Steady State Conduction Multilayer Cylinder Calculation

Heat Transfer Engineering | Thermodynamics

The following equation will calculate the temperature on one side of an isothermal constant temperature multilayer cylinder. The heat load (q) conducted from the interior to the exterior layers as well as the temperature of the interior wall (T0 or Tn) are required as well. For each layer you must define the layer thickness (ti) as well as the layer conductivity ki.

 

or 

 

Where:

Tn   = Outer surface temperature oC
T0
   = Inner surface temperature oC
q    = Heat flow (positive heat flow is from T0 to Tn)
ri
    = Outer radius of the layer i ,  (Meters)
ri-1
  = Inner radius of the layer i,   (Meters)
ki
    = Thermal conductivity of layer i,  (W/m-oC) 
L    =  Length of the cylinder (Meters)

The end walls of the cylinder are assumed adiabatic. That is, only radial heat flow is accounted for. 

Positive values of heat (q) result in T0 being hotter than Tn. Negative values of heat (q) result in T0 being cooler than Tn.

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