9.28. Heat transmission by convection, which is usually concerned with the transfer of heat across a solid-fluid interface, involves macroscopic motion of the fluid. In free convection, the motion is a consequence of the buoyant forces generated in the fluid due to temperature differences within it. In forced convection, on the other hand, the fluid is moved by mechanical means, e. g., by a pump. When applied to heat removal in reactors, two aspects of convection heat transmission must be considered; there is, first, transfer of heat from the material which is being cooled, e. g., the fuel element, to the coolant; and, second, the transport of this heat, usually in sensible form, by flow of the coolant from one point in the system to another. Fluid flow is thus an important problem, as will be seen later, in the study of reactor cooling systems.

9.29. The fundamental equation of convection heat transfer, for both free and forced motion of the fluid, is the so-called Newton’s law of cooling, which may be written as

q = hAhAt, (9.9)

where q is the rate of convection heat transfer to or from a surface of area Ah when the temperature difference is At. The quantity h, defined by equation (9.6), is commonly called the heat-transfer coefficient and is ex­pressed in units of W/m2 • K. It should be noted that equation (9.9) applies to convection heat flow in either direction, i. e., from solid to fluid or from fluid to solid; the actual direction of the flow depends, of course, upon the sign of At.

9.30. Although the value of h is dependent upon the physical properties of the fluid medium, it is also a function of the shape and dimensions of the interface, and of the nature, direction, and velocity of the fluid flow. Thus, the heat-transfer coefficient is a property of the particular system under consideration. Another factor which determines h is the exact def­inition of At, i. e., the temperature difference between the surface and the fluid. Whereas the surface temperature of the solid is uniquely defined, that of the fluid is subject to several arbitrary definitions. The latter is usually taken as the “mixed-mean (or bulk) fluid temperature” tm given by

where p, cp, and v are the density, specific heat, and flow velocity, re­spectively, of the fluid, and Af is the cross-sectional (or transverse) flow area of the fluid. The value of the heat-transfer coefficient in any given circumstances can be determined experimentally, but for design purposes, the general practice is to use results predicted by means of various theo­retical and semiempirical expressions (see §9.78 et seq.).

9.31. By slight rearrangement, equation (9.9) can be written in the Ohm’s law form

l/hAh

so that, as before, q and At are analogous to current and potential differ­ence, respectively, but VhAh now represents the thermal resistance to convection-heat transfer. Thermal circuits can thus be constructed with one or more stages of thermal conduction combined with convection for the solution of problems involving both types of heat transfer, as will be shown in the succeeding paragraphs.