Similarity solutions of a Blasius flow with variable fluid properties and viscous dissipation

Abstract

An analytical model of the Blasius flow is studied including temperature-dependent fluid properties and viscous dissipation. The friction coefficient and Nusselt number at the wall are calculated from the resulting dimensionless velocity and temperature fields. The variable properties model is compared to a constant properties model to verify if and under which conditions this simplification is valid. Air, water and oil are analyzed as fluids over a representative operating regime, respectively. For air, the variable properties do not influence the friction coefficient and the Nusselt number. For water, the influence of the variable properties is present for both parameters but limited since no large temperature difference can occur in water without a phase change. New correlations for the friction coefficient and Nusselt number were derived for water and oil over a large range of operating conditions. Viscous dissipation does not significantly affect these parameters for air and water because of their relatively low Prandtl numbers. The high Prandtl number of oil in combination with a viscosity that is strongly decreasing with increasing temperature, leads to a more complex behavior. The friction coefficient as well as the Nusselt number are strongly dependent on the fluid properties. Dissipation effects cannot be neglected above an Eckert number of around 0.01. The superposition principle to evaluate wall heat flux in experiments is based on the assumption of constant fluid properties. It can be used without restrictions for air but should be thoroughly checked for all other fluids, especially liquids, using the presented methodology.