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. © 2011 Institute of Thermomechanics AS CR, v.v.i.