Temperature distribution in a hot-wire anemometer

Input(s)

D: Diameter $(\mathrm{ft})$

L: Length ( $\mathrm{ft}$ )

I: Current (Amp)

$\mathrm{h}$: Heat Transfer Coefficient $\left(\mathrm{btu} / \mathrm{h} \mathrm{ft}^{2} \mathrm{~F}\right)$

$\mathrm{k}_{\mathrm{e}}$: Thermal Conductivity of Ambiance $(1 / \Omega \mathrm{ft})$

$\mathrm{z}$: Distance $(\mathrm{ft})$

Output(s)

$\mathrm{T}$: Temperature increase $(\mathrm{F})$

Formula(s)

$$ \mathrm{T}=\left(\frac{\mathrm{D} *\left(\mathrm{I}^{2}\right)}{4 * \mathrm{~h} * \mathrm{k}_{\mathrm{e}}}\right) *\left(1-\left(\frac{\cosh \left(\left(\frac{4 * \mathrm{~h}}{\mathrm{k} * \mathrm{D} * \mathrm{z}}\right)^{0.5}\right)}{\cosh \left(\left(\frac{4 * \mathrm{~h}}{\mathrm{k} * \mathrm{D} * \mathrm{~L}}\right)^{0.5}\right)}\right)\right) $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 10, Page: 328.