Numerical study of transport phenomena in a nanofluid using fractional relaxation times in Buongiorno model

Convective phenomena in a nanofluid flow under the influence of gravitational and magnetic body forces is analyzed in this communication. Nanofluid is of viscoelastic nature that preserves viscosity as well as elasticity. In order to capture the more realistic behavior of the convective phenomena Caputo fractional derivative and fractional relaxation time are introduced in the Buongiorno nanofluid model. Fractional derivative and relaxation time are used for controlled flow mechanism and to overcome infinite propagation speed for the temperature and concentration. The proposed model will also help to understand the hereditary and memory properties of the viscoelastic nanofluid. In order to more closely analyze the buoyancy forces nonlinear convection is introduced in the mathematical modeling of the flow problem. Finite difference-finite element numerical computations are carried out for the governing nonlinear partial differential equations. Quantities of physical interest are computed and discussed for the fractional model. The proposed fractional model can be used to realistically simulate various flow problems in polymer and chemical industries. (paper)