Some solutions for unsteady flow of viscous fluids over an infinite plate and in pipe-like domains

Abstract

The velocity profile and the associated tangential stress corresponding to the oscillatory flow of Maxwell fluid with non-integer order derivative, within double infinite circular cylinders,areobtainedwiththehelpofthemethodsofLaplaceandfiniteHankeltransformations. Moreover, the exact solutions for the rotational flow of Oldroyd-B, Burgers’ and generalized Burgers’ fluids, passing through the single circular cylinder with fractional order rate of change, are derived by using the integral transform methods. At first, we assumed there is no motion (in these different fluids) and afterward the motion is due to the oscillatory movement of the inner cylinder for Maxwell fluid and for the Oldroyd-B fluid the motion is due to the effect of shear stress exerted from boundaries. Similarly, for theBurgers’andgeneralizedBurgers’fluids,therotationalmotioniscreatedthroughfixed axis of rotation of the circular cylinder with an unsteady angular velocity. These solutions are in series form in the terms of the generalized Ga,b,c(.,t)-function. The corresponding obtained solutions can be easily specified to the similar solutions for Burgers’, OldroydB, Maxwell, second grade and Newtonian fluids respectively. Conclusively, the impact of the physical and fractional parameters on the fluid motion and their co-relations are presented by several graphical interpretations. The MHD flow of Burgers’ fluid flowing through porous material pipe under the effect of pressure gradient is also solved by using dimensionlessvariabletechnique. Theeffectofphysicalparametersarealsoshowngraphically. Furthermore, the first order uniform chemical reaction of a viscous incompressible unsteady flow of fluid passing on an oscillatory infinite long vertical plate is studied. The modified temperature and uniform mass diffusivity are taken for the problem of the plate oscillationaboutitsmainaxisoftheposition. TheLaplacetransformationprocess/method is used to obtained the analytical solutions for the non-dimensional governing equations. The variation in the velocity, temperature and concentration is investigated through detailed graphical analysis.