Steady-state temperature controller

Input(s)

ToT_{o}: Outlet Temperature (K)

Tm\mathrm{T}_{\mathrm{m}}: Maximum Controller Temperature (K)(\mathrm{K})

b: Constant (dimensionless)

U: Overall Heat Coefficient (W/ft K)

A: Area (ft)

Output(s)

TiT_{i}: Initial Temperature (K)

Formula(s)

Ti=To(1(bU A))+b TmU A\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 .

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