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.

The peristaltic transport of Jeffrey fluid through the rectangular duct is investigated. The effect of porosity under the influence of partial slip is also taken into consideration. The equations describing the flow transport along with boundary conditions are first made dimensionless using appropriate transformations and are then solved to get the exact solutions. The role of pressure rise generated by the fluid is also presented. The obtained results are examined graphically through pertinent parameters affecting the flow. The streamlines have also beendisplayed to analyse the trapping phenomenon.