Steady State Conduction Multilayer Cylinder Calculator and Formulas

Heat Transfer Engineering
Thermodynamics

Steady State Conduction Multilayer Cylinder Calculator and Formulas

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 T_n) are required as well. For each layer you must define the layer thickness (t_i) as well as the layer conductivity k_i.

Preview: Steady State Conduction Multilayer Cylinder Calculator

 

or 

 

Where:

T_n   = Outer surface temperature ^oC
T₀   = Inner surface temperature ^oC
q    = Heat flow (positive heat flow is from T₀ to T_n)
r_i    = Outer radius of the layer i ,  (Meters)
r_i-1  = Inner radius of the layer i,   (Meters)
k_i    = 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 T_n. Negative values of heat (q) result in T₀ being cooler than T_n.

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