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.