2D Unsteady Heat Transfer Problem

IntroductionIn this project, you will solve an unsteady 2D heat conduction problem using the finite difference method. You are required to discretize the governing equation, implement a numerical solution for a system with spatially varying material properties, and advance this solution in time. Governing EquationThe governing equation for 2D steady-state heat conduction with variablethermal conductivity, κ(x, y), is given by:where T(x, y) is the temperature field, κ is the thermal conductivity, ρ isthe density, and cp is the specific heat capacity of the material, all of whichvary spatially. Boundary ConditionsYour task is to solve the proposed PDE for the rectangular domain shownin Fig. 1. The image shows a composite square block of dimensions 10cm ×10cm, originally at a uniform temperature of 20°C. The top section of theblock can be approximated as a semi-circle. At t = 0, the left and rightboundaries are heated and maintained at 35°C, while the top boundary iscooled to 10°C, and the bottom boundary is held at 20°C. Assume that theupper section is made of stainless steel, and test your algorithm by selectingdifferent materials for the lower section. Choose real-world materials with arange of thermal properties.