Increasing the mixed convection parameter significantly increases fluid velocity and heat transfer rate, while greater nanoparticle volumes increase the Nusselt number and skin friction.
A mathematical model demonstrates that in a coupled hybrid nanofluid, increasing the mixed convection parameter increases fluid velocity and heat transfer, while magnetic parameters decrease velocity but increase temperature.
Purpose The aim of this research is to analyse the heat transfer phenomena in steady two-dimensional mixed-convection magneto-hydrodynamics (MHD) flow of a coupled hybrid nanofluid over a nonlinear stretching/shrinking surface with temperature-dependent viscosity, and to examine the effects of Joule heating. This research also aims to determine the effects of the other primary physical features of advanced thermal systems on the velocity, temperature, skin-friction coefficient, and Nusselt number. Design/methodology/approach Using boundary-layer approximations, a complete mathematical model is developed for the coupled hybrid nanofluid (which comprises four types of nanoparticles dispersed in two base fluids, i.e. blood and kerosene). The governing nonlinear partial differential equations are simplified to ordinary differential equations through similarity transformations. The resulting boundary-value problem is solved semi-analytically using the Homotopy Analysis Method (HAM), implemented in the BVPh 1.0 and BVPh 2.0 Mathematica solvers. A parametric analysis is performed on the stretching parameter, mixed convection parameter, magnetic parameter, nanoparticle volume fraction, and variable viscosity to analyse their effects. Findings Results show that increasing the mixed convection parameter significantly increases the fluid velocity and the heat transfer rate due to buoyancy-assisted flow. The magnetic parameter decreases velocity due to the Lorentz force, but increases temperature due to Joule heating. Greater nanoparticle volumes increase the Nusselt number and also increase the skin friction at the surface due to increased effective viscosity. The temperature-dependent viscosity influences the thickness of the boundary layer and the behaviour of thermal transport. The overall heat transfer of hybrid nanoparticles is much better than that of ordinary nanofluids. Originality/value Unlike other studies that considered single-particle nanofluids with constant rheological and thermal characteristics and simple linear stretching configurations, this work presents the first-ever coupled hybrid nanofluid model with four types of nanoparticles in two different base fluids as well as temperature-dependent viscosity and conductivity. The viscous and conductive effects of nonlinear stretching and shrinking surfaces, mixed convection, magnetohydrodynamic (MHD) forces, and Joule heating are coupled and solved using a semi-analytical homotopy analysis method–boundary value problem (HAM–BVP) approach. This type of simultaneous modelling offers a better understanding of and ability to predict the design of advanced thermal and MHD-type heat transfer systems.
Rehman et al. (2026) studied this question. Coupled hybrid nanofluid model vs. Ordinary nanofluids was evaluated on Velocity, temperature, skin-friction coefficient, and Nusselt number. Increasing the mixed convection parameter significantly increases fluid velocity and heat transfer rate, while greater nanoparticle volumes increase the Nusselt number and skin friction.