Heat transfer coefficient

Categories: Heat

The heat transfer coefficient is used as a fudge factor in calculating heat transfer in thermodynamics. The heat transfer coefficent is often calculated from the Nusselt number (a dimensionless number). Below is an example where it is used to find the heat lost from a hot tube to the surrounding area.

<math>Q=h\cdot A\cdot \Delta T</math>

where

Q = power input or heat lost
h = overall heat transfer coefficient
A = outside surface area of tubing
ΔT = difference in temperature between tubing surface and surrounding area

There are different heat transfer relations for different liquids, flow regimes, and thermodynamic conditions. A common example pertinent to many of the necessary power plant efficiency and thermal hydraulic calculations is the Dittus-Boelter heat transfer corelation, valid for water in a circular pipe with Reynolds numbers between 100 000 and 120 000 and Prandtl numbers between 0.7 and 120. An example is shown below where it is used to calculate the heat transfer from a tubing wall to water.

<math>h={{k_w \cdot Nu}\over{D_H}}</math>

where

Nu = <math>{0.024} \cdot Re^{0.8} \cdot Pr^{0.4}</math> => Dittus-Boelter correlation
<math>k_w</math> = thermal conductivity of water
Nu = Nusselt number
Pr = Prandtl number = <math>{C_p \cdot \mu}\over{k_w}</math>
Re = Reynolds number = <math>{\dot m \cdot D_H}\over{\mu \cdot A }</math>
<math>D_H</math> = hydraulic diameter
<math>\dot m</math> = mass flow rate
μ = water viscosity
Cp = heat capacity at constant pressure
A = cross-sectional area of flow

The heat transfer coefficient has SI units in watts per meter squared-kelvin. Often it can be estimated by dividing the thermal conductivity by a length scale. Heat transfer coefficients add inversely, like resistances. It can be thought of as a thermal resistance. Shown below is an addition of heat transfer coefficients where one is estimated as a thermal conductivity divided by a length scale.

<math>Q=\left( {1\over{{1 \over h}+{t \over k}}} \right) \cdot A \cdot \Delta T</math>

where

Q = power input
h = heat transfer coefficient
t = tubing thickness
k = thermal conductivity of metal tube
A = cross-sectional area of flow
<math>\Delta T</math> = difference in temperature between outer wall of tubing and sample water.
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See also