Marangoni abnormal convection heat transfer of power-law fluid driven by temperature gradient in porous medium with heat generation

•Marangoni abnormal convection of power-law fluids in porous medium is studied.•The surface tension is assumed to be a quadratic function of the temperature.•New heat conductivity constitutive equation is proposed based on N-diffusion.•Governing partial differential equations are solved analytically by (HAM).•Transport characteristics of velocity and temperature fields are analyzed.

In this paper we investigate Marangoni convection heat transfer of power-law fluids in porous medium with heat generation. The convection is driven by a temperature gradient that the surface tension is a quadratic function of the temperature. A new heat transfer constitutive equation is proposed based on N-diffusion proposed by Philip and the abnormal convection–diffusion model proposed by Pascal in which we assume that the heat diffusion depends non-linearly on both the temperature and the temperature gradient with modified Fourier heat conduction for power-law fluid. The governing partial differential equations are reduced to ordinary differential equations by suitable similarity transformations. Approximate analytical solution is obtained using homotopy analytical method (HAM) which is compared with numerical ones for particular cases in good agreement. The transport characteristics of velocity and temperature fields are analyzed in detail.