Effect of temperature dependent viscosity on the flow and heat transfer over an accelerating surface

The effect of temperature dependent viscosity on the boundary layer flow over a linearly stretching surface is investigated. This solid elastic flat surface remains at a constant temperature higher than ambient, and moves in its own plane at a velocity varying linearly with the distance from the discharge slit. In many liquids, such as water and oils, the variation in viscosity due to temperature change is more dominant than other effects. The authors adopt two approaches to deal with the effect of temperature dependent viscosity by (1) setting a known function describing the mathematical modelling of the viscosity-temperature relation into the governing equations (direct method) and (2) using the perturbation expansion technique for small heat transfer rates (perturbation method). In the direct method the viscosity-temperature relationship follows an exponential function. In the perturbation method a Taylor expansion is used on viscosity, velocity and temperature on a small quantity that is defined as the ratio of temperature differences between the moving surface and the ambient to the ambient temperature. The perturbation expansion method is independent of any choice of-the viscosity-temperature function. Following the similarity transformation, the governing partial differential equations reduce to ordinary equations. The results obtained by the direct method indicate that the velocity and temperature distributions depend upon the Prandtl number as well as the viscosity ratio that implicitly represents the temperature difference between the moving surface and the ambient. The results by the perturbation method can effectively describe the flow and temperature fields with perturbation series truncated after linear terms even though the perturbation quantity is not so small.