Steady state numerical computations and experiments were performed to study three-dimensional, conjugate laminar natural convection heat transfer from multiple identical heat generating modules (heat sources) in a vertical duct. The heat sources were mounted on a wall at different positions in a defined grid of 5 × 5 positions. Air is used as the cooling medium. The governing flow and energy equations were solved using FLUENT 6.3. The optimum geometric configuration of the five heat sources that maximizes the heat transfer was determined by the introduction of a dimensionless distance parameter and an exhaustive search. The heuristic procedure based on the geometric parameter was tested for varying number of heat sources and for different heat source strengths. Experiments were performed to study the effect of modified Grashof number and the duct spacing on maximum temperatures of different configurations in order to support the numerical findings. Additionally, the temperatures of the heat sources arranged in the optimum configuration obtained by the heuristic approach have been experimentally validated. © 2009 Elsevier Ltd. All rights reserved.

C. Balaji

Department of Mechanical Engineering

T. V V Sudhakar

CONJUGATE NATURAL CONVECTION

COOLING MEDIUM

DISTANCE PARAMETER

Energy equation

EXHAUSTIVE SEARCH

Geometric configurations

Geometric parameter

Heat sources

Heuristic approach

HEURISTIC PROCEDURES

Laminar natural convection

Maximum temperature

MULTIPLE HEAT SOURCES

Numerical

Numerical computations

Numerical optimizations

Optimal arrangement

Optimum configurations

steady state

Surface radiation

Atmospheric radiation

Electromagnetic wave emission

Experiments

Heat exchangers

Heat transfer

Heuristic methods

Optimization

three dimensional

Natural convection

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

International Journal of Heat and Mass Transfer

This article presents experimental and numerical investigation on natural convection air-cooling of discrete square heat source array in a vertical channel. Conjugate heat transfer for three-dimensional laminar developing flows over an array of square heat sources representing integrated circuit components for electronic cooling has been studied. Experiments are conducted using three-substrate board materials viz. FR4, Bakelite, and copper clad board having thermal conductivities of 0.3, 1.4, and 8.8 W/m K to study the effects of substrate thermal conductivity on fluid flow and heat transfer. A finite element-based software is used to solve the coupling between heat transfer in solids and fluid region. Incompressible flow over discrete square heat sources is modeled using Navier–Stokes equations under Boussinesq approximation. Air-cooling of circuit boards populated with heat sources is modeled and simulated to present heat transport in combination with the fluid flow resulting from the natural air circulation at constant heat fluxes of 1,000, 2,000, and 3,000 W/m 2 . Multilayer copper clad board of thermal conductivity of 40.5 W/m K have been studied numerically. The results show that single sided copper clad board is the preferred candidate. Experiments indicate a deviation of under 5% with simulations. © 2019, © 2019 Taylor & Francis Group, LLC.

Heat Transfer Engineering

Effect of Thermal Conductivity on Cooling of Square Heat Source Array under Natural Convection in a Vertical Channel

Steady state experiments are conducted in a low speed horizontal wind tunnel under mixed convection for five discrete heat sources (aluminum) of nonidentical sizes arranged at different positions on a substrate board (bakelite) to determine the optimal configuration. The optimal configuration is one for which the maximum temperature excess (difference between the maximum temperature among the heat sources of that configuration, and the ambient temperature) is the lowest among all the other possible configurations and is determined by a heuristic nondimensional geometric parameter λ. The maximum temperature excess is found to decrease with λ, signifying an increase in heat transfer coefficient. In view of this, the configuration with highest λ is deemed to be the optimal one. The effect of surface radiation on the heat transfer characteristic of heat sources is also studied by painting their surface with black, which reduces their temperature by as much as 12%. An empirical correlation is developed for the nondimensional maximum temperature excess (θ) in terms of λ, by taking into account the effect of surface radiation. The correlation when applied for highest λ of the configuration returns the minimum value of θ at the optimal condition, which is a key engineering quantity that is sought in problems of this class. © 2014 by ASME.

Journal of Heat Transfer

Optimal distribution of discrete heat sources under mixed convection-A heuristic approach

Steady state experiments are conducted in a low speed horizontal wind tunnel under mixed convection regime, for five discrete heat sources (Aluminum) of different sizes arranged at different positions on a substrate board (Bakelite), to determine the optimal configuration. The characteristic length of heat sources varies from 0.005 to 0.011 m. The optimal configuration is one whose maximum temperature excess (temperature difference between the heat source and ambient) is minimum among all the possible configuration of heat sources mounted on the substrate board, and is determined by a heuristic non-dimensional geometric parameter l. The maximum temperature excess is found to decrease with l, signifying an increase of heat transfer coefficient. In view of this, configuration with the highest 7lambda; value is the optimal one. The effect of surface radiation on the heat transfer characteristic has also been studied by painting the surface of heat sources with black paint, which reduces their temperature by as much as 12%. An empirical correlation is developed for the non-dimensional temperature excess (q) by taking into account the effect of surface radiation. The correlation when applied for the highest l to the configuration, returns the maximum value of q at the optimal value, which is a key engineering quality that is sought in problems of this class. Copyright © 2013 by ASME.

ASME 2013 Heat Transfer Summer Conf. Collocated with the ASME 2013 7th Int. Conf. on Energy Sustainability and the ASME 2013 11th Int. Conf. on Fuel Cell Science, Engineering and Technology, HT 2013

Optimal distribution of discrete heat sources under mixed convection - A heuristic approach

Natural convection is the governing phenomena in many material processing applications. The conventional method of uniform heating at the bottom wall of an enclosure may result in inadequate thermal mixing and poor temperature distribution leading energy wastage. In this work, an alternative, energy-efficient method of distributed heating of the cavity is studied and compared with the isothermal bottom wall heating case in enhancing the thermal mixing and improving the temperature distribution in the cavity. Steady laminar natural convection of various fluids of industrial importance (Pr=0.015, 07, 10, 1000) in the range of Ra=103-105 is studied in a differentially heated cavity and in two cases of discretely heated square cavities. Detailed analysis is carried out by visualizing the heat flow by heatlines. The thermal mixing and temperature uniformity in each case are quantified in terms of cup-mixing temperature and root-mean square deviation (RMSD), respectively. It is found that thermal management policy of distributed heating significantly influences the thermal mixing and temperature uniformity in the enclosures. In a case with multiple discrete heat sources, a remarkable uniformity in temperature across the cavity is achieved with moderate thermal mixing. © 2010 Elsevier Ltd.

Energy

Analysis of distributed thermal management policy for energy-efficient processing of materials by natural convection

This paper reports the efficacy of the Least Square Residual (LSR) method in parameter estimation when more than one mode of heat transfer is encountered. A vertical flat plate, made of aluminium, to ensure that lumped formulation is valid, is allowed to cool in quiescent air. The novelty arises in coating the plate with a paint of known emissivity, in this case black board paint with ε = 0.85 and using the experimentally obtained transient temperature history to develop an expression for convective Nusselt number. The same plate is then given a different coating of unknown emissivity, and using the just established relationship for convective Nusselt number, by a regular parameter estimation using LSR, the emissivity is calculated. The synergy arises by using known information on emissivity to estimate convection in the first case and the reverse to back calculate an unknown emissivity. The ubiquitous vertical flat plate, thus serves as a simple, inexpensive, yet a potent emissivity comparator. © 2003 Elsevier Science Ltd.

International Communications in Heat and Mass Transfer

A synergistic approach to parameter estimation in multimode heat transfer

Applied Energy

The area-point constructal optimization for discrete variable cross-section conducting path

Journal of Physics D: Applied Physics

Constructal entransy dissipation minimization for ‘volume-point’ heat conduction

Design with Constructal Theory

Constructal entropy generation minimization for heat and mass transfer in a solid–gas reactor based on triangular element

A heuristic approach to optimal arrangement of multiple heat sources under conjugate natural convection

Journal	International Journal of Heat and Mass Transfer
ISSN	00179310
Open Access	No