Natural convection flow in vertical channel due to ramped wall temperature at one boundary

An exact solution of unsteady natural convection of a viscous incompressible fluid in a vertical channel due to ramp heating at one boundary is presented. The temperature at one channel plates increases linearly over a certain time period, then remains constant. That at the other plate is maintained at the initial fluid temperature. The influence of the physical parameters on the velocity field, the temperature field, rate of heat transfer, skin-friction and volumetric flux of the fluid are analyzed systematically. Natural convection due to ramp heating is compared with the baseline case of flow with constant temperature