Overall Heat Transfer Coefficients
Walls or heat exchangers - calculate 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/(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)