# Convective-radiative moving porous fin with temperature-dependent thermal conductivity, heat transfer coefficient and wavelength-dependent surface emissivity

Parvinder Kaur (Department of Mathematics, Eternal University Baru Sahib HP, Raggarh, India)
Surjan Singh (Department of Mathematics, Eternal University Baru Sahib HP, Raggarh, India)

ISSN: 1573-6105

Article publication date: 2 January 2023

Issue publication date: 24 February 2023

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## Abstract

### Purpose

In this paper, temperature distribution and fin efficiency in a moving porous fin have been discussed. The heat transfer equation is formulated by using Darcy's model. Heat transfer coefficient and thermal conductivity vary with temperature. The surface emissivity of the fin varies with temperature as well as with wavelength. Thermal conductivity is taken as a linear and quadratic form of temperature. The entire analysis of the paper is presented in non-dimensional form.

### Design/methodology/approach

In this study, a new mathematical model is investigated. The novelty of this model is surface emissivity which is considered temperature and wavelength dependent. Another interesting point is the addition of porous material. The Legendre wavelet collocation method has been used to solve the nonlinear heat transfer equation. Numerical simulations are carried out in MATLAB software.

### Findings

An attempt has been made to discuss temperature distribution in the presence of porosity and wavelength-temperature-dependent surface emissivity. The effect of various parameters on temperature has been discussed, including thermal conductivity, emissivity, convection-radiation, Peclet number, sink temperature, exponent “n” and porosity. Fin efficiency is also calculated for some parameters. According to the study, heat transfer rate increases with higher radiation-convection, emissivity, wavelength and porosity parameters.

### Originality/value

The numerical results are carried out by using the Legendre wavelet collocation method, which has been compared with exact results in a particular case and found to be in good agreement. The percent error is calculated to find the error between the current method and the exact result. A comparison of the obtained results with the previous data is presented to validate the numerical results.

## Acknowledgements

The authors are grateful to the Vice-Chancellor of Eternal University, Baru Sahib, India, for providing the necessary facilities. The authors also gratefully acknowledge the contribution of the reviewers, which significantly improved the paper.

## Citation

Kaur, P. and Singh, S. (2023), "Convective-radiative moving porous fin with temperature-dependent thermal conductivity, heat transfer coefficient and wavelength-dependent surface emissivity", Multidiscipline Modeling in Materials and Structures, Vol. 19 No. 2, pp. 176-196. https://doi.org/10.1108/MMMS-07-2022-0120

## Publisher

:

Emerald Publishing Limited