Transient response of longitudinal rectangular fins to step change in base temperature and in base heat flow conditions

被引：27

作者：

Mhlongo, M. D. ^{[1
]}

Moitsheki, R. J. ^{[2
]}

Makinde, O. D. ^{[3
]}

机构：

[1] CSIR, ZA-0001 Pretoria, South Africa

[2] Univ Witwatersrand, Ctr Differential Equat Continuum Mech & Applicat, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa

[3] Cape Peninsula Univ Technol, Inst Adv Res Math Modelling & Computat, ZA-7535 Bellville, South Africa

来源：

INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER | 2013年 / 57卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Symmetry analysis; Exact analytical steady state solutions; Ermakov-Penny equation; Numerical solutions; Heat transfer; Fins; THERMAL-CONDUCTIVITY; SYMMETRY ANALYSIS; STRAIGHT FINS; PERFORMANCE; EQUATION;

D O I：

10.1016/j.ijheatmasstransfer.2012.10.012

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

In this paper, we construct solutions for model describing heat transfer in longitudinal rectangular fins. The imposed boundary conditions are the step change in the base temperature and the step change in base heat flow. Both the thermal conductivity and the heat transfer coefficients are assumed to be power law temperature dependent. We employ the local and nonlocal symmetry techniques to analyze the problem at hand. In one case the reduced equation transforms to the tractable Ermakov-Pinney equation. Nonlocal symmetries are admitted when some arbitrary constants appearing in the governing equations are specified. The exact analytical steady state solutions which satisfy the prescribed boundary conditions are constructed. Since the obtained general exact analytical solutions for the transient state satisfy only the zero initial temperature and adiabatic boundary condition at the fin tip, we sort numerical solutions. The effects of the thermo-geometric fin parameter and the power law exponent on temperature distribution are studied. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：117 / 125

页数：9

共 31 条

[1] HEAT-TRANSFER IN STRAIGHT FINS OF ARBITRARY PROFILE SUBJECTED TO PERIODIC BASE AND ENVIRONMENT TEMPERATURES [J].