Determining the temperature distribution within a heat exchanger involves searching for an accurate mathematical expression known as the analytical solution of the conduction equation. These solutions, however, are only viable for simple geometries and boundary conditions. The complexity of the heat exchanger geometry or boundary conditions in practical cases often renders analytical solutions unattainable. Analytical solutions can be derived for simple geometries, such as a 1D heat conduction problem in a rod.
In scenarios where the heat exchanger exhibits more intricate geometries and boundary conditions, numerical methods are employed to solve the conduction equation. These numerical methods provide comprehensive solutions for 1D, 2D, or 3D heat exchange processes, taking into account time dependence. By utilizing numerical methods, engineers can gain a deeper understanding of the heat transfer process within the system, allowing for more complex geometries and boundary conditions to be accurately addressed.
