Steady-state temperature controller
Input(s)
\(T_{o}\): Outlet Temperature (K)
\(\mathrm{T}_{\mathrm{m}}\): Maximum Controller Temperature \((\mathrm{K})\)
b: Constant (dimensionless)
U: Overall Heat Coefficient (W/ft K)
A: Area (ft)
Output(s)
\(T_{i}\): Initial Temperature (K)
Formula(s)
\[
\mathrm{T}_{\mathrm{i}}=\mathrm{T}_{\mathrm{o}} *\left(1-\left(\frac{\mathrm{b}}{\mathrm{U} * \mathrm{~A}}\right)\right)+\frac{\mathrm{b} * \mathrm{~T}_{\mathrm{m}}}{\mathrm{U} * \mathrm{~A}}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 15, Page: 470 .