Effect of variable thermal conductivity on entropy generation in a plate with internal energy generation

T K Favas,G Jilani,P.B Raghuvir,T.M Mathew

doi:10.1051/matecconf/201714404001

Abstract

The current numerical investigation aims at analyzing the effect of variable thermal conductivity on local and global entropy generation rates in an energy generating plate dissipating heat by conjugate conduction-forced convection heat transfer. In order to fulfill this objective, the physical model of the plate dissipating heat into surrounding coolant is transformed into a mathematical model governing the temperature field in the plate as well as flow and thermal fields in the fluid. The resulting mathematical model, being a set of coupled and non linear partial differential equations, is solved by adopting stream function-vorticity formulation and by employing Alternating direction implicit scheme. Keeping Prandtl number of the fluid, temperature of the free stream coolant and maximum permissible plate temperature as fixed, numerical predictions are obtained for wide range of values of aspect ratio, conduction-convection parameter, energy generation parameter and flow Reynolds number. It is concluded that unrealistic constant thermal conductivity assumption leads to underestimation of entropy generation rates. It is also found that an increase in energy generation parameter results in significant increase in underestimation of global entropy generation rate.

Highlights

Plates with volumetric energy source find application in nuclear reactors [1], printed circuit boards [2], thermal insulation, metal casting, heat transfer gauges [3], hardening of structural materials [4], wall heating systems [5], laser irradiation [6], blade shaped electrical resistance heater [7], curing of concrete slabs [8] etc
The partial differential equations governing the plate temperature field, fluid flow and coolant thermal fields are solved at the same time in an iterative manner
Keeping Prandtl number of the fluid, temperature of the free stream coolant and maximum permissible plate temperature as fixed, results are expressed in terms of local and global entropy generation rates for different values of plate aspect ratio, conduction-convection parameter, flow Reynolds number and energy generation parameter

Summary

Introduction

Plates with volumetric energy source find application in nuclear reactors [1], printed circuit boards [2], thermal insulation, metal casting, heat transfer gauges [3], hardening of structural materials [4], wall heating systems [5], laser irradiation [6], blade shaped electrical resistance heater [7], curing of concrete slabs [8] etc. If the temperature rises above this ceiling value, the error-free operation of the electronic device is threatened and heat dissipation to the surrounding cooling medium is highly essential [9] These heat transfers, occurring in electronic boards and nuclear fuel elements, through finite temperature difference will definitely lead to entropy generation [11]. A brief review of the literature which is closely related to the present study is illustrated below

Objectives

Results

Conclusion