Heat and Mass Transfer Effect on Peristalsis of Jeffrey Fluid in a Vertical Channel with Thermal Radiation and Heat Sources

Abstract

Non-Newtonian fluids are referred to those materials that cannot be adequately described by the Navier-Stokes equations. There are materials such as drilling muds, soaps, apple sauce, sugar solution, foams, paste, certain oils, lubricants, clay coating, colloidal and suspension solution, and ketchup, which are now declared as non-Newtonian fluids. Many models in view of diverse properties of such fluids were suggested. For instance, Jamil et al. [14] studied the oscillating flows in a generalized second grade fluid. The unsteady Couette flow of the fractional Maxwell fluid was examined by Athar et al. [4]. Qi and Jin[28] extended such analysis for the generalized Oldroyd-B fluid. Rashidi et al. [30] constructed approximate solutions for the flow and heat transfer in a micropolar fluid. Effects of Soret and Dufour in the magnetohydrodynamic (MHD) flow of the Casson fluid were examined by Hayat et al. [8]. Motsa et al. [24] presented the MHD flow of the upper-convected Maxwell fluid over a porous stretching surface. They used the successive Taylor series linearization method for the solutions of the resulting problem. Effects of MHD and mass transfer of the chemically reactive Maxwell fluid past a porous surface were studied by Vajravelu et al. [35]. It is noticed from the mentioned studies that the rheological parameters in constitutive equations of non-Newtonian fluids make their resulting differential systems more nonlinear and higher order. Such differential systems offer interesting challenges to the researchers from different quarters. The Jeffrey fluid is also one of the models for the non-Newtonian fluids describing the effects of the ratio of relaxation to retardation times and retardation time. Kothandapani and Srinivas [17] used this model for the MHD peristaltic flow of the Jeffrey fluid in an asymmetric channel. Nadeem and Akbar [25] extended the analysis of Ref. [17] for the variable viscosity. Thermal radiation effects in the mixed convection flow of the Jeffrey fluid past a stretching sheet were examined by Hayat et al. [11]. Effects of heat generation/absorption in the Jeffrey fluid flow by a porous stretching sheet were also studied by Hayat et al. [10]. Heat transfer process with radiation effects is very interesting in electrical power generation, solar system technology, space vehicles, missiles, propulsion devices for aircraft, nuclear plants, astrophysical flows, and many other industrial and engineering applications. Although ample studies were generated for the boundary layer flow in the presence of thermal radiation, the fluid thermal conductivity in such cases is treated as a constant. This perhaps is not realistic because it is now proven that the thermal conductivity of liquid metals varies linearly with temperature from 0◦F to 400◦F [Kay [16]]. Thus, the effects of viscous dissipation Abstract: We analyse the combined influence of thermal radiation and heat sources on peristaltic flow of a conducting Jeffrey fluid in a vertical porous channel with heat and mass transfer is studied. Using the perturbation technique, the nonlinear governing equations are solved. The expressions for velocity, temperature and concentration the pressure rise per one wave length are determined. The effects of different parameters on the temperature and the pumping characteristics are discussed through graphs.