Heat Conduction Equation

We summarise the process and results for finding analytical solutions to the one-dimensional, steady heat conduction equation with various boundary conditions.

The solution to radial heat conduction with convective boundaries can find the temperature distribution and heat transfer rate which is useful in pipe flow.

Here we cover the process of finding solutions for the cylindrical heat equation. We consider one-dimensional, steady cases which for the radial heat equation.

Here we look at a more general boundary which combines multiple boundary conditions. The distribution produced can be used for a wide range of scenarios.

In this post we look at solutions to the heat conduction equation in Cartesian coordinates with mixed temperature, heat flux and convective boundary conditions.

Here we derive the analytical solution to the heat equation with convective boundary conditions. These common conditions represent fluid flow over a surface.

We discuss the heat flux boundary condition and attempt to find the analytical solution for a one-dimensional, steady Cartesian system with flux boundaries.

Boundary conditions are essential to solving the heat conduction equation. Here we look at some common thermal boundary conditions encountered in practice.

Here we find the analytical solution to the steady, one-dimensional spherical heat equation. This is useful for heat transfer within special pressure vessels.

Here we find the analytical solution to the steady, one-dimensional cylindrical heat equation. This is useful for heat transfer within pipes.