Correlation
A dimensionless correlation has been developed which correlates all the
data collected in this study. It is mentioned earlier and shown in the
graphs that a few common relations are found between heat transfer
coefficient and other operating parameters. These common relations may
be shown mathematically as\(h=f(\rho\left(p\left(q\right)\right))\)
In a dimensionless relation, the above function can be rewritten along
with the calculated constants as follows.
\begin{equation}
\frac{h}{h_{\text{eff}}}=0.93\left(\frac{{q"}_{e,\text{eff}}}{{q"}_{e,s}}\right)^{0.731}\left(\frac{{q"}_{c,s}}{{q"}_{c,\text{eff}}}\right)^{0.014}\left(\frac{P}{{P}_{\text{eff}}}\right)^{0.863}\left(\frac{\rho_{c}}{\rho_{e}}\right)^{0.438}\left(\frac{d_{T}}{d_{H}}\right)^{1.000}\left(\left\{\frac{l}{l_{\text{eff}}}\right\}^{\sin\theta\cos\theta}\right)^{1.534}\nonumber \\
\end{equation}Graphical representation of all the correlated data is shown in Figure
23, and 95% of them are found to be within ±15% range of the
regression line.
[CHART]
Figure 23. Graphical representation of the developed
correlation of TMMHP