New higher-order super-compact finite difference scheme to study three-dimensional natural convection and entropy generation in power-law fluids

This work introduces a new higher-order super-compact implicit finite difference scheme for analyzing three-dimensional (3D) natural convection and entropy generation in generalized Newtonian fluids governed by the power-law model. The proposed scheme achieves fourth-order accuracy in space and second-order accuracy in time. “Super-compact” term signifies its efficiency, utilizing 19 grid points at the current time level (nth time level ) and only seven directly adjacent grid points at the subsequent time level [(n+1)th time level] around which the finite difference discretization is made. To the best of our knowledge, this is the first higher-order accurate finite difference scheme proposed to study 3D natural convection and entropy generation in power-law fluids. This advancement marks a significant step forward in the computational modeling of power-law fluids, addressing the limitations of lower-order methods that often compromise accuracy and computational efficiency. A time-marching technique is applied, where pressure corrections are addressed using a modified artificial compressibility method. Numerical simulations explore the effects of Rayleigh numbers (Ra=102–105) and power-law indices (n = 0.75–1.25) on natural convection and entropy generation within a 3D cubic cavity. Validation of the proposed scheme demonstrates excellent agreement with existing benchmark results. The numerical study reveals that as Ra increases, the maximum value of average Nusselt number (Nuavg) also increases, whereas an opposite trend is observed with n values. Shear-thinning fluids demonstrate the highest convection efficiency compared to Newtonian and shear-thickening fluids at any specific Ra.