Magneto-hydro dynamic squeezed flow of Williamson fluid transiting a sensor surface

Abstract

The present article reports the combined effects of radiation and heat origination on the electro-kinetically induced hydromagnetic squeezed flow of a pseudoplastic fluid. The fluid is passing over a microcantilever sensor surface positioned in the superficial free stream. Microcantiliver sensor can detect the flow rate and the variance in the temperature of the fluid. The thermal conductivity and fluid viscosity are assumed as a function of temperature. Boundary layer approximations are considered to construct a pseudoplastic fluid flow model. The governing system is then resolved into a non-dimensional form with the assistance of an appropriate set of control parameters. The solution to these non-dimensional equations has calculated with the assistance of familiar numerical techniques i.e. Shooting technique. The results specify that flow of fluid, temperature, and velocity profiles are remarkably influenced by the radiation parameter, fluid parameter, heat generation parameter, thermal relaxation parameter, magnetic parameter, and the squeezing number. A comprehensive graphical and tabular study is constructed to check the convergence of the obtained results. One can detect that the temperature curve is changing slightly for the Christov-Cattaneo heat transfer model as compared to classical Fourier's law of heat transfer. Further, the physical quantities, i.e. free stream velocity, variable viscosity, thermal conductivity, Weissenberg number, and Prandtl number have strong impacts on the boundary layer flow equations. It is perceived that the fluid velocity profile rises for the growing value of the magnetic parameter, but reduces for squashed flow index b. Also, a positive variation is found in the temperature profile for rising values of $\beta$ and $Q$ .

Keywords: Applied mathematics; MHD Flow; Mechanical engineering; Sensor surface; Squeezed flow; Thermodynamics; Variable thermal conductivity.