Empirical Relations for Pipe and Tube Flow

The analysis of Sec. 5-10 has shown how one might analytically attack the problem of heat transfer in fully developed laminar tube flow. The cases of undeveloped laminar flow, flow systems where the fluid properties vary widely with temperature, and turbulent-flow systems are considerably more complicated but are of very important practical interest in the design of heat exchangers and associated heat-transfer equipment. These more complicated problems may sometimes be solved analytically, but the solutions, when possible, are 

First let us give some further consideration to the bulk-temperature concept which is important in all heat-transfer problems involving flow inside closed channels. In Chap. 5 we noted that the bulk temperature represents energy average or mixing cup conditions. Thus, for the tube flow depicted in Fig. 6-1 the total energy added can be expressed in terms of a bulk-temperature difference by 

For fully developed turbulent flow in smooth tubes the following relation is recommended by Dittus and Boclter [1]  

The properties in this equation are evaluated at the fluid bulk temperature, and the exponent n has the following values  

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The radiator pipe is the structure through which heat is rejected to space. Wall friction is turned off in favor of representing the desired friction factor with the Reynolds number dependent form loss coefficient option in RELAP5-3D. Idel chik (Reference 12-23) Section 8-2, paragraph 15, provides an empirical relation to determine the friction factor for flow past a bundle of vertically arranged tubes uniformly distributed over conduit cross sections. For a duct that is 3.8 cm wide with heat pipes in one row that have 12.5 cm between heat pipe centers and 2.2 cm outside diameters the equation for friction factor is ... 

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