Forced Convection Heat Transfer of Giesekus Viscoelastic Fluid in Concentric Annulus with both Cylinders Rotation

Abstract

A theoretical solution is presented for the forced convection heat transfer of a viscoelastic fluid obeying the Giesekus constitutive equation in a concentric annulus under steady state, laminar, and purely tangential flow. A relative rotational motion exists between the inner and the outer cylinders, which induces the flow. A constant temperature was set in both cylinders, in this study. The fluid properties are taken as constants and axial conduction is negligible, but the effect of viscous dissipation is included. The dimensionless temperature profile, the normalized bulk temperature, and the inner and outer Nusselt numbers are derived from solving non-dimensional energy equation as a function of all relevant non-dimensional parameters. The effects of Deborah number (De), mobility factor (α), Brinkman number (Br) and velocity ratio (β) on the normalized temperature profile and Nusselt number are investigated. The results indicate the significant effects of these parameters on the dimensionless temperature distribution and Nusselt number.

Keywords

• viscoelastic fluid
• giesekus model
• elasticity
• viscous dissipation
• nusselt number