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 .