Finite Volume Simulation of Nanofluid Heat Transfer with Free Slip (Journal of Mathematical Modeling and Fractional Calculus, 2025)
This study numerically investigates the viscous heating mechanism in a nanofluid-filled cavity subjected to external forces applied to the top lid, combined with laminar mixed convection of the nanofluid. The vertical walls of the cavity are assumed to be insulated, non-conductive, and impermeable to mass transfer. The horizontal walls are differentially heated, with the lower wall maintained at a higher temperature while the upper wall remains cooler. The primary objective of this research is to introduce a novel method that accurately incorporates height in the solution of heat transfer equations, using transient analysis for numerical iterations. Although the fluid flow reaches a steady state, the square cavity’s walls are fully insulated, and a constant heat flux is generated by the motion of the top lid. This work aims to analyze the effects of viscous heating in a fully insulated lid-driven cavity with Neumann boundary conditions under both no-slip and free-slip conditions, while varying Rayleigh and Prandtl numbers as independent parameters. The simulations are performed for a specific case where the Prandtl number Pr = 6.2 is fixed, while Rayleigh numbers and the volume fraction of the nanofluid (water mixed with copper nanoparticles) range from 0% to 5%. The time dependent vorticity-stream function and thermal energy equations are discretized and solved using a custom finite volume method combined with the artificial compressibility approach, implemented in MATLAB. Despite viscous heating having a limited effect, the Neumann boundary conditions with no-slip and free-slip assumptions influence heat retention within the insulated cavity. The free-slip condition acts as a lubricant, leading to reduced temperature distribution, particularly under lower Rayleigh numbers and higher Prandtl numbers, compared to the no-slip condition. This is attributed to the free-slip effects under these conditions, which enhance heat dissipation and increase the fluid velocity, further stabilizing the system.
Keywords: Nanofluid; Mixed Convection; Free Slip Lubrication; FVM