In this article, effects of heat transfer on particle–fluid suspension induced by metachronal wave have been examined. The influence of magnetohydrodynamics (MHD) and thermal radiation are also taken into account with the help of Ohm’s law and Roseland’s approximation. The governing flow problem for Casson fluid model is based on continuity, momentum and thermal energy equation for fluid phase and particle phase. Taking the approximation of long wavelength and zero Reynolds number, the governing equations are simplified. Exact solutions are obtained for the coupled partial differential equations. The impact of all the embedding parameters is discussed with the help of graphs. In particular, velocity profile, pressure rise, temperature profile and trapping phenomena are discussed for all the emerging parameters. It is observed that while fluid parameter enhances the velocity profile, Hartmann number and particle volume fraction oppose the flow.

In this article, the effect of thermo-diffusion and diffusion-thermo on hyperbolic tangent magnetised nanofluid with Hall current past a nonlinear porous stretching surface has been analysed numerically. The impact of thermal slip and chemical reaction are also examined in our current analysis. Runge–Kutta–Merson method and shooting method have been successfully employed to obtain numerical results for the governing nonlinear differentialequations. The impact of Hartmann number, Hall parameter, porosity parameter, fluid parameter, Weissenberg number, Richardson number, concentration buoyancy parameter, Schmidt number, Dufour parameter, Soret number, Prandtl number, chemical reaction parameter, and power-law exponent are discussed and demonstrated graphicallyfor the flow phenomena. Furthermore, the description for Sherwood number, rate of shear stress, and Nusselt number are displayed using tables against all the pertinent parameters. A detailed numerical comparison for the power-law exponent and Prandtl number has been elaborated via tables.