Combined Effects of Nonlinear Thermal Radiation and Internal Heat Generation/Absorption on Heat and Mass Transfer in a Thin Liquid Film on a Permeable Unsteady Stretching Surface with Convective Boundary Condition

Abstract

An analysis has been carried out to study the combined effects of nonlinear thermal radiation and internal heat source/sink on heat and mass transfer in a thin liquid film over a permeable unsteady stretching sheet with suction/injection in the presence of chemical reaction. Since the momentum, energy and mass diffusion equations are highly non-linear, the problem is solved numerically. The governing equations are first reduced to a set of ordinary differential equations by using the similarity transformations and then the resulting nonlinear ordinary differential equations are solved using Runge–Kutta–Fehlberg method with shooting technique. The effects of various physical parameters on heat and mass transfer in a thin liquid film are presented graphically and in tabular forms. Numerical results are compared with the published results for some limiting cases. It is found that increase in the unsteadiness parameter leads to increase in the velocity distribution, temperature gradient and concentration gradient due to reduction in the thin film thickness. Also, increase in the thermal radiation parameter decreases the temperature gradient whereas reverse effect is seen on the concentration gradient by increasing the values of the Schmidt number.