A flat plate has thickness 5 cm, thermal conductivity 1 W/mK, convective heat transfer coefficients on its two flat faces of 10 W/m²K and 20 W/m²K. The overall heat transfer coefficient for such a flat plate is

Concept:

Overall heat transfer coefficient:

The thermal resistance network associated with this heat transfer process involves two convection and one conduction resistances.

It is convenient to combine all the thermal resistances in the path of heat flow into a single resistance R and to express the rate of heat transfer between the two fluids as:

\(̇ q = \frac{{{\rm{\Delta T}}}}{{\rm{R}}} = U{\rm{\Delta }}T ⇒ R = \frac{1}{{U}}\)

\(U = \frac{1}{{\Sigma R}} = \frac{1}{\frac{1}{h_i} + \frac{l}{k} + \frac{1}{h_o}}\)

where q̇ is the heat flux, U is the overall heat transfer coefficient.

Calculation:

Given:

l = 5 cm ⇒ 0.05 m, k = 1 W/mK, h_i = 10 W/m²K, h_o = 20 W/m²K

\(U = \frac{1}{{\Sigma R}} = \frac{1}{\frac{1}{h_i} + \frac{l}{k} + \frac{1}{h_o}}\)

\(U = \frac{1}{{\Sigma R}} = \frac{1}{\frac{1}{10} + \frac{0.05}{1} + \frac{1}{20}}=5\;W/m^2K\)