Flow and heat transfer of a generalized Maxwell fluid with modified fractional Fourier's law and Darcy's law

• Flow and heat transfer of a generalized fractional Maxwell fluid in porous medium are studied.
• Temperature dependent fluid viscosity and thermal conductivity are taken into account.
• Modified fractional Fourier's law and Darcy's law are proposed in constitutive relations.
• Solutions are obtained by implicit difference method based on non-shifted Grünwald formula.
• Effects of involved parameters on the velocity and temperature fields are analyzed.

We present an investigation for coupled flow and heat transfer of a generalized fractional Maxwell fluid in a porous medium between two infinite parallel plates. Unlike most classical works, the temperature dependent fluid properties (variable fluid viscosity and thermal conductivity) are taken into account by modified fractional Fourier's law and Darcy's law to describe the constitutive relations in highly coupled velocity and temperature fields in porous medium. The fractional governing equations are solved numerically using implicit finite difference method based on non-shifted Grünwald formula. The effects of pertinent physical parameters on the velocity and temperature fields are presented graphically and analyzed.