Chapter 7 - Free and mixed convection from cylinders

Abstract

The boundary-layer approximation usually leads to the neglect of the curvature effects and the pressure difference across the boundary-layer. On using the approximation, the simplified boundary-layer equations are solved using similarity techniques and series methods. The finite-difference method is applied to study the steady free convection boundary layers on horizontal circular and elliptical cylinders, which are maintained at either a uniform temperature or uniform heat flux. On starting at the lowest point of the cylinder, the fluid flow reaches the top point without separating and at this point the boundary-layer has a finite thickness. Flows over horizontal and vertical cylinders are usually considered to be two-dimensional as long as the radius of the body is large compared to the boundary-layer thickness. For slender cylinders, the boundary-layer thickness may be of the same order as their radius and thus the governing equations must be solved for axisymmetric flows. In this case, the equations contain the transverse curvature term, which can considerably influence the fluid velocity and the temperature profiles, and the corresponding skin friction and heat transfer rate as the ratio of the radius of the cylinder to the boundary-layer thickness becomes small.