Heat equation model for rod and thin plate by partial q-difference operator

Heat equation model for homogeneous rod and thin plate based on Newton’s law of cooling is constructed by partial q-difference operator. The propagation of heat, the nature of material used and its corresponding solutions of heat equations are the focus of this paper. In particular, logarithmic solution for this heat equation model is arrived. Through numerical simulations and diagrams generated using MATLAB, solutions are validated and relevant applications are derived.