Wilson plot technique

Primarily, three different test techniques are used to determine the surface heat transfer characteristics. These techniques are based on the steady-state, transient, and periodic nature of heat transfer modes through the test sections. We will cover here the most common steady-state techniques used to establish the j versus Re characteristics of a recuperator surface. Different data acquisition and reduction methods are used depending upon whether the test fluid is a gas (air) or a liquid. The method used for liquids is generally referred to as the Wilson plot technique. Refer to Ref. 15 for the transient and periodic techniques. Generally, the isothermal steady-state technique is used for the determination of/factors. These test techniques are now described. 

The limitations of the Wilson plot technique may be summarized as follows. (1) The fluid flow rate and its log-mean average temperature on the fluid 2 side must be kept constant so that C2 is a constant. (2) The Re exponent in Eq. 17.77 is presumed to be known (such as 0.82 or 0.8). However, in reality it is a function of Re, Pr, and the geometry itself. Since the Re exponent is not known a priori, the Wilson plot technique cannot be utilized to determine the constant C0 of Eq. 17.77 for most heat transfer surfaces. (3) All the test data must be in one flow region (e.g., turbulent flow) FIGURE 17.40 Original Wilson plot of Eq. 17.79. on fluid 1 side, or the Nu correlation must be expressed by an... 

In the preceding case of Eq. 17.79, unknowns are Ct (means unknown C ) and C2. Alternatively, it should be emphasized that if Rsc, R, and R, are known a priori, then an unknown C2 means that only its C0 and a for fluid 2 are unknown. Thus the heat transfer correlation on fluid 2 side can also be evaluated using the Wilson plot technique if the exponents on Re in Eq. 17.77 are known on both fluid sides. The Wilson plot technique thus represents a problem with two unknowns. 

If all test points are not in the same flow regime (such as in turbulent flow) for the unknown side of the exchanger using the Wilson plot technique or its variant, use the method recommended in Refs. 15 and 42 to determine h or Nu on the unknown side. 

R. K. Shah, Assessment of Modified Wilson Plot Techniques for Obtaining Heat Exchanger Design Data, Heat Transfer 1990, Proc. of 9th Int. Heat Transfer Conf, Vol. 5, pp. 51-56,1990. 

D. E. Briggs and E, H, Young, Modified Wilson Plot Techniques for Obtaining Heat Transfer Correlations for Shell-and-Tube Heat Exchangers, Chem. Eng. Progr. Symp. Ser. No. 92, Vol. 65, pp. 35-45,1969. 

In principle, the parameters can be evaluated from minimal experimental data. If vapor-liquid equilibrium data at a series of compositions are available, the parameters in a given excess-free-energy model can be found by numerical regression techniques. The goodness of fit in each case depends on the suitability of the form of the equation. If a plot of GE/X X2RT versus X is nearly linear, use the Margules equation (see Section 3). If a plot of Xi X2RT/GE is linear, then use the Van Laar equation. If neither plot approaches linearity, apply the Wilson equation or some other model with more than two parameters. 

Figure 2.44. Critical indices ft and 7 a,s parameters of plotting the order parameter dimension n U.S the space dimension

The pressure-induced semiconductor-metal transitions of SmSei xSx solid solutions are discontinuous for x>0.2 and continuous forx<0.2 as detected by electrical resistivity q versus pressure measurements. The strength of the first-order phase transition (expressed by Ag/g p where Ag is the resistivity jump and Qtr s the resistivity at the transition pressure Ptr) decreases smoothly to zero at x = 0.2. This composition is characterized by a sharp break in slope at 34.6 kbar when q versus p is plotted but no hysteresis is noticed as pressure is released. Transition pressure p r and Ag/ptr in comparison with the theoretical phase transition strength (calculated with a modified Falicov-Kimball model) as a function of composition are shown in Fig. 81, p. 170, Bucher, Maines [2], also see Bucher et al. [3]. The change from continuous to discontinuous transition is interpolated to be at x = 0.28 the experimental value is 0.25 (determination technique not given in the paper), Narayan, Ramaseshan [4]. The course of the configuration crossover f d°- f d for Sm(Se,S) under pressure is illustrated by Wilson [5]. 

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