Analytical solutions for a generalized non-newtonian fluid: Sisko fluid

In this thesis, the flow of a non-Newtonian fluid in a heat transfer channel under the influence of a pressure gradient is analytically investigated based on the Sisko fluid model. The flow geometry is an infinitely long planar parallel plate and constant heat flux and constant temperature conditions are considered to investigate the heat transfer issues. The flow is assumed to be laminar, steady, incompressible and fully developed. Under these conditions, the energy and momentum equations in dimensionless form are obtained and approximate solutions for small values of a dimensionless parameter of the Sisko fluid are obtained by perturbation techniques. From these solutions, the Nusselt number, which is an important heat transfer dimensionless parameter, is calculated and it is shown that the Sisko fluid satisfies the Newtonian and power-law fluids covered by the Sisko fluid. In addition, for the first time in the literature, the solutions we have found for this flow problem for Sisko fluid have been numerically verified with a special algorithm. As far as we observe from the effects of dimensionless parameters, the increase in the power-law constant in the Sisko model weakens the viscous effects, while the initial and limit viscosity values increase these effects and thicken the fluid. As the fluid thickens, that is, as it becomes more viscous, heat transfer by convection increases compared to conduction and therefore the Nusselt number increases.