Temperature profile after viscous heat transfer
Input(s)
\(\mathrm{T}_{\mathrm{b}}\): Temperature of Outer Perimeter \((\mathrm{K})\)
b: Distance of Outer Boundary ( \(\mathrm{ft}\) )
Br: Brinkman (dimensionless)
\(\mathrm{T}_{\mathrm{o}}\): Temperature of Inner Perimeter \((\mathrm{K})\)
\(\mathrm{x}\): Distance from Centre of Pipe \((\mathrm{ft})\)
Output(s)
T: Temperature at Distance \(X(K)\)
Formula(s)
\[
\left(\frac{\mathrm{T}-\mathrm{T}_{\mathrm{o}}}{\mathrm{T}_{\mathrm{b}}-\mathrm{T}_{\mathrm{o}}}\right)=\frac{1}{2} * \mathrm{Br} *\left(\frac{\mathrm{x}}{\mathrm{b}}\right) *\left(1-\frac{\mathrm{x}}{\mathrm{b}}\right)+\frac{\mathrm{x}}{\mathrm{b}}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 10, Page: 300 .