarizes the natural convection studies in the nanofluid filled enclosures. Studies have been performed for the enclosures subjected to different thermal boundary conditions. A number of the studies demonstrated that the variation of the aspect ratio and base angle of the triangular and rhombic/parallelogrammic enclosures had a wide influence on the flow distribution pattern. In the trapezoidal enclosure, the aspect ratio of the cavity as well as the presence of the baffles along the walls played a significant role in the temperature and flow distribution. The flow patterns within the complex enclosures were found to be largely dependent on the amplitude-wavelength ratio and number of undulations of the wavy walls. In addition, the researchers have also studied the effect of the various parameters such as the Rayleigh numbers, Prandtl numbers, Darcy numbers, Darcy–Rayleigh number, irreversibility distribution ratios, volume fraction of the nanoparticles, etc. Overall, the current review paper presents an useful insight into the potential strategies for enhancing the convection heat transfer performance.

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.

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.