A new time and spatial fractional heat conduction model for Maxwell nanofluid in porous medium

Abstract A new time and spatial fractional heat conduction model with Brownian diffusion and thermophoresis is presented to investigate the heat and mass transfer of Maxwell viscoelastic nanofluid over a moving flat plate in porous medium. New dimensionless variables are introduced to nondimensionalize the governing equations which are solved numerically by L1 algorithm and shifted Grunwald formula. The main observations of the model are the effects of embedded time and space fractional parameters on velocity, temperature and concentration profiles which are analyzed graphically. Numerical computations for a comparison between the heat conduction model with the time and spatial fractional derivatives and the model with spatial fractional derivative are made. It is found that the heat transfer is enhanced by the time and spatial fractional heat conduction model. Moreover, the larger fractional derivatives refer to the stronger memory characteristic which exhibits the physical meanings of fractional derivative.

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