LAUSR

The present study investigated the variable viscosity and multiple slips on two-dimensional magnetohydrodynamic Carreau fluids due to slendering sheet filled with microorganisms. The Carreau model is used to characterize the behavior of the fluids with shearing thickening properties using the various values of exponent of power law. The diffusion-thermo and thermos diffusion effects are taken into account. The nonlinear sets of ordinary differential equations are treated numerically by shooting technique with Runge–Kutta Fehlberg method. Different parameters like magnetic interaction parameter $$ M $$M, Weissenberg number $$ We $$We, the index of power law $$ m $$m, various multiple slip parameters like the velocity slip parameter $$ \tau_{1} $$τ1, the temperature jump parameter $$ \tau_{2} $$τ2, the concentration $$ \tau_{3} $$τ3, and the concentration jump parameter $$ \tau_{4} $$τ4 are analyzed. The velocity, the skin friction, the rate of heat transport namely Nusselt number and rate of mass transport as Sherwood number are elaborated graphically and computed in tabular benchmark. The analysis found that the density of motile organism grows with the growing magnetic field parameter, diffusion-thermo number, thermo-diffusion number and Weissenberg number.