Numerical simulation of Boger nanofluids with heat source, magnetic field, and Cattaneo–Christov heat flux model between two parallel permeable porous plates via finite difference method

Stable viscosity is a significant part of any thermal system. Boger provides a unique idea for stable viscosity, especially in nanofluid flow simulation, regardless of shear stress and enhanced thermal properties, significantly improving heat transfer efficiency. Their predictable flow behavior ensures energy savings and reduced pressure drops, enhancing performance and reliability in various thermal management systems. Nanofluids are used in applications like electronics cooling, automotive engine cooling, industrial processes, solar energy systems, and heat exchangers. In this study, we scrutinize the complex flow time-dependent behavior system of the two-dimensional rotational Boger nanofluids flow model with the effect of magnetohydrodynamic. This fluid contains graphene-type Single-wall carbon nanotubes (SWCNTs) that are ambient by permeable plates. In addition, we also deliberated the tenders of irregular heat sink/source, Cattaneo–Christov heat flux, associated with thermal radiation. Nonlinear partial differential equations (PDEs) are converted into dimensionless (PDEs) forms using suitable similarity variables. A stable and precise finite difference method (FDM) has been implemented to solve the nonlinear and complex flow equations, incorporating the relevant boundary conditions. Investigated the characteristics of the penalty method applied to pressure terms in the momentum equations and then solved the system developed by omitting the pressure term. The finite difference scheme, implemented in MATLAB, is used to compute numerical and graphical results, illustrating the effect of various factors on flow characteristics across different profiles. These results demonstrate two distinct behaviors with varying time in both two dimensional (2D) and three dimensional (3D). Increasing the relaxation time ratio parameter and Darcy number reduces the nanofluid velocity profile U(τ∗,ξ∗,η∗) in both porous plates, while increasing the penalty number and porosity parameter enhances the velocity profile V(τ∗,ξ∗,η∗) at the bottom and top porous plates. Boosting the values of the irregular heat source/sink parameter and the thermal relaxation parameter enhances the heat transfer rate θ(τ∗,ξ∗,η∗) in both porous plates. Higher values of the magnetic parameter (M) results in opposite effects on Cf(η=1) and the Nusselt number Nu(η=1) at the upper porous plates. Higher values of expansion ratio parameter (α) improve both the Cf(η=1) and the Nusselt number Nu(η=1) on the upper porous surface, with more significant effects observed at τ=2.