Impact of variable viscosity, thermal conductivity, and Soret–Dufour effects on MHD radiative heat transfer in thin reactive liquid films past an unsteady permeable expandable sheet

Significance of magnetohydrodynamic effect on a viscous (temperature-dependent) and chemically reactive thin fluid film flow past an unsteady permeable stretchable plate with Soret–Dufour effects, nonlinear thermal radiative, and suction under the action of a convective type of boundary condition is analyzed. The problem consists of nonlinear governing basic equations that are highly nonlinear due to the existence of nonlinear thermal radiative terms in the energy equation. Analytical solutions are challenging to achieve for such types of problems, so a numerical scheme adopts the numerical solution. Computed solutions indicate that decreasing the Dufour number (and simultaneously increasing the Soret number) enhances heat flux, whereas the reverse trend is estimated for the concentration gradient field. The influence of magnetization indicates a decrement in the thin liquid film velocity distribution, whereas an increment is observed in temperature and solutal gradient profiles. Further, an enhancement in thermoradiative values focuses on decreasing the heat flux profiles, whereas a decreasing trend is determined in the solutal gradient by incrementing the Schmidt number. The variations of the velocity field, temperature, and concentration gradients are shown for the unsteady parameter $S$ lying in the range [0.8, 1.4]. Similarly, the range of different parameters utilized are ${\theta }_r$ [0.0, 1.0], $Nr$ [0.0, 2.0], $Pr$ [0.8, 1.5], $Sc$ [0.5, 2.0], $B^{*}$ [0.0, 1.0], $k_1$ [0.2, 3.0], $f_w$ [1.0, 2.0], $M$ [0.0, 3.0], $Du$ [0.4, 1.0], and $Sr$ [0.4, 1.0]. The novelty of the present study lies in its analysis of complex fluid dynamics phenomena and their implications for various industrial processes and engineering applications, including coating processes, heat exchangers, microfluidics, and biomedical engineering. The insights gained from the study can contribute to developing more efficient and innovative research in these areas. Further, we have compared the present results with those available in the literature under some special cases and found them to be in excellent agreement.