A study on cylindrical moving boundary problem with variable thermal conductivity and convection under the most realistic boundary conditions

Abstract

The melting of a phase change material is the most applicable process in thermal energy storage system to capture heat transfer phenomena arising in a class of moving boundary problem. Demand of present technology motivates researchers to develop new theories and techniques for thermal management of a material. Experimental work on melting of a material may be difficult and development of robust theoretical formulation in cylindrical geometry with convection is critical. While there is already available study on cylindrical moving boundary problem, but still insufficient modeling of a size-dependent thermal conductivity and convection effect is not addressed properly, which is being considered in this paper and is expected to improve the previous understanding. In this work, a one-dimensional moving boundary problem with size-dependent heat conductivity and convection effect is analyzed in cylindrical geometry. In the mathematical model, we have considered a time-dependent temperature boundary condition which later assumed in periodic form, and a convective boundary condition at the outer surface of the body. The numerical result of the problem is obtained successfully via heat-balance integral method. Our numerical result is compared with a previous work and found in good acceptance. From mathematical framework, it is found that convection delayed melting process. With a size-no independent thermal conductivity, the rate of moving front decreases more in comparison to the fixed thermal conductivity.