Effects of stretching velocity on double fractional Jeffreys fluids with rheological synergistic heat conductivity

Double fractional Jeffreys fluids are widely used in production and life. In this paper, the effects of stretching velocity on the flow and heat transfer of double fractional Jeffreys fluid are studied. Three types of stretching velocity are considered, i.e., (i) uniform velocity; (ii) acceleration; and (iii) deceleration. The rheological synergistic thermal conductivity model introduced to the energy equation is formulated based on experiments. The governing equations are solved by using a combination of the finite difference technique and the L1 algorithm. Results show that there is an inflection point on each velocity profile which divides the velocity field into two sections, convex (the elasticity plays a primary effect) and concave (the viscosity plays a primary effect). As the stretching velocity parameter increases, the thickness of the region where the elasticity plays a major role does not change in case (i), however, it reduces in case (ii) and grows in case (iii). We also found that, compared with uniform stretching, accelerated stretching can lead to higher heat transfer, while decelerated stretching causes less heat transfer. And for uniform velocity stretching, the stretching velocity parameter has little effect on the temperature field. In the case of accelerated stretching, increasing the stretching velocity parameter enhances heat transfer, however, for decelerated stretching, it weakens heat transfer. These results are instructive for industrial design.