Comparison of Homogeneous and Non-Homogeneous Onedimensional Heat Equation

Heat equation is a partial differential equation that contains derivatives for two or more independent variables of an unknown function. There are heat equations that are homogenous and non-homogeneous. The non-homogeneous heat equation can be defined as there are source term in the partial differential equations, while there is no source term for the homogeneous heat equation. To solve the nonhomogeneous, the heat equation need to be homogeneous by measure the displacement of the temperature of the heat from the equilibrium temperature. To obtain the exact solution of partial differential equation, an analytical solution is required. The suitable boundary and initial conditions are required to solve these partial differential equations. In the present research, the homogeneous and nonhomogeneous one-dimensional heat equation will be solved analytically by using superposition principle (non-homogeneous) and separation of variables method (homogeneous). Our main objective is to compare the flow characteristics of heat equation on homogeneous and non-homogeneous heat equation. The heat equation will be solved based on Dirichlet boundary conditions to verify our objective. The finding results have been compared on the temperature profile for homogeneous and non-homogeneous heat equations. The temperature profile on the non-homogeneous Dirichlet boundary conditions show that it can be changed the profile and remain the same as temperature profile on homogeneous Dirichlet boundary condition when there is no source term.