Effective use of thermal energy is the key for the energy-efficient processing of materials. A proper understanding of heat flow would be very useful in designing the systems of high energy efficiency with a minimal waste of precious energy resources. In the current study, a distributed heating methodology is proposed for the efficient thermal processing of materials. A detailed investigation on the processing of various fluids of industrial importance (with a Prandtl number of Pr = 0.015, 0.7, 10, and 1000) in differentially and discretely heated porous square cavities is presented. Analysis of laminar convective heat flow within a range of Darcy number, Da = 10-6-10-3 and Rayleigh number, Ra = 103-10 6 has been carried out, based on a heatline visualization approach. The effect of Da and the role of distributed heating in enhancing the convection in the cavities is illustrated via heatline distributions, which represent the paths of the heat flow, the magnitude of heat flow, and zones of high heat transfer. It is observed that distributed heating plays an important role in enhancement of thermal mixing and temperature uniformity. Furthermore, the effect of Da for various Pr values on the variation of local Nusselt number (Nu) is analyzed, based on heatline distributions. © 2010 American Chemical Society.

Tanmay Basak

Department Of Chemical Engineering

Ram Satish Kaluri

Convective heat

DARCY NUMBER

Energy efficient

Heat flows

HIGH ENERGY EFFICIENCY

Local Nusselt number

Rayleigh number

Square cavity

TEMPERATURE UNIFORMITY

THERMAL CONVECTIONS

THERMAL MIXING

THERMAL PROCESSING

Energy conversion

Energy efficiency

Heat flux

heating

Nusselt number

Visualization

Heat convection

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IIT Madras

Industrial and Engineering Chemistry Research

Purpose: The purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles triangle) subjected to discrete heating with various locations of double heaters along the vertical (square) or inclined (triangular) arms. Design/methodology/approach: Galerkin finite element method is used to solve the governing equations for a wide range of modified Darcy number, Dam = 10−5–10−2 with various fluid saturated porous media, Prm = 0.015 and 7.2 at a modified Rayleigh number, Ram = 106 involving the strategic placement of double heaters along the vertical or inclined arms (types 1-3). Adaptive mesh refinement is implemented based on the lengths of discrete heaters. Finite element based heat flow visualization via heatlines has been adopted to study heat distribution at various portions. Findings: The strategic positioning of the double heaters (types 1-3) and the convective heatline vortices depict significant overall temperature elevation at both Dam = 10−4 and 10−2 compared to type 0 (single heater at each vertical or inclined arm). Types 2 and 3 are found to promote higher temperature uniformity and greater overall temperature elevation at Dam = 10−2. Overall, the triangular design 2 geometry is also found to be optimal in achieving greater temperature elevation for the porous media saturated with various fluids (Prm). Practical implications: Multiple heaters (at each side [left or right] wall) result in enhanced temperature elevation compared to the single heater (at each side [left or right] wall). The results of the current work may be useful for the material processing, thermal storage and solar heating applications. Originality/value: The heatline approach is used to visualize the heat flow involving double heaters along the side (left or right) arms (square and triangular geometries) during natural convection involving porous media. The heatlines depict the trajectories of heat flow that are essential for thermal management involving larger thermal elevation. The mixing cup or bulk average temperature values are obtained for all types of heating (types 0-3) involving all geometries, and overall temperature elevation is examined based on higher mixing cup temperature values. © 2019, Emerald Publishing Limited.

International Journal of Numerical Methods for Heat and Fluid Flow

Analysis of efficiency of convection in porous geometries (square vs triangular) with multiple discrete heaters on walls: A heatline perspective

Heatline concept has been used in order to estimate thermal performance of various energy related systems. Heatlines and streamlines are found to be adequate to visualize and understand heat distribution and thermal mixing occurring inside a inclined porous square cavity. At high Darcy number, Dam (Dam=10-2), heatlines take the shapes of streamlines at the central core of the cavity resulting in enhanced thermal mixing as seen from closed convective heatline cells with high magnitudes. Heat transfer rates are discussed based on local and average Nusselt numbers and further, these are adequately explained based on heatlines. The inclined cavity with higher inclination angle (φ=75°) provides the higher Nu-<inf>BC</inf> whereas higher Nu-<inf>DA</inf> is observed for the small inclination angles (φ=15°) at Dam=10-2. Note that, BC and DA denote the right and left walls, respectively. The larger inclination angle may be optimal for the energy efficient processes involving inclined enclosures due to larger heat flow circulations with enhanced thermal mixing. © 2015 Elsevier Ltd.

International Journal of Heat and Mass Transfer

Heatlines and thermal management analysis for natural convection within inclined porous square cavities

One of the important objectives in thermal systems engineering is to analyze utilization of thermal energy in an efficient manner. Analysis based on second law of thermodynamics may give an insight about efficient usage of thermal energy in various industrial systems. In this regard, entropy generation analysis during conjugate natural convection within a differentially heated square cavity enclosed by vertical conducting walls of different thicknesses (t1 and t2) has been carried out for various thermal systems. Finite element based numerical simulations are carried out for various location of vertical wall thicknesses (cases 1, 2, and 3) in the range of parameters, Ra (103 ≤ Ra ≤ 105), Pr (Pr = 0.015-1000), wall thicknesses (t = 0.2 and 0.8), and conductivity ratios (K = 0.1,1 10 and ∞). Maximum entropy generation due to heat transfer (S θ,max) occurs near the solid-fluid interface region due to high temperature gradient whereas maximum magnitude of the entropy generation due to fluid friction (Sψ,max) occurs near the cavity walls due to friction between the circulation cells and cavity walls. Larger heat transfer and high intensity fluid flow lead to larger Sθ,max and S ψ,max for K = 10 compared to that of K = 0.1 and K = 1 irrespective of Pr and location of solid wall thickness. Qualitative features of θ, ψ, Sθ and Sψ for t1 + t2 = 0.8 are identical with t1 + t2 = 0.2. However, the magnitude of Sθ,max and Sψ,max is less for t1 + t2 = 0.8 compared to t1 + t 2 = 0.2. Based on detailed discussion of average Nusselt number (Nul), average Bejan number (Beavg) and total entropy generation (Stotal) vs various governing parameters (Ra, Pr and t), it may be concluded that thermal processing is invariant of K in conduction dominant region (103 ≤ Ra ≤ 104) irrespective of Pr and t. On the other hand, K ≤ 1 with t1 + t2 ≈ 0.8 may be optimal for thermal processing within the convection dominant region (104 ≤ Ra ≤ 105) due to less entropy generation and reasonable heat transfer rate, irrespective of Pr. © 2014 American Chemical Society.

Analysis of entropy generation during conjugate natural convection within a square cavity with various location of wall thickness

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 103 ≤ Ra ≤ 105 and Prandtl number Pr, 0.7 ≤ Pr ≤ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented. © 2006 Elsevier Ltd. All rights reserved.

Effects of thermal boundary conditions on natural convection flows within a square cavity

Who's Who

Levin, David Saul, (born 28 Jan. 1962), Chief Executive, McGraw-Hill Education, New York, since 2014

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Journal	Industrial and Engineering Chemistry Research
ISSN	08885885
Open Access	No