Free convection flow and heat transfer between two vertical parallel plates with variable temperature at one boundary

An exact solution to the problem of unsteady free convection flow and heat
transfer in a viscous incompressible fluid between two long vertical parallel plates is presented.
The temperature at one of the plates increases linearly with time while that at the other plate
remains constant at the initial fluid temperature. The dimensionless governing equations are
solved using Laplace transform technique. The solutions are obtained in the forms of rapidly
converging infinite series. Computed velocity and temperature profiles as well as the shear
stress and heat flux at the plates are presented. The parametric and temporal variations of
the relevant quantities are discussed