Effect of convection boundary condition on hyperbolic heat conduction in thermoelastic medium

Abstract

This paper aims to study the effect of heat transfer by convection on thermoelastic rectangular solid medium in the context of hyperbolic heat conduction. The studied geometry is a two dimensional finite thin rectangular plate without internal heat generation, which is initially at a uniform temperature and subjected to convection heat transfer from the extreme edge(y=a) while the opposite side is kept insulated and remaining two sides are at a constant temperature. The material properties are assumed to be constant. The differential transform method is applied to solve the hyperbolic heat conduction equation to obtain temperature distribution in the spatial and temporal domain. Then by applying the obtained temperature in the thermoelastic equation, the displacement component, and the stress field are calculated. Also, the effect of convection boundary conditions on temperature distribution and thermoelastic field are illustrated numerically and graphically for a copper plate. It is observed that the compressive and tensile stress occurs along y-direction due to heat transfer through convection at one end.