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 and .

The current article addresses the unsteady squashing hydromagnetic transport of an electrically conductive pseudoplastic fluid traversing across a sensor surface. The fluid flow phenomenon is happening under the thermic radiation and heat origination effects. The sensor surface is positioned in the superficially free stream. The viscosity and thermic conductivity are taken as a concomitant of temperature. The magnetic field is acting transversely to the phenomenon. The energy equation is assimilated with the non-conventional heat transfer model. This type of assimilation is established instead of conventional Fourier's law for expressing the heat generation, thermic radiation and especially thermal relaxation times. To construct the simpler non-dimensional structure of the arising energy, continuity and momentum equations, suitable controlling parameters have been utilized. A well-known numerical method has adopted to construct the solutions of the constructed equations. To check the convergence of the obtained numerical solutions, a comprehensive graphical analysis has been presented. The consequences of impressive parameters like heat origination parameter, radiation parameter, boundary layer, thermal relaxation times, magnetic factor and the squeezing number on the flow structure are deliberated graphically. Also, the things of engineering importance, such as the variation in squeezed flow index factor, Prandtl number, thermal conductivity, variable thickness, free stream velocity, Weissenberg number, have sturdy impacts on the flow and energy equation.

The current mathematical formulation is dedicated to investigate the Darcy‐Forchheimer boundary layer–squeezed hydromagnetic flow of a Casson fluid passing through a sensor surface. The flow phenomenon is occurring in a locally free stream under the combined sway of heat generation and thermic radiation. The energy equation is deliberated with the assistance of Cattaneo‐Christov theory rather than using Fourier's law for conduction of heat. Here, the thermic conductivity is being presumed as a function of temperature. The governing mathematical structure consists of highly nonlinear terms, so a set of regulatory parameters is being accomplished to attain the unpretentious dimensionless equations. This nondimensional structure is then treated numerically to attain the nearly converging results. The significance of substantial parameters such as magnetic factor, radiation parameter, Casson fluid parameter, heat origination, and thermal relaxation time on the flow phenomenon is estimated and presented graphically. Besides this, the factors of engineering interest like the Prandtl number and squeezed flow index with vacillating thermic conductivity have strong effects on the flow behavior of the fluid. It is observed that the magnetic effect causes an expansion in the velocity curve while a reduction is found for squeezed flow index parameter.