Influence of pressure gradient and buoyancy on viscous dissipation and Joule heating in Carreau nanofluid flow

Abstract Efficient control of heat and mass transport in non-Newtonian nanofluids plays a vital role in several engineering fields, including polymer extrusion, thermal regulation of electronic components, and waste-energy recovery. Although numerous investigations have been reported, many of them address only one or two effects separately, which limits a full understanding of the combined physical mechanisms involved. In the present work, we analyze the time-dependent, axisymmetric motion of a Carreau-type nanofluid past a porous disk that stretches radially. The formulation incorporates the influence of pressure gradients, buoyancy, magnetic effects, viscous dissipation, Joule heating, and radiative heat flux. Porosity and inertial resistance are represented through the Darcy–Forchheimer approach. After applying suitable similarity transformations, the resulting nonlinear ordinary differential equations are solved numerically using a Runge–Kutta-based shooting algorithm. The numerical results indicate that stronger magnetic intensity reduces the fluid velocity but increases the surface friction coefficient. Periodic pressure gradients significantly affect both velocity and temperature fields, while the combined action of viscous dissipation and thermal radiation thickens the thermal boundary layer. Comparisons with previously published data show excellent agreement, confirming the accuracy of the proposed formulation. This investigation unifies several thermal–physical effects that were previously treated separately and thus provides an extended theoretical basis for Carreau nanofluid transport, with direct implications for industrial systems where simultaneous control of flow and heat transfer is essential.