Numerical Solutions Using MATLAB

Much of our discussions in the previous chapters have revolved around deriving a differential equation that models heat transfer in a domain and applying proper initial and boundary conditions to obtain an exact or approximate closed-form solution to the original equation. It is, however, not always possible to obtain a closed-form solution to the heat equation, especially if the differential equation or boundary conditions are nonlinear or the domain under consideration is irregular. Problems such as these and more may be solved by discretizing the domain and numerically solving the heat equation at each discretization. Generally, the smaller the discretization, the more accurate the solution. Due to the number and complexity of the calculations involved in most cases, this process is often performed using a computer, either through user-written code or pre-packaged routines in software such as MATLAB.