The theoretical solution of the coefficient of heat transfer by cooling or heating (without change in phase) of a Newtonian fluid in laminar flow have already been proposed by Graetz, Nusselt, etc.
Referring to those solutions, the author has tried to solve the heat transfer in laminar flow of a pseudoplastic fluid. Hasegawa has found that the velocity distribution of pseudoplastic fluids flowing in a tube can be represented by the following equation
by making use of which, the author has obtained the approximate solution for pseudoplastic fluids as follows:
provide,
The author's theoretical solution has been further developed into
in which, when n=2, the numerical calculation is as follows:
The curve n=2 in Figure 3 shows the theoretical relation of (
hMD/λ) plotted as ordinated against (
WCp/λl). The curve n=∞ shows the theoretical relation based on a rod-like flow, and the curve n=1, a Newtonian fluid. Based upon the theoretical and approximate solutions, it is to be found that (
hMD/λ) of a pseudoplastic fluids is in the zone where the curve n=∞ is lines superior and the curve n=1 is lines inferior.
Hence by the approximate solution, the author has rearranged (
WCp/λl)as{(
WCp/λl)(n+3)/4}. The theoretical relation may be represented by
The author has found that the logarithmic mean of the temperature difference between the bulk temperature of a fluid and the temperature of the wall is theoretically correct. The temperature profiles in the case of (
WCp/λl)<0.1 are shown in Figure 5.
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