It is convenient, therefore, to represent the heat transfer at the wall by the expression The nature of the surface, for example the degree or type of roughness, usually affects heat transfer to or from it, and in some circumstances to a large extent. Turbulent flows can give rise to heat transfer rates which are much larger than those of laminar flows, and are caused by the manner in which the turbulent fluctuations increase mixing they also affect the heat transfer to and from the surface, especially where the free-stream fluid is able to penetrate to the wall even for short periods of time. With laminar flows, heat transfer to or from the wall varies with distance from the leading edge of a boundary layer. It is well known that even comparatively simple geometrical configurations, such as those of Figure 1, can give rise to heat transfer rates which vary considerably depending on the nature of the flow and of the surface. It is known, for example, that the rate of heat transfer can become high at the location of reattachment of the upstream flow on to the surface of the step, as is also the case at the leading edge of a cylinder in cross-flow, but the detailed mechanisms remain incompletely understood and research continues. The details of flows of this type are not well-understood so it is difficult to identify the characteristics of the boundary layers and it can be imagined that the shapes of the velocity and temperature profiles- and therefore of the local heat transfer within the fluid and to the wall-will vary considerably from one location to another. The backward-facing step of Figure 1 results in a more complicated flow and several boundary layers can be identified within the flow as a consequence of separation and reattachment. In the latter case, the free-stream velocity would be zero so that the corresponding profile would have zero values at the wall and far from the wall. It should be noted that the surface can be horizontal as shown, with air flow driven by a fan or a liquid flow by a pump, and that it can equally be vertical, with buoyancy providing the driving force for the flow. The same expression applies to any region of the flow and also in the case of the adiabatic wall where zero temperature gradient implies zero heat transfer. Where q represents the rate of heat transfer per unit surface area, λ is the thermal conductivity, T is the temperature and y is distance measured from the surface. Examples are given later in this Section and are shown in Figure 1 to facilitate introduction to terminology and concepts. The flow may give rise to convective heat transfer where it is driven by a pump and is referred to as forced convection, or arise as a consequence of temperature gradients and buoyancy, referred to as natural or free convection. It may also occur in flows which are more complicated, such as those which are separated, for example, in the aft region of a cylinder in cross-flow or in the vicinity of a backward-facing step. Convective heat transfer may take place in boundary layers, that is, to or from the flow over a surface in the form of a boundary layer, and within ducts where the flow may be boundary-layer-like or fully-developed. Heat transfer by convection may occur in a moving fluid from one region to another or to a solid surface, which can be in the form of a duct, in which the fluid flows or over which the fluid flows. This article is concerned with the transfer of thermal energy by the movement of fluid and, as a consequence, such transfer is dependent on the nature of the flow.
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