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/(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 multilayered 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
Multilayered Walls  Heat Transfer Calculator
This calculator can be use to calculate the overall heat transfer coefficient and the heat transfer through a multilayered 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 (m^{2}, ft^{2})
t_{1}  temperature 1 (^{o}C, ^{o}F)
t_{2}  temperature 2 (^{o}C, ^{o}F)
h_{ci}  convective heat transfer coefficient inside wall (W/(m^{2 }K), Btu/(ft^{2} h ^{o}F))
s_{1}  thickness 1 (m, ft)
k_{1}  thermal conductivity 1 (W/(m K), Btu/(hr ft °F))
s_{2}  thickness 2 (m, ft)
k_{2}  thermal conductivity 2 (W/(m K), Btu/(hr ft °F))
s_{3}  thickness 3 (m, ft)
k_{3}  thermal conductivity 3 (W/(m K), Btu/(hr ft °F))
h_{co}  convective heat transfer coefficient outside wall (W/(m^{2 }K), Btu/(ft^{2} h ^{o}F))
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 ^{o}C and outside temperature is 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 HeatTransfer 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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