Computational investigation on non-Fourier heat transfer in polymeric liquid with multi-nanoscale and microscale structures in Forchheimer porous medium using Galerkin finite element method

Several physical phenomena associated with fluid–solid interaction occur in the presence of granular, micro, nanoscale, and crystal structures. Heat transfer in fluids containing such microbodies cannot be studied using conventional rheological stress–strain relations. Eringen developed the micropolar theory for the rheology of such fluids to investigate related fields and flow behavior. In contrast to the classical law of heat conduction, polymeric liquids display thermal relaxation time and heat conduction. To avoid any discrepancy, a generalized non-Fourier law is used for studying heat transfer. A theoretical approach is used via micropolar and non-Fourier heat flux theories with conservation laws. The Galerkin finite element method is implemented to visualize and record simulations to study the mixed convection heat transfer in fluids exhibiting couple stresses, microinertia, spin gradients, viscosity effects, and wall vorticity behavior. The heat transfer rate in fluids $${\mathrm{with\ \ Co}} + {\mathrm{Cu}} + {\mathrm{Ni}}$$ has the highest value in comparison with mono and di nanofluids. The shear stress of ternary nanofluids on the surface of the sheet is noted to be the highest relative to mono and hybrid nanofluids. Moreover, wall shear stress for Newtonian fluid is less than that for micropolar fluid. The relaxation time phenomenon in ternary nanofluids is less strong than that in $${\mathrm{Cu}}$$-micropolar and $${\mathrm{Co}} + {\mathrm{Cu}}$$-micropolar fluids. The mono nanofluid bears the maximum retarding force from the porous medium in comparison with ternary and hybrid nanofluids. Moreover, the porous medium force in the case of Newtonian fluid is weaker than that in the case of micropolar fluid.