In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ΔT ). It is used to calculate heat transfer between components of a system; such as by convection between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter kelvin (W/(m2K)). The total heat transfer rate for combined modes and system components is usually expressed in terms of an overall heat transfer coefficient, thermal transmittance or U-value. The heat transfer coefficient is the reciprocal of thermal insulance. This is used for building materials (R-value) and for clothing insulation. There are numerous methods for calculating the heat transfer coefficient in different heat transfer modes, different fluids, flow regimes, and under different thermohydraulic conditions. Often it can be estimated by dividing the thermal conductivity of the convection fluid by a length scale. The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). There are also online calculators available specifically for Heat-transfer fluid applications. Experimental assessment of the heat transfer coefficient poses some challenges especially when small fluxes are to be measured (e.g. < 0.2 W/cm2).
Definition The general definition of the heat transfer coefficient is:
h = q Δ T {\displaystyle h={\frac {q}{\Delta T}}}
where:
q {\displaystyle q} : heat flux (W/m2); i.e., thermal power per unit area, q = d Q ˙ / d A {\displaystyle q=d{\dot {Q}}/dA}
Δ T {\displaystyle \Delta T} : difference in temperature (K) between the solid surface and surrounding fluid area The heat transfer coefficient replaces the thermal conductivity within a generalization of Fourier's law postulated to also describe convection flows (including conduction). Upon reaching a steady state of flow, the heat transfer rate is:
Q ˙ = h A ( T 2 − T 1 ) {\displaystyle {\dot {Q}}=hA(T_{2}-T_{1})}
where (in SI units):
Q ˙ {\displaystyle {\dot {Q}}} : Heat transfer rate (W)
h {\displaystyle h} : Heat transfer coefficient (W/m2K)
A {\displaystyle A} : surface area where the heat transfer takes place (m2)
T 2 {\displaystyle T_{2}} : temperature of the surrounding fluid (K)
T 1 {\displaystyle T_{1}} : temperature of the solid surface (K) In much practical application, a heat transfer coefficient has a relatively constant value over its specified temperature range of usefulness.
Composition
A simple method for determining an overall heat transfer coefficient that is useful to find the heat transfer through a sequence of simple elements such as walls in buildings or across heat exchangers is shown below. This method most readily accounts for conduction and convection. Effects of radiation can be similarly estimated, but introduce non-linear temperature dependence. The method is as follows:
1 U ⋅ A = 1 h 1 ⋅ A 1 + d x w k ⋅ A + 1 h 2 ⋅ A 2 {\displaystyle {\frac {1}{U\cdot A}}={\frac {1}{h_{1}\cdot A_{1}}}+{\frac {dx_{w}}{k\cdot A}}+{\frac {1}{h_{2}\cdot A_{2}}}}
Where:
U {\displaystyle U} = the overall heat transfer coefficient (W/(m2·K))
A {\displaystyle A} = the contact area for each fluid side (m2) (with A 1 {\displaystyle A_{1}} and A 2 {\displaystyle A_{2}} expressing either surface)
k {\displaystyle k} = the thermal conductivity of the material (W/(m·K))
h {\displaystyle h} = the individual convection heat transfer coefficient for each fluid (W/(m2·K))
d x w {\displaystyle dx_{w}} = the wall thickness (m). As the areas for each surface approach being equal the equation can be written as the transfer coefficient per unit area as shown below:
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