In the current article, we have performed computational analysis on convection heat transfer of a hybrid nanofluid in occurrences where porous media and the effect of magnetic force are involved. In order to assess the time-fractional derivatives, Caputo's notion is utilized while the Darcy-Forchheimer model is applied due to the involvement of the porous medium. Moreover, the boundary conditions are assumed to be nonuniform through the equilibrium between the surface tension and shear stress over a semi-infinite permeable flat surface. Keeping in view the complexity of the fractional derivative model and nonuniform boundary conditions, the problem in question is a complicated one. Accordingly, the coupled momentum and energy equation is linearized and the finite difference scheme is then applied and implemented in MATLAB Code R2020b. Furthermore, we have also offered a comprehensive analysis regarding error and convergence of the proposed numerical method. The newly introduced numerical technique to determine the numerical solutions and some unique and interesting deductions are established. From the computational results, one can conclude that the fluid motion in both hybrid and single nanofluids slows down due to magnetic field, porosity, and inertia coefficient as the magnetic and electric fields are synchronized due to the formation of the Lorentz force and viscous interference. We believe that our proposed numerical technique regarding employment of the fractional model for heat transfer application to the hybrid nanofluid over a semi-infinite nonuniform permeable surface along with variable heat flux is not found in the literature so far. Furthermore, the obtained results will be a valuable addition to fractional calculus from an engineering point of view.
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