HEAT TRANSFER IN TRANSIENT FLOW OF RATE-TYPE FLUID IN A POROUS MEDIUM: FRACTIONAL MODELS OF CAPUTO, CAPUTO–FABRIZIO AND ATANGANA–BALEANU DERIVATIVES

Rate type fluid model is considered in this work. This fluid is viscoelastic in nature under the influence of an applied magnetic field and passing through a porous medium, which corresponds to a generalized Darcy’s law. Heat is transferred through convection and the fluid near the plate experiences heat transfer of a ramped nature. The influence of thermal radiation and heat generation is investigated. It is important to mention that the regular fluid models are unable to explain the memory effect, and hence, it is important to generalize the usual classical model to a generalized form including fractional derivatives. The fractional modelling is done using Caputo, Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) time-fractional operators. Solutions of velocity and temperature equations have been obtained by a numerical algorithm. The effect of physical parameters has been shown through graphical analysis for velocity and temperature profiles. A comparative analysis of the Caputo, CF and AB fractional derivatives is made with the observation that the AB fractional derivative shows good memory effect on the dynamics of the Oldroyd-B fluid. A comparison with published work shows excellent agreement. The Oldroyd-B fluids have several industrial applications such as polymer solutions, melts and other complex fluids.