Analysis of Different Boundary Conditions on Homogeneous One-Dimensional Heat Equation

An equation that involves derivatives of an unknown function with respect to two or more independent variables is known as a partial differential equation. To obtain the exact solution of a partial differential equation, an analytical solution is necessary. The suitable boundaries and initial conditions are required to solve these partial differential equations. Not only the equation, but also the boundary conditions depend on the general solution. Specifically, when coupled with varying sets of boundary conditions, these partial differential equations would have distinct general solutions. The homogeneous one-dimensional heat equation will be analytically solved in the current analysis using the process of variable separation. Our primary objective is to determine the flow characteristics of the heat equation with boundary conditions of different forms. The heat equation will be solved based on Dirichlet, Neumann and mixed boundary conditions to verify our goal. The findings have been carried out by different boundary conditions values, but the initial value remains the same. The results show that changes in the profile of the temperature depend on the types of boundary conditions. The flow characteristics of the heat equation can influence the boundary conditions