In this paper, a convection and heat transfer problem of power-law fluid in a three-dimensional porous media with complex surface is studied. The Buoyancy-Marangoni convection for non-Newtonian power-law fluids in porous media is solved using a compact high-order finite volume method. For this single-phase model, the left wall is kept at high temperature and high concentration, the right wall is affected by lower temperature and lower concentration, the upper wall is a complex surface, and the remaining walls are considered to be adiabatic and impermeable. The Weierstrass-Mandelbrot function is used to simulate the shape of the upper surface. The fluid in the porous cavity is a power-law nanofluids containing copper oxide nanoparticles. The solid material of the porous medium is aluminum foam. Numerical simulations can be used to determine the power law exponent, Marangoni number, Rayleigh number, and aspect ratio on the flow, heat transfer, and mass transfer rate. (C) 2019 Elsevier Ltd. All rights reserved.