Effects of thermal radiation and mass diffusion on free convection flow past an impulsively started infinite vertical plate with ramped temperature

The effects of thermal radiation on unsteady free convection flow of a viscous incompressible fluid past an impulsively started infinite vertical plate in the presence of chemical species concentration and a temperature boundary condition which follows a ramp function up until some specified time and then remains constant has been investigated. The fluid is assumed to be gray, emitting–absorbing but non-scattering medium, and the optically thin radiation limit is considered. The dimensionless governing equations are solved using Laplace transform technique. The velocity and temperature profiles and the Nusselt number are shown on graphs for different air flows. The variation of skin-friction is also shown in tabular form. The effects of different parameters like radiation parameter, thermal
Grashof number, Schmidt number, mass to thermal buoyancy ratio parameter and time are discussed. It is observed that the velocity increases with decreasing radiation parameter.
The Nusselt number increases as time increases to unity and thereafter decreases to the steady state gradually. The interaction of free convection with thermal radiation near a
ramped temperature plate has also been compared with the flow near a plate with constant temperature.