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.