Thin film flow and heat transfer over an unsteady stretching sheet with thermal radiation, internal heating in presence of external magnetic field

TL;DR

This paper analyzes the effects of magnetic fields, thermal radiation, internal heat sources, and unsteady stretching on thin film flow and heat transfer, using similarity transformations and numerical solutions to non-linear differential equations.

Contribution

It introduces a mathematical model for unsteady thin film flow with thermal effects and solves it numerically, providing new insights into the influence of various parameters.

Findings

Magnetic field and thermal radiation significantly affect temperature distribution.

Unsteadiness parameter influences film thickness and flow behavior.

Results agree with existing literature for special cases.

Abstract

In this paper we present a mathematical analysis of thin film flow and heat transfer to a laminar liquid film from a horizontal stretching sheet. The flow of thin liquid film and subsequent heat transfer from the stretching surface is investigated with the aid of similarity transformations. Similarity transformations are used to convert unsteady boundary layer equations to a system of non-linear ordinary differential equations. The resulting non-linear differential equations are solved numerically using Runge-kutta-Fehlberg and Newton-Raphson schemes. A relationship between film thickness $\beta$ and the unsteadiness parameter $S$ is found, the effect of unsteadiness parameter $S$, and the Prandtl number $Pr$, Magnetic field parameter $Mn$, Radiation parameter $Nr$ and viscous dissipation parameter $Ec$ and heat source parameter $\gamma$ on the temperature distributions are presented and discussed in detail. Present analysis shows that the combined effect of magnetic field, thermal radiation, heat source and viscous dissipation. The results which form special case of the present study are in excellent agreement with the results reported in the literature.