Chebyshev finite difference approach to modeling the thermoviscosity effect in a power-law liquid film on an unsteady stretching surface

The effect of thermoviscosity (temperature-dependent viscosity) on the heat transfer in a power-law liquid film over an unsteady stretching sheet is investigated. Similarity analysis is used to transform the governing equations for mass, momentum and energy into a system of ordinary differential equations, which contain a thermoviscosity parameter θr, unsteadiness parameter S, generalized Prandtl number Pr and power-law index n. The film thickness, the temperature distributions, the local heat transfer rate, and the local skin-friction coefficient were obtained using the Chebyshev finite difference method (ChFD). The results show that thermoviscosity significantly increases the film thickness and the local heat transfer rate while decreasing the local skin-friction coefficient as θr → 1. It is found that liquids with a higher power-law index will have a larger film thickness and a higher free-surface temperature, which indicate a lower local heat transfer rate, −θ′(0).