# Overall Heat Transfer Coefficient

## Calculate overall heat transfer coefficients for walls or heat exchangers

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The overall heat transfer coefficient for a wall or a heat exchanger can be calculated as:

1 / U A = 1 / h_{1}A_{1}+ dx_{w}/ k A + 1 / h_{2}A_{2}(1)

where

U= the overall heat transfer coefficient (W/m^{2}K)

A= the contact area for each fluid side (m^{2}^{})

k= the thermal conductivity of the material (W/mK)

h= the individual convection heat transfer coefficient for each fluid (W/m^{2}K)

dx_{w}= the wall thickness (m)

The thermal conductivity - *k -* for some typical materials (varies with temperature)

- Polypropylene PP :
*0.1 - 0.22 W/mK* - Stainless steel :
*16 - 24 W/mK* - Aluminum :
*205 - 250 W/mK* *1 W/(m*^{2 }K) = 0.85984 kcal/(h m^{2}^{o}C) = 0.1761 Btu/(ft^{2}h^{o}F)

The convection heat transfer coefficient - *h* - depends on

- the type of fluid - gas or liquid
- the flow properties such as velocity
- other flow and temperature dependent properties

Convective heat transfer coefficient for some common fluids:

- Air -
*10 to 100 W/m*^{2}K - Water -
*500 to 10 000 W/m*^{2}K

### Thermal resistance

The overall heat transfer coefficient can also be calculated by the view of thermal resistance - *R*. The wall is split in areas of thermal resistance where

- the heat transfer between the fluid and the wall is one resistance
- the wall it self is one resistance
- the transfer between the wall and the second fluid is a thermal resistance

Surface coatings or layers of "burned" product adds extra thermal resistance to the wall decreasing the overall heat transfer coefficient.

#### Some typical heat transfer resistances

- static layer of air,
*40 mm (1.57 in)*:*R = 0.18 m*^{2}K/W - inside heat transfer resistance, horizontal current :
*R = 0.13 m*^{2}K/W - outside heat transfer resistance, horizontal current :
*R = 0.04 m*^{2}K/W - inside heat transfer resistance, heat current from down upwards :
*R = 0.10 m*^{2}K/W - outside heat transfer resistance, heat current from above downwards :
*R = 0.17 m*^{2}K/W

### Example - Heat Transfer in an Air Heat Exchanger

A single plate exchanger with media A transfers heat to media B. The wall thickness is *0.1 mm* and the material is polypropylene PP, aluminum or stainless steel.

Media A and B are **air** with a convection heat transfer coefficient of *h _{air} = 50 W/m^{2}K.*

The overall heat transfer coefficient U per unit area can be expressed as:

U = 1 / (1 / h_{A}+ dx_{w}/ k + 1 / h_{B})(1b)

The overall heat transfer coefficient for heat exchanger in

- polypropylene with thermal conductivity
*0.1 W/mK*:

*U = 1 / (1 / ( 50 W/m^{2}K) + (0.1 mm) (10^{-3} m/mm)/ (0.1 W/mK) + 1 / (50 W/m^{2}K))*

* = 24.4 W /m ^{2}K*

- stainless steel with thermal conductivity
*16 W/mK*:

*U = 1 / (1 / ( 50 W/m^{2}K) + (0.1 mm) (10^{-3} m/mm)/ (16 W/mK) + 1 / (50 W/m^{2}K))*

* = 25 W /m ^{2}K*

- aluminum with thermal conductivity
*205 W/mK*:

*U = 1 / (1 / ( 50 W/m^{2}K) + (0.1 mm) (10^{-3} m/mm)/ (205 W/mK) + 1 / (50 W/m^{2}K))*

* = 25 W /m ^{2}K*

*1 W/(m*^{2 }K) = 0.85984 kcal/(h m^{2}^{o}C) = 0.1761 Btu/(ft^{2}h^{o}F)

### Typical Overall Heat-Transfer Coefficients

- Free Convection Gas - Free Convection Gas :
*U = 1 - 2 W/m*^{2}K (typical window, room to outside air through glass) - Free Convection Gas - Forced liquid (flowing) water :
*U = 5 - 15 W/m*^{2}K (typical radiator central heating) - Free Convection Gas - Condensing Vapor Water :
*U = 5 - 20 W/m*^{2}K (typical steam radiators) - Forced Convection (flowing) Gas - Free Convection Gas :
*U = 3 - 10 W/m*^{2}K (superheaters) - Forced Convection (flowing) Gas - Forced Convection Gas :
*U = 10 - 30 W/m*^{2}K (heat exchanger gases) - Forced Convection (flowing) Gas - Forced liquid (flowing) water :
*U = 10 - 50 W/m*^{2}K (gas coolers) - Forced Convection (flowing) Gas - Condensing Vapor Water :
*U = 10 - 50 W/m*^{2}K (air heaters) - Liquid Free Convection - Forced Convection Gas :
*U = 10 - 50 W/m*^{2}K (gas boiler) - Liquid Free Convection - Free Convection Liquid :
*U = 25 - 500 W/m*^{2}K (oil bath for heating) - Liquid Free Convection - Forced Liquid flowing (Water) :
*U = 50 - 100 W/m*^{2}K (heating coil in vessel water, water without steering), 500 - 2000 W/m^{2}K (heating coil in vessel water, water with steering) - Liquid Free Convection - Condensing vapor water :
*U = 300 - 1000 W/m*^{2}K (steam jackets around vessels with stirrers, water), 150 - 500 W/m^{2}K (other liquids) - Forced liquid (flowing) water - Free Convection Gas :
*U = 10 - 40 W/m*^{2}K (combustion chamber + radiation) - Forced liquid (flowing) water - Free Convection Liquid :
*U = 500 - 1500 W/m*^{2}K (cooling coil - stirred) - Forced liquid (flowing) water - Forced liquid (flowing) water :
*U = 900 - 2500 W/m*^{2}K (heat exchanger water/water) - Forced liquid (flowing) water - Condensing vapor water :
*U = 1000 - 4000 W/m*^{2}K (condensers steam water) - Boiling liquid water - Free Convection Gas :
*U = 10 - 40 W/m*^{2}K (steam boiler + radiation) - Boiling liquid water - Forced Liquid flowing (Water) :
*U = 300 - 1000 W/m*^{2}K (evaporation of refrigerators or brine coolers) - Boiling liquid water - Condensing vapor water :
*U = 1500 - 6000 W/m*^{2}K (evaporators steam/water)

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