The test data tabulated on the next page were reduced from measurements made to determine the heat-transfer coefficient inside tubes at Reynolds numbers only slightly above transition and at relatively high Prandtl numbers (as associated with oils). Tests were made in a double-tube exchanger with a counterflow of water to provide the cooling. The pipe used to carry the oils was 1.5 cm-OD, 18 BWG, 3 m-long. Correlate the data in terms of appropriate dimensionless parameters.
Hint: Start by correlating Nu and ReD irrespective of the Prandtl numbers, since the influence of
the Prandtl number on the Nusselt number is expected to be relatively small. By plotting Nu vs.
Re on log-log paper, one can guess the nature of the correlation equation, Nu = f1 (Re). A plot of
Nu/f1 (Re) vs. Pr then reveals the dependence upon Pr. For the final equation, the influence of
the viscosity variation also is considered.
GIVEN
Oil in a counterflow heat exchanger
Pipe specifications: 1.5 cm-OD, 18 BWG
Pipe length (L) = 3 m
The experimental data above
FIND
Correlate the data in terms of appropriate dimensionless parameters
ASSUMPTIONS
The data represents the steady state for each case
PROPERTIES AND CONSTANTS
From Appendix 2, Table 42: for 1.5 cm OD, 18 BWG tubing, the inside diameter D = 1.338 cm
The appropriate dimensionless parameters are the average Nusselt number (Nu = hc D/kf). The
Reynolds number (ReD = puD/?f) and the Prandtl number (Pr = Cp ?f/k). The values of the
dimensionless parameters for each test are listed below.
Plotting log Nu vs. log ReD reveals a roughly linear relationship.
Fitting a least squares regression line to the data
The variation of Nu with Prf can be determined by plotting log [Nu/(0.0931 Re0.812)] vs. log Prf.
Although there is considerable scatter in this plot, it does follow a trend of increasing log Prf with
increasing log [Nu/(0.0931 Re0.812)] and will be fit with a straight least squares regression line.
A least squares fit yields
Plotting log [Nu/0.0567 Re0.812 Prf0.108] vs. log (?f /?b)
Fitting these points with a straight least squares regression line
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