The effects of variable fluid properties and viscous dissipation on forced convection of viscoelastic liquids in a thin film over an unsteady stretching sheet

摘要

An analysis is performed to study the effect of variable viscosity and variable thermal conductivity on the flow and heat transfer of a thin viscoelastic liquid (obeying Walters' liquid B model) film on a horizontal unsteady stretching sheet taking into account the effect of viscous dissipation. The fluid viscosity is assumed to decrease exponentially with temperature but the thermal conductivity is assumed to vary as a linear function of temperature. Numerical solutions are obtained for some representative values of the viscosity and thermal conductivity variation parameters, unsteadiness parameter, and Eckert number. Typical temperature and velocity profiles, dimensionless film thickness, free-surface velocity and temperature, local skin-friction coefficient, and the local surface heat flux are obtained for a wide range of governing parameters. In general, it is found that a viscoelastic fluid is more sensitive to the variable fluid properties effect than a Newtonian fluid. Also, for constant and (or) variable fluid properties, the film thickness and the local surface heat flux of a viscoelastic fluid is small compared to that of a Newtonian fluid. For all values of the variable viscosity parameter and for both viscoelastic and Newtonian fluid films, the viscous dissipation effect increases the free-surface temperature significantly whereas it reduces the heat transfer rate markedly. However, viscous dissipation does not influence the velocity profiles of both Newtonian and viscoelastic liquid films impressively although the film thickness changes noticeably.