Heat Transfer Coeffient Model
1.3. Heat Transfer Coeffient Model¶
The key performance parameter for the heat transfer device is the overall heat transfer coefficient \(U\). The overall heat transfer coefficient is established by series of transport mechanisms …
convective heat transfer from the bulk of the hot fluid to the wall of the exchanger tube,
conductive heat transfer through the wall of the tube,
convective heat transfer from the wall to the tube to the bulk of the cold fluid.
For a series of transport mechanisms, the overall heat transfer coefficient
\(U_{tube}\) is a constant for these devices. \(U_h\) and \(U_c\) varying with flowrate and proporitonal to dimensionless Nusselt number. For fully developed turbulent flow in a pipe, the Dittus-Boelter equation provides an explicit function for estimating the Nusselt number
where \(C\) is a constant, \(Re\) is the Reynold’s number that is proportional to flowrate \(\dot{q}\), and \(Pr\) is the Prandtl number determined by fluid properties.
Experimentally, consider a set of values for \(U\) determined by varying volumetric flowrates \(\dot{q}_h\) and \(\dot{q}_c\) over range of values. Because Reynold’s number is proportional to flowrate, we propose a model
This suggests a regression procedure:
Plot \(\frac{1}{U}\) as a function of \(\dot{q}_h^{-0.8}\) for fixed values of \(\dot{q}_c\). Esitmate \(r_h\) from the slope.
Plot \(\frac{1}{U}\) as a function of \(\dot{q}_c^{-0.8}\) for fixed values of \(\dot{q}_h\). Estimate r_c from the slope.
Use the data and estimates of \(r_h\) and \(r_c\) to estimate \(R_{tube}\).
Alternatively, one could consider using a regression procedure from the scikit-learn machine learning toolkit where
is the variable to predicted, and where
are the features. The linear model to be fitted is then
where \(w_0\), \(w_h X_h\) and \(w_c X_c\) correspond to resistances to heat transfer. The range of regression techniques available in scikit-learn opens up opportunities to explore alternative feature sets and models for heat transfer.