Solving One-Dimensional Heat Conduction Equation Using Finite Volume Method

We can employ the finite volume method to solve the one-dimensional heat conduction equation, a technique widely used in computational simulations. When implementing this method, we first discretize the conduction equation, then represent it as a large matrix equation system. The solution process typically involves defining control volumes, applying energy balance equations at each node, and assembling the resulting algebraic equations into a coefficient matrix and source vector. Key implementation aspects include proper handling of boundary conditions through specialized matrix entries and implementing efficient solvers like TDMA (TriDiagonal Matrix Algorithm) for the tridiagonal matrix system. This matrix equation can be computationally solved using numerical methods to obtain predicted temperature distribution results. Due to its straightforward programming structure and clear physical interpretation, this method finds extensive applications in various engineering fields, particularly in computational fluid dynamics and heat transfer analysis.