In this paper, a convection and heat transfer problem of power-law fluid in a three-dimensional porous media with complex evaporating 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 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 evaporating surface. The Weierstrass–Mandelbrot function is used to approximate the shape of the evaporation interface, the analytical solution of its fractal dimension can be obtained by the pore area fractal dimension, and the volume percentage of liquid. The fluid in the porous cavity is a power-law fluid containing copper oxide nanoparticles. The solid material of the porous medium is aluminum foam. Numerical simulations can be used to determine Marangoni number, Rayleigh number and the pore area fractal dimension on the flow, heat transfer, and mass transfer rate.

中文翻译：

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具有复杂蒸发面的分形多孔介质中幂律纳米流体的传热传质研究

本文研究了具有复杂蒸发面的三维多孔介质中幂律流体的对流和传热问题。使用紧凑的高阶有限体积法求解多孔介质中非牛顿幂律流体的浮力-马兰戈尼对流。对于该模型，左壁保持高温高浓度，右壁受低温低浓度影响，上壁是复杂的蒸发面。Weierstrass-Mandelbrot 函数用于近似蒸发界面的形状，其分形维数的解析解可以通过孔隙面积分形维数和液体的体积百分比得到。多孔腔中的流体是含有氧化铜纳米颗粒的幂律流体。多孔介质的固体材料为泡沫铝。数值模拟可用于确定马兰戈尼数、瑞利数和孔隙面积分形维数对流动、传热和传质速率的影响。