Heat transfer coefficient

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The heat transfer coefficient is used in calculating the convection heat transfer between a moving fluid and a solid in thermodynamics. The heat transfer coefficient 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.

$Q=h \cdot A \cdot \Delta T$

where

Q = power input or heat lost

h = overall heat transfer coefficient

A = outside solid-fluid contact surface area

ΔT = difference in temperature between the solid surface and surrounding fluid 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 correlation, valid for water in a circular pipe with Reynolds numbers between 10 000 and 120 000 (in the turbulent pipe flow range) 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.

$h={{k_w \cdot Nu}\over{D_H}}$

where

k w

= thermal conductivity of water

Nu = Nusselt number

= ${0.024} \cdot Re^{0.8} \cdot Pr^{0.4}$ => Dittus-Boelter correlation for pipe flow with fluid heated by wall

Pr = Prandtl number = ${C_p \cdot \mu}\over{k_w}$

Re = Reynolds number = ${\dot m \cdot D_H}\over{\mu \cdot A }$

D H

= hydraulic diameter

$\dot m$ = mass flow rate

μ = water viscosity

C_p = 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 of the convection fluid by a length scale. Heat transfer coefficients add inversely, like resistances. It can be thought of as a thermal resistance. Consider again a pipe of fluid, the rate of heat transfer between the bulk of the fluid and the pipe surface is given by:

$Q=\left( {1\over{{1 \over h}+{t \over k}}} \right) \cdot A \cdot \Delta T$