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# Overall Heat Transfer Coefficient

## Calculate overall heat transfer coefficients for walls or heat exchangers 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/(m2K), Btu/(ft2 h oF))

A = wall area (m2, ft2)

dT = (t1 - t2)

= temperature difference over wall (oC, oF)

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 / hci Ai + Σ (sn / kn An) + 1 / hco Ao                                      (2)

where

U = the overall heat transfer coefficient (W/(m2 K), Btu/(ft2 h oF))

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

hc i,o = inside or outside wall individual fluid convection heat transfer coefficient (W/(m2 K), Btu/(ft2 h oF))

sn = thickness of layer n (m, ft)

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

1 / U = 1 / hci + Σ (sn / kn) + 1 / hco                               (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 oF)
• 1 W/(m2 K) = 0.85984 kcal/(h m2 oC) = 0.1761 Btu/(ft2 h oF)

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/m2K
• Water - 500 to 10 000 W/m2K

### 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.

A - area (m2, ft2)

t1 - temperature 1 (oC, oF)

t2 - temperature 2 (oC, oF)

hci - convective heat transfer coefficient inside wall (W/(m2 K), Btu/(ft2 h oF))

s1 - thickness 1 (m, ft) k1 - thermal conductivity 1 (W/(m K), Btu/(hr ft °F))

s2 - thickness 2 (m, ft) k2 - thermal conductivity 2 (W/(m K), Btu/(hr ft °F))

s3 - thickness 3 (m, ft) k3 - thermal conductivity 3 (W/(m K), Btu/(hr ft °F))

hco - convective heat transfer coefficient outside wall (W/(m2 K), Btu/(ft2 h oF))

### Heat Transfer Thermal Resistance Heat transfer resistance can be expressed as

R = 1 / U                               (4)

where

R = heat transfer resistance (m2K/W, ft2 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 m2K/W
• inside heat transfer resistance, horizontal current : R = 0.13 m2K/W
• outside heat transfer resistance, horizontal current : R = 0.04 m2K/W
• inside heat transfer resistance, heat current from down upwards : R = 0.10 m2K/W
• outside heat transfer resistance, heat current from above downwards : R = 0.17 m2K/W

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

An air to air plate exchanger with area 2 m2 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/m2K. Inside temperature in the exchanger is 100 oC and outside temperature is 20 oC.

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

U = 1 / (1 / hci + s / k + 1 / hco)                                               (3b)

The overall heat transfer coefficient for heat exchanger in

• polypropylene with thermal conductivity 0.1 W/mK is

UPP = 1 / (1 / (50 W/m2K) + (0.1 mm) (10-3 m/mm)/ (0.1 W/mK) + 1 / (50 W/m2K))

= 24.4 W /m2K

The heat transfer is

q = (24.4 W /m2K) (2 m2) ((100 oC) - (20 oC))

= 3904 W

= 3.9 kW

• stainless steel with thermal conductivity 16 W/mK:

USS = 1 / (1 / (50 W/m2K) + (0.1 mm) (10-3 m/mm)/ (16 W/mK) + 1 / (50 W/m2K))

= 25 W /m2K

The heat transfer is

q = (25 W /m2K) (2 m2) ((100 oC) - (20 oC))

= 4000 W

= 4 kW

• aluminum with thermal conductivity 205 W/mK:

UAl = 1 / (1 / (50 W/m2K) + (0.1 mm) (10-3 m/mm)/ (205 W/mK) + 1 / (50 W/m2K))

= 25 W /m2K

The heat transfer is

q = (25 W /m2K) (2 m2) ((100 oC) - (20 oC))

= 4000 W

= 4 kW

• 1 W/(m2 K) = 0.85984 kcal/(h m2 oC) = 0.1761 Btu/(ft2 h oF)

### Typical Overall Heat-Transfer Coefficients

• Free Convection Gas - Free Convection Gas : U = 1 - 2 W/m2K  (typical window, room to outside air through glass)
• Free Convection Gas - Forced liquid (flowing) water : U = 5 - 15 W/m2K  (typical radiator central heating)
• Free Convection Gas - Condensing Vapor Water : U = 5 - 20 W/m2K  (typical steam radiators)
• Forced Convection (flowing) Gas - Free Convection Gas : U = 3 - 10 W/m2K (superheaters)
• Forced Convection (flowing) Gas - Forced Convection Gas : U = 10 - 30 W/m2K (heat exchanger gases)
• Forced Convection (flowing) Gas - Forced liquid (flowing) water  : U = 10 - 50 W/m2K (gas coolers)
• Forced Convection (flowing) Gas - Condensing Vapor Water  : U = 10 - 50 W/m2K (air heaters)
• Liquid Free Convection - Forced Convection Gas : U = 10 - 50 W/m2K (gas boiler)
• Liquid Free Convection - Free Convection Liquid : U = 25 - 500 W/m2K (oil bath for heating)
• Liquid Free Convection - Forced Liquid flowing (Water) : U = 50 - 100 W/m2K (heating coil in vessel water, water without steering), 500 - 2000 W/m2K (heating coil in vessel water, water with steering)
• Liquid Free Convection - Condensing vapor water : U = 300 - 1000 W/m2K (steam jackets around vessels with stirrers, water), 150 - 500 W/m2K (other liquids)
• Forced liquid (flowing) water - Free Convection Gas : U = 10 - 40 W/m2K (combustion chamber + radiation)
• Forced liquid (flowing) water - Free Convection Liquid : U = 500 - 1500 W/m2K (cooling coil - stirred)
• Forced liquid (flowing) water - Forced liquid (flowing) water : U = 900 - 2500 W/m2K (heat exchanger water/water)
• Forced liquid (flowing) water - Condensing vapor water : U = 1000 - 4000 W/m2K (condensers steam water)
• Boiling liquid water - Free Convection Gas : U = 10 - 40 W/m2K (steam boiler + radiation)
• Boiling liquid water - Forced Liquid flowing (Water) : U = 300 - 1000 W/m2K (evaporation of refrigerators or brine coolers)
• Boiling liquid water - Condensing vapor water : U = 1500 - 6000 W/m2K (evaporators steam/water)

## Related Topics

• Heat Loss and Insulation - Heat loss from pipes, tubes and tanks - with and without insulation - foam, fiberglass, rockwool and more
• Insulation - Heat transfer and heat loss from buildings and technical applications - heat transfer coefficients and insulation methods and to reduce energy consumption
• Steam - Heat Loss and Insulation - Steam and condensate pipes - heat loss uninsulated and insulated pipes, insulation thickness and more
• Thermodynamics - Effects of work, heat and energy on systems

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## Citation

• Engineering ToolBox, (2003). Overall Heat Transfer Coefficient. [online] Available at: https://www.engineeringtoolbox.com/overall-heat-transfer-coefficient-d_434.html [Accessed Day Mo. Year].

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