Marangoni‐bioconvectional flow of Reiner–Philippoff nanofluid with melting phenomenon and nonuniform heat source/sink in the presence of a swimming microorganisms

Abstract

The nanofluids are more practical to enhance the heat transfer compared to regular fluids. Such effectiveness in mind causes this communication's concern to investigate the Darcy–Forchheimer flow of Reiner–Philippoff nanofluid with heat source/sink, thermal conductivity in the occurrence of motile microorganisms over the stretching surface. The melting phenomenon is also considered. For this purpose, the set of nonlinear partial differential equation (PDE) is converted into ordinary differential equation (ODE) using the required translation of similarities. These obtained simple ordinary differential equations are solved using the built‐in MATLAB computational tool bvp4c method. The graphical outcomes are delineated for velocity, temperature, concentration, and motile microorganisms profiles via Lewis number, fluid parameter, radiation parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number, bioconvection Lewis number, Reynolds number, Peclet number, and bioconvection Rayleigh number, respectively. The numerical data confirm that the coefficient of wall heat transfer reduces for the greater values of the Schmidt number and thermophoresis parameter. The heat profile is reduced for the higher magnitude of the Prandtl number while boosted up for the higher estimations of thermal radiation parameter. The mass transfer of microorganisms is boosted via the Peclet and bioconvection Lewis number.