Simulations of a fractional rate type nanofluid flow with non-integer Caputo time derivatives

Unsteady developed flow of a rate type anomalous nanofluid with non integer Caputo fractional derivatives is studied numerically in this article. Mixed convection and diffusion are taken into account while analyzing transport phenomena in the flow field. Thermophoresis and pedesis effects are also incorporated. Fluid is confined between nonisothermal parallel plates and flows by the moving lower plate. Variable concentration is assumed at both the plates. In literature no such result exists with non integer Caputo fractional derivatives. Boundary layer flow is modeled with the help of fractional calculus approach. Governing flow partial differential equations with appropriate conditions are solved by finite difference-finite element scheme. Given scheme is flexible for the solution of non-linear flow problems. Local Nusselt and Sherwood numbers are computed for the fractional model. Flow behavior is presented for various values of involved parameters. Influence of different dimensionless quantities on the Nusselt and Sherwood numbers is discussed by tabular results. The acquired results revealed that fractional exponents α,β have opposite effects on the velocity profiles. It is also noted that thermophoresis and pedesis parameters have similar effects on heat flux while opposite effects are observed for mass flux at both the plates. Various stretching flows particularly in paper, polymeric and food production processes can be modeled in a similar manner.