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This article presents a numerical investigation of the pulsatile flow of non-Newtonian Casson fluid through a rectangular channel with symmetrical local constriction on the walls. The objective is to study the heat transfer characteristics of the said fluid flow under an applied magnetic field and thermal radiation. Such a study may find its application in devising treatments for stenosis in blood arteries, designing biomechanical devices, and controlling industrial processes with flow pulsation. Using the finite difference approach, the mathematical model is solved and is converted into the vorticity-stream function form. The impacts of the Hartman number, Strouhal number, Casson fluid parameter, porosity parameter, Prandtl number, and thermal radiation parameter on the flow profiles are argued. The effects on the axial velocity and temperature profiles are observed and argued. Some plots of the streamlines, vorticity, and temperature distribution are also shown. On increasing the values of the magnetic field parameter, the axial flow velocity increases, whereas the temperature decreases. The flow profiles for the Casson fluid parameter have a similar trend, and the profiles for the porosity parameter have an opposite trend to the flow profiles for the magnetic field parameter. The temperature decreases with an increase in the Prandtl number. The temperature increases with an increase in the thermal radiation parameter. The profile patterns are not perfectly uniform downstream of the constriction. [ABSTRACT FROM AUTHOR]