The effect of heat transfer on the nonlinear peristaltic transport of a Jeffrey fluid through a finite vertical porous channel. (English) Zbl 1331.76019
Summary: In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both viscous and Darcy dissipations. The coupled nonlinear governing equations are solved analytically. The expressions for the temperature, the axial velocity, the local wall shear stress and the pressure gradient are obtained. The effects of various physical parameters such as the Jeffrey parameter \(\lambda_1\), the permeability parameter \(\sigma\) and the heat source/sink parameter \(\beta\) are analyzed through graphs, and the results are discussed in detail. It is observed that the velocity field increases with increasing values of the Jeffrey parameter but it decreases with increasing values of the permeability parameter. It is found that the pressure rise increases with decreasing Jeffrey parameter and increasing permeability parameter. We notice that the effect of the permeability parameter \(\sigma\) is the strongest on the bolus trapping phenomenon. For \(\lambda_1 = 0\), \(N=0\), the results of the present study reduce to the results of D. Tripathi [“Study of transient peristaltic heat flow through a finite porous channel”, Math. Comput. Modelling 57, No. 5–6, 1270–1283 (2013; doi:10.1016/j.mcm.2012.10.030)]. Further the effect of viscous and Darcy dissipations is to reduce the rate of heat transfer in the finite vertical porous channel under peristalsis.
MSC:
| 76A05 | Non-Newtonian fluids |
Keywords:
peristaltic transport; heat transfer; Jeffrey fluid; porous medium; vertical channel; trapping phenomenaReferences:
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