Transient and steady-state numerical solutions in natural convection

A flat vertical plate, of finite thickness and appreciable thermal capacity, was assumed to be suddenly loaded internally with a constant and uniform flux while immersed in an extensive body of quiescent and unstratified fluid. The partial differential equations describing the conservation of mass, momentum, and energy were solved in their time-dependent forms, using a finite-difference technique. The computed transient velocity and temperature fields are in good agreement with the results of previous integral and numerical analyses and with experimental data. The final steady-state profiles are also in good agreement with the similarity solution for the uniform surface flux condition. For some conditions, with plates of small thermal capacity, the transient temperature and velocity levels locally exceeded the final steady-state distributions.