# Surface temperature of a heating coil

## Input(s)

$$T_{o}$$: Initial Surface Temperature $$(\mathrm{K})$$

$$\mu$$: Viscosity (Pa s)

$$\rho$$: Density $$\left(\mathrm{g} / \mathrm{m}^{3}\right)$$

g: Gravitational Acceleration $$\left(\mathrm{ft} / \mathrm{s}^{2}\right)$$

$$\beta$$: Velocity Flux (1/s)

D: Diameter (m)

Q: Net Energy Input Rate $$(\mathrm{J} / \mathrm{s})$$

$$\mathrm{k}$$: Thermal Conductivity $$(\mathrm{J} / \mathrm{m} \mathrm{s} \mathrm{K})$$

## Output(s)

$$T_{1}-T_{o}$$: Final Temperature of Surface (K)

## Formula(s)

$\mathrm{T}_{1}-\mathrm{T}_{\mathrm{o}}=\frac{\mu^{2}}{\left(\rho^{2}\right) * \mathrm{~g} * \beta *\left(\mathrm{D}^{3}\right)} * \varnothing\left(\frac{\mathrm{Q} *\left(\rho^{2}\right) * \mathrm{~g} * \beta *\left(\mathrm{D}^{2}\right)}{\mathrm{k} *\left(\mu^{2}\right)}\right)$

## Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 11, Page: 361.

## Related

### Electrical heating of a pipe

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