Conductive Heat Transfer

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Conduction will take place if there exist a temperature gradient in a solid (or stationary fluid) medium.

Energy is transferred from more energetic to less energetic molecules when neighboring molecules collide. Conductive heat flow occur in direction of the decreasing temperature since higher temperature are associated with higher molecular energy.

Fourier's Law express conductive heat transfer as

q = k A dT / s         (1)

where

A = heat transfer area (m², ft²)

k = thermal conductivity of the material (W/m.K or W/m ^oC, Btu/(hr ^oF ft²/ft))

dT = temperature difference across the material (K or ^oC, ^oF)

s = material thickness (m, ft)

Example - Heat Transfer by Conduction

A plane wall constructed of solid iron with thermal conductivity 70 W/m^oC, thickness 50 mm and with surface area 1 m by 1 m, temperature 150 ^oC on one side and 80 ^oC on the other.

Conductive heat transfer can be calculated as:

q = 70 (W/m^oC) 1 (m) 1 (m) (150 (^oC) - 80 (^oC)) / 0.05 (m)

    = 98,000 (W)

    = 98 (kW)

Heat Transfer through Plane Walls In Series

Heat conducted through several walls in good thermal contact can be expressed as

q = (T₁ - T_n) / ((s₁/k₁A) + (s₂/k₂A) + ... + (s_n/k_nA))     (2)

where 

T₁ = temperature inside surface (K or ^oC, ^oF)

T_n = temperature outside surface (K or ^oC, ^oF)

Example - Heat Transfer through a Furnace Wall 

A furnace wall of 1 m² consist of a 1.2 cm thick stainless steel inner layer covered with a 5 cm this outside insulation layer of asbestos board insulation. The inside surface temperature of the steel is 800 K and the outside surface temperature of the asbestos is 350 K. The thermal conductivity for stainless steel is 19 W/m.K and for asbestos board 0.7 W/m.K. 

The conductive heat transport through the wall can be calculated as

q =(800 (K) - 350 (K)) / ((0.012 (m) / 19 (W/mK) 1 (m²)) + (0.05 (m) / 0.7 (W/m.K) 1 (m²)))

          = 6245 (W)

Thermal Conductivity and Common Units

• Btu/(h ft^2 oF/ft)
• Btu/(h ft^2 oF/in)
• Btu/(s ft^2 oF/ft)
• MW/(m² K/m)
• kW/(m² K/m)
• W/(m² K/m)
• W/(m² K/cm)
• W/(cm^2 oC/cm)
• W/(in^2 oF/in)
• kJ/(h m² K/m)
• J/(s m^2 oC/m)
• kcal/(h m^2 oC/m)
• cal/(s cm^2 oC/cm)

• Convert between thermal conductivity units

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