Effect of thermocapillarity and variable thermal conductivity on the heat transfer analysis of a non-Newtonian liquid thin film over a stretching surface in the presence of thermal radiation and heat source/sink

Abstract

An analysis illustrating the flow of an Ostwald-de-Waele liquid film on an unsteady stretching sheet under the influence of thermocapillary force, magnetic field and viscous dissipation is carried out. In this study, thermal conductivity is assumed to be a function of fluid temperature. Numerical solutions for the partial differential equations governing the flow are obtained by employing the elegant Runge-Kutta-Fehlberg method for certain representative values of controlling parameters, such as thermocapillarity number, magnetic field parameter, etc. Film thickness is calculated for various values of flow parameters. Film thickness of shear thinning fluids is found to be smaller than that of a Newtonian fluid and a converse trend holds true for shear thickening fluids. Thicker films are noticed for increasing values of thermocapillarity number. In the presence of thermocapillary force, an initial decrease in the velocity of a shear thinning fluid occurs before fluid velocity experiences a significant increase towards the free surface. Stronger magnetic field strengths are seen to increase the free surface velocity. Themocapillary force on temperature in a shear thinning fluid is more prominent.

Keywords

• ostwald-de-waele fluid
• thin liquid film
• magnetic field
• thermocapillarity
• variable thermal conductivity