An exact periodic solution for the time dependent flow of a viscoelastic fluid in the presence of transverse magnetic field is derived. It is assumed that on one plate the fluid is injected with certain velocity and that it is sucked off at the other plate with the same velocity. Both plates are oscillating with a known velocity in their own plane. A perturbation method has been employed by treating the viscoelastic parameter to be small. Effects of viscoelastic parameter, cross-flow Reynolds number, frequency parameter, and Hartmann number on the velocity as well as wall shear stress of the flow are discussed here with graphs.
The boundary layer flow of a steady incompressible and visco-elastic fluid with short memory (obeying Walters' B fluid model) passing over a hot vertical porous plate has been investigated in the presence of transverse magnetic field. The momentum and energy equations are reduced to couple non-linear partial differential equations along with the boundary conditions by using a suitable similarity transformation. These partial differential equations are transformed to a system of coupled non-linear ordinary differential equations by employing a perturbation technique. The system is solved by developing a suitable numerical procedure such as implicit finite difference scheme along with Newton's linearization method. The computational results for the flow quantities have presented graphically for the effects of thermal radiation, viscous dissipation, heat generation/absorption, visco-elasticity, Hartmann number and the permeability parameter. Results demonstrated that Prandtl number has more pronouncing effect on the temperature distribution rather than the viscosity parameter as well as the thermal radiation parameter. Further the velocity gradient changes significantly due to the presence of temperature dependent variable viscosity.
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