MHD Williamson Nanofluid Flow over a Slender Elastic Sheet of Irregular Thickness in the Presence of Bioconvection

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge–Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter [Formula: see text] , variable viscosity parameter [Formula: see text] and wall thickness parameter [Formula: see text] impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter [Formula: see text] and thermophoresis parameter [Formula: see text]. The boosted value of Brownian motion [Formula: see text] and Lewis number [Formula: see text] reduce the concentration of nanoparticles. The higher inputs of Peclet number [Formula: see text] and bioconvection Lewis number [Formula: see text] decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely.