Nonlinear analysis of convective-radiative longitudinal fin of various profiles

Abstract

Purpose

This paper aims to study nonlinear heat transfer through a longitudinal fin of three different profiles.

Design/methodology/approach

A truly meshfree method is used to undertake a nonlinear analysis to predict temperature distribution and heat-transfer rate.

Findings

A longitudinal fin of three different profiles, such as rectangular, triangular and concave parabolic, are analyzed. Temperature variation, along with the fin length and rate of heat transfer in steady state, under convective and convective-radiative environments has been demonstrated and explained. Moving least square (MLS) approximants are used to approximate the unknown function of temperature T(x) with Th(x). Essential boundary conditions are imposed using the penalty method. An iterative predictor–corrector scheme is used to handle nonlinearity.

Research limitations/implications

Modelling fin in a convective-radiative environment removes the assumption of no radiation condition. It also allows to vary convective heat-transfer coefficient and predict the closer values to the real problems for the corresponding fin surfaces.

Originality/value

The meshless local Petrov–Galerkin method can solve nonlinear fin problems and predict an accurate solution.

Citation

Vyas, P.D., Thakur, H.C. and Darji, V.P. (2020), "Nonlinear analysis of convective-radiative longitudinal fin of various profiles", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 6, pp. 3065-3082. https://doi.org/10.1108/HFF-08-2018-0444