9.84. For ordinary fluids, the principal mechanism of heat transport is by the effect of turbulence, as a result of which a “parcel” of fluid is rapidly moved from a region close to the hot wall into the main body of fluid. In liquid metals, however, thermal transport occurs mainly by molecular con­duction. Whereas this mechanism may provide 70 percent of the heat transfer for a liquid metal, it contributes only about 0.2 percent to heat transfer in water. This means that the laminar boundary thickness, which is important for ordinary liquids, is not significant for liquid metals, and heat-transfer relationships applicable to gases and nonmetallic liquids can­not be used.

9.85. The essential difference between the heat-transfer properties of liquid metals and ordinary fluids is illustrated by the temperature profiles in a heated tube shown in Fig. 9.12 [8]. In these curves, the approach of the fluid temperature to the tube-wall temperature is represented by the dimensionless quantity (tw — t)/(tw — t0), where tw and t0 are the wall and centerline temperatures, respectively. The abscissa is the ratio y/r0, where у is the distance from the wall at which the fluid temperature is t, and r0 is the tube radius. The Prandtl numbers are the parameters for the various curves, and the Reynolds number is 104 in all cases.

9.86. For Pr = 1, the velocity and temperature profiles are identical; most of the resistance to heat transfer occurs in the laminar sublayer and

in the buffer layer, and there is little further change in temperature as the center of the tube (ylr0 = 1) is approached. For liquid metals (Pr « 1), however, molecular conduction is so significant that there is a marked thermal gradient from the buffer layer boundary all the way to the center, much as would be observed for a solid rod (Pr = 0). The heat-transfer coefficient is normally based on a mixed-mean temperature obtained by integration of the thermal profile (§9.30). It can be seen that for fluids of low Prandtl number this temperature may be quite different from that at the centerline.