Convection Fundamentals

Abstract

Convection coefficients are used as a boundary condition in transient and steady-state conduction problems. An appreciation for the underlying physics of Newton’s “Law” of Cooling requires a closer look at the fluid in the immediate vicinity of a solid object at a different temperature. In this chapter, a 1-node analysis of the flow across a thin flat plate is developed that reveals the underlying physics of convection. The concept of a boundary layer is central to understanding convection coefficients. A boundary layer is a layer of fluid immediately adjacent to a solid that is generally thin compared to a characteristic dimension of the solid object. Outside the boundary layer, the fluid has the properties of the free stream (temperature and flow velocity). At the solid surface, the fluid properties are those of the solid. In between, there are large spatial gradients in velocity and temperature that occur across the boundary layer. In heat transfer, there are two boundary layers that develop simultaneously; a momentum boundary layer and a thermal boundary layer. The retarding effects of viscosity occur within the momentum boundary layer. In fluid mechanics, the forces exerted by a fluid on an object are of primary interest and these are determined by the momentum boundary layer. In heat transfer, heat exchange between the solid object and the free stream occurs across a thermal boundary layer. However, the thermal boundary layer is influenced by the momentum boundary layer, so an understanding of both is needed. Models are developed for both forced convection (with an imposed fluid velocity) and natural convection (where the fluid flow is driven by gravity).

Workshop 10.1. Boundary Layer Thickness for the Mug of Coffee

Calculate the thickness of the boundary layer and the corresponding characteristic flow velocity on the air and the coffee sides of the mug wall for the base coffee case at a time when the coffee is at 70 °C (results from Chap. 9, Figs. 10.9–10.11). Compare the boundary layer thickness to the diameter of the mug to determine whether the boundary layer is truly thin compared to the relevant physical dimension.