The magnetohydrodynamic (MHD) movement of fluids through a porous material has a variety of uses such as distillation towers, heat exchangers, catalytic processes, magnetic field‐based wound treatments, cancer therapy and hyperthermia. This paper explores the complex dynamics of a three‐phase flow utilizing MHD Jeffrey fluid, which sits in between nano and hybrid (molybdenum disulphide [MoS2] and multi‐walled carbon nanotubes [MWCNTs]) nanofluids. The governing differential equations are derived for the physical flow model. The equations are reduced to dimensionless equations by using dimensionless parameters. The resultant equations are solved by using the regular perturbation technique. The results are analysed for various physical pertinent parameters through 2D/3D graphs. The heat transfer rate and volume flow rate are calculated for the left and right plates. This analysis also considers how the system's overall behaviour would be affected by radiation and dissipation effects. The results indicate that the magnetic parameter, electric parameter, quadratic convective parameter, Brinkman number and Grashof number significantly affect heat transfer enhancement. Fluid velocity can be reduced using radiation parameters, porosity, electric and magnetic parameters and velocity declines by Jeffrey parameters.