Overall Heat Transfer Coefficient

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

1 / U A = 1 / h₁ A₁ + dx_w / k A + 1 / h₂ A₂                                      (1)

where

U = overall heat transfer coefficient (W/m²K)

A = contact area for each fluid side (m²)

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

h = individual convection heat transfer coefficient for each fluid (W/m²K)

dx_w = 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/(m² K) = 0.85984 kcal/(h m^{2 o}C) = 0.1761 Btu/(ft² h ^oF)

• Conductive heat transfer
• Thermal conductivity of commonly used materials

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/m²K
• Water - 500 to 10 000 W/m²K

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 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 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/m²K.

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

   = 24.4 W /m²K

• stainless steel with thermal conductivity 16 W/mK:

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

   = 25 W /m²K

• aluminum with thermal conductivity 205 W/mK:

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

   = 25 W /m²K

• 1 W/(m² K) = 0.85984 kcal/(h m^{2 o}C) = 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)

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