Abstract
The present investigation is concerned with the flow of a third grade fluid and heat transfer through a pipe with a side branch. Fluid viscosity, considered in the present study varies with the distance from the axis of the tube as well as temperature. Perturbation methods have been employed to derive an analytical approximate solution for velocity, temperature distribution, mass flux and hematocrit distribution with the use of small visco-elastic coefficient as a perturbation parameter. For the investigation to the application to human circulatory system, blood is modeled as third grade fluid. Three model equations for the discharge of hematocrit have been taken for the estimation of blood cell entrainment in to the side branch with arbitrary branching angle. Evaluation of velocity, mass flux and fluid as well as its constituent discharge shown by the figures are quite significant. Parameter arises in the momentum and energy equations have substantial control on the fluid flow and heat transfer; however important observation of this study is the effect of viscous dissipation parameter and non-Newtonian fluid parameter on the mass flux through side branch and hematocrit discharge. It is observed that the variable viscosity has pronounced effect on the hematocrit distribution in the side branch.
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