Capturing the onset of thermocapillary convection in the Cattaneo–Christov flow of electrically conducting thin film of Welan gum solution

Abstract

An investigation of heat transfer characteristics of electrically conducting Welan gum solution over a sheet, influenced by thermocapillary convection (thermal Marangoni convection) and magnetic field is carried out. In order to correctly predict the heat transfer characteristics, the more realistic heat flux model i.e. Cattaneo–Christov model has been utilized whereas the Maxwell-power-law model is used to capture the rheological attribute of Welan gum liquid. The Joule dissipation effect produced by the interaction between magnetic field and fluid is also considered in the energy equation. Simplified Navier–Stokes equation under above-mentioned assumptions/considerations have been obtained and are metamorphosed to a set of ODEs using appropriate Lie-group transforms. Set of ODEs are solved by Runge–Kutta fourth-order method facilitated by the shooting technique. Numerical results are displayed via graphs and tables. One of the key findings of this research work is the evidence of Marangoni convection altering the two boundary layers near the interfacial region and having almost no effect on the flow near the sheet. It has been found that the temperature and velocity of Welan gum solution can be decreased by increasing the thermal relaxation time. It has also been observed that the skin friction coefficient, a representative of shear stress is higher for a more solid-like material.