The subject of this work is the study of the effect of secondary flow on heat transfer from a rotating sphere to Oldroyd-B fluid. The Navier-Stokes equations governing the steady axisymmetric flow can be written as two coupled, nonlinear partial differential equations for the stream function and rotational velocity component. Slow flow approximation is used to solve the equations of motion and the energy equation. Therefore, all dynamical variables in the governing equations are expanded in power series in terms of Reynolds number Re, and Deborah number De. The solution of the obtained partial differential equations is valid for small values of Re and De, and all values of Prandtl number Pr. The analysis of the obtained solution shows that, the stream function consists of two additional secondary flow parts caused by elastic and inertia effects. So, the properties of the resultant stream line pattern depend on the relative magnitudes of the two parts. If Re and De differ from each other appreciably, then one is dominant and imprints its character on what happens. Under certain conditions, the superposition leads to a different situation. At some critical values of Re and De it is noticed that, a spherically shaped stagnation stream surface is formed in the fluid. The radius of this surface is calculated. The effect of the secondary flow on the temperature distribution and heat transfer rate are calculated and analyzed. Flow patterns of velocity distribution, temperature profile and Nusselt number are presented at and for different values of Re and De. |
