Error in thermocouple temperature measurement
Input(s)
\(\mathrm{T}\): Temperature indicated by Thermocouple (K)
\(\mathrm{T}_{\mathrm{w}}\): Temperature of Wall (K)
\(\mathrm{h}\): Heat Conduction Constant (dimensionless)
L: Length \((\mathrm{cm})\)
k: Thermal Conductivity \((\mathrm{W} / \mathrm{m} \mathrm{K})\)
B: Breadth \((\mathrm{cm})\)
Output(s)
\(\mathrm{n}\): Constant \((\mathrm{K})\)
\(\mathrm{T}_{\mathrm{a}}\): Actual Thermocouple Temperature (K)
Formula(s)
\[
\begin{gathered}
\mathrm{n}=\left(\cosh \left(\left(\mathrm{h} * \frac{\mathrm{L}^{2}}{\mathrm{k}} * \mathrm{~B}\right)^{0.5}\right)\right)^{-1} \\
\mathrm{~T}_{\mathrm{a}}=\frac{\mathrm{T}-\mathrm{n} * \mathrm{~T}_{\mathrm{w}}}{1-\mathrm{n}}
\end{gathered}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 10, Page: 310.