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 .