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The goal of this research is to investigate the behaviours of porosity and squeezing phenomena in the presence of time-dependent heat flow that affect the flow rate and improve the system’s heating/cooling mechanism, reduce non-Newtonian fluid turbulence and scale-up flow tracers. Squeezing discs in the presence of no-slip velocity and convective surface boundary conditions induces a laminar, unstable and incompressible non-Newtonian fluid. The convective form of the momentum, concentration and energy equations are modelled for smooth discs to evaluate and offer an analytical and numerical examination of the flow for heat and mass transfer, which are further transformed to a highly non-linear system of ordinary differential equation using similarity transformations. In the case of smooth disks, the self-similar equations are solved using Homotopy Analysis Method (HAM) with appropriate initial guesses and auxiliary parameters to produce an algorithm with an accelerated and assured convergence. The comparison of HAM solutions with numerical solver programme BVP4 c proves the validity and correctness of HAM results. It is found that increasing or bypassing the Hartman number reduces the capillary region, making the Lorentz force effect more visible for small values of non-Newtonian parameter. The concentration rate at the bottom disc rises rapidly as the thermal diffusivity rises. In addition, because the rate of outflow from the flow domain increases, the suction/injection parameter lowers the radial velocity. Additionally, as the non-Newtonian parameter is increased, skin friction and heat/mass flux rise. In the suction/injection situation, all physical characteristics have the opposite effect on flow field profiles.

Flow dynamics of a time-dependent non-Newtonian and non-isothermal fluid between coaxial squeezing disks