Explicit analytical solutions of 2-D laminar natural convection

There are many natural convection processes in various fields, and it is still a hot topic to investigate the fluid dynamics and heat transfer of natural convection. The analytical solutions are meaningful in both theoretical investigation and practical applications. Specially, they are very useful to computational fluid dynamics and heat transfer as the benchmark solutions to check the numerical solutions and to develop numerical differencing schemes, grid generation methods and so forth. Two explicit analytical solutions of 2-D steady laminar natural convection along a vertical porous plate and between two vertical plates were derived for better understanding the flow and heat transfer as well as promoting the computational fluid dynamics and computational heat transfer.