Sahooley 



The analytical solution to this well-defined problem is 



T{z,T) = Tj 1 - erf(x/2VDt)] + Tg (2) 



where 



erfCx/zVot) = 2/>Arr 



/aySt 



e du. 



From (1) the gradient of T at the boundary z is 



8T 



VirDt 



or 



fill LlsVi) 



[az I J irDVt / 



(3) 



and 



-<-oA,[f/(fjn 



(4) 



Since T^/jr is constant for any one experiment, a plot of 

 for the data points should give a straight line 



(^T/Az)^ 





through the origin with slope Dtt/Tq . Figure 4 is such a plot for 

 the experiment of Fig, 2. A mean square fit gives a slope of 0.66 

 with a correlation coefficient of 0.99* Since To = 2.45°C, in this 

 case the eddy diffusivity is D = 2,45 (0.66)/^ = 1.26 cm /sec. 



In practice all plots of the experimental data do not yield 

 perfectly straight lines, particularly for larger values of t (smaller 

 values of l/t) than are shown in Fig, 4. Calibration and experimental 

 errors are always present. In addition, as is Illustrated in Fig. 3, 

 the effective vedue of Tq is not constant for extended lengths of time 

 (t = tp -^ too) because the experiments were necessarily conducted 

 in a finite size container. However, Fig. 4 does represent con- 

 sistency of the data with the simple analytical theory under the 

 assumptions that have been made. 



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