# Overall Heat Transfer Coefficients

Heat transfer through a surface like a wall can be calculated as

*q = U A dT (1)*

*where*

*q = heat transfer (W (J/s), Btu/h)*

*U = overall heat transfer coefficient (W/(m ^{2}K), Btu/(ft^{2} h ^{o}F))*

*A = wall area (m ^{2}, ft^{2})*

*dT = (t _{1} - t_{2}) *

* = temperature difference over wall ( ^{o}C, ^{o}F)*

The overall heat transfer coefficient for a multi-layered wall, pipe or heat exchanger - with fluid flow on each side of the wall - can be calculated as

1 / U A = 1 / h_{ci}A_{i}+ Σ (s_{n}/ k_{n}A_{n}) + 1 / h_{co}A_{o}(2)

where

U = the overall heat transfer coefficient (W/(m^{2 }K), Btu/(ft^{2}h^{o}F))

k_{n}= thermal conductivity of material in layer n (W/(m K), Btu/(hr ft °F))

h_{c i,o}= inside or outside wall individual fluid convection heat transfer coefficient (W/(m^{2 }K), Btu/(ft^{2}h^{o}F))

s_{n }= thickness of layer n (m, ft)

A plane wall with equal area in all layers - can be simplified to

*1 / U = 1 / h _{ci} + Σ (s_{n} / k_{n}) + 1 / h_{co} (3)*

Thermal conductivity - *k -* for some typical materials (not that conductivity is a property that may vary with temperature)

- Polypropylene PP :
*0.1 - 0.22 W/(m K)* - Stainless steel :
*16 - 24 W/(m K)* - Aluminum :
*205 - 250 W/**(m K)*

#### Convert between Metric and Imperial Units

*1 W/(m K) = 0.5779 Btu/(ft h*^{o}F)*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

- type of fluid - if its gas or liquid
- flow properties like 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

### Multi-layered Walls - Heat Transfer Calculator

This calculator can be use to calculate the overall heat transfer coefficient and the heat transfer through a multi-layered wall. The calculator is generic and can be used for metric or imperial units as long as the use of units is consistent.

### Heat Transfer Thermal Resistance

Heat transfer **resistance** can be expressed as

*R = 1 / U (4)*

*where *

*R = heat transfer resistance (m ^{2}K/W, ft^{2} h°F/ Btu)*

The wall is split in sections 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 Air to Air Heat Exchanger

An air to air plate exchanger with area *2 m ^{2}* and wall thickness

*0.1 mm*can be made in polypropylene PP, aluminum or stainless steel.

The heat transfer convection coefficient for air is *50 W/m ^{2}K*. Inside temperature in the exchanger is

*100*and outside temperature is

^{o}C*20*.

^{o}C

The overall heat transfer coefficient U per unit area can be calculated by modifying *(3)* to

U = 1 / (1 / h_{ci}+ s / k + 1 / h_{co}) (3b)

The overall heat transfer coefficient for heat exchanger in

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

*U _{PP} = 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*

The heat transfer is

*q = (24.4 W /m ^{2}K) (2 m^{2}) ((100 ^{o}C) - (20 ^{o}C))*

* = 3904 W*

* = 3.9 kW ** *

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

*U _{SS} = 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*

The heat transfer is

*q = (25 W /m ^{2}K) (2 m^{2}) ((100 ^{o}C) - (20 ^{o}C))*

* = 4000 W*

* = 4 kW *

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

*U _{Al} = 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*

The heat transfer is

*q = (25 W /m ^{2}K) (2 m^{2}) ((100 ^{o}C) - (20 ^{o}C))*

* = 4000 W*

* = 4 kW *

*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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