43 



T_ = 75 F 

 U^ = 4.4 ft/sec 

 X = 5.5 inches 

 Theory Experiment: 

 O s = 0.0 

 n s = 0.35 

 A s = 0.68 



200 400 



600 



800 



FIGURE 14. Mean temperature 

 profiles at x = 5.5" for step 

 changes in wall temperature . 



Temperature profiles measured at x^^f = 5.5" for 

 several values of S = Xg/Xj-gf, with AT = 5°F, are 

 compared to analytic results in Figure 14. The 

 actual wall temperature does not undergo a steep 

 step change due to conduction of heat through the 

 plate upstream of the first heater used in each 

 case. As a result there is not a unique value of 

 Xg , the step change "location". For purposes of 

 comparison solutions were obtained to the constant 

 property energy equation assuming that the temper- 

 ature profile developed entirely within the linear 

 portion of the velocity profile. This is a reason- 

 able assumption for the Prandtl number of water. 

 Comparison of the measured profiles with these 

 approximate step change solutions indicates that 

 the best agreement between theory and experiment 

 results when Xg is taken as the x-location at 

 which the wall temperature first begins to rise 

 above the free stream temperature. The choice of 

 X3 is used in all of the results reported herein. 



The agreement between measured and predicted 

 temperature profiles shown in Figures 13 and 14 



for T„(Xj,gf)-T„ = 5°F is typical of that obtained 

 at local wall temperature differences of 3°F and 

 S^F as well. 



Disturbance Growth Rates - Disturbance growth 

 rate characteristics for vaying values of n at a 

 fixed Reynolds number near R|5* = 800 with T^^{Xj-gf) 

 -Tco = 5°, are shown in Figure 15. The unheated 

 case is included for reference. The curves shown 

 are faired through the measured (a£,Uj.) points, 

 which are not shown for the sake of clarity. For 

 n = +1.0 the maximum disturbance growth rate is 

 greater than that for n=0 at a given value of T„ 

 {Xj,gf)-T^, and the band of amplified disturbance 

 frequencies moves to a higher frequency range. 

 Similar results are obtained for T^{Xj-^f)-T^ = S'F 

 and 5°F. 



Disturbance growth rates vs. frequency for 

 various values of s, with AT = S^F are shown in 

 Figure 15 at a nominal Reynolds number of Rg* = 800. 

 The unheated case is included for reference and 

 measured points {aj^,ijj^) are once again not plotted 

 for the sake of clarity. The case s = corresponds 



»'" 



LU" 

 < 



I 

 I- 



g 

 o 



GC 



ej 



LU 



o 



z 

 < 



o 



_1 



< 



1- 

 < 



95\ co^ X 10^ 



FIGURE 15. Measured disturbance growth characteristics 

 for power law wall temperature distributions T„(x) - Too 



X 



a" 



llT 

 I- 

 < 

 tr 



I 

 I- 

 g 



o 

 e) 



LU 



o 



< 



□0 



IT 



H 

 CO 

 D 

 _I 

 < 

 I- 

 < 



-2 



Ax", 



'"6* 



800. 



FIGURE 16. Measured growth characteristics for a step 

 change increase in wall temperature, Rg* = 800. 



