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 (T_{0 }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}.
or
Where:
T_{n} = Outer surface temperature ^{o}C
T_{0} = Inner surface temperature ^{o}C
q = Heat flow (positive heat flow is from T_{0} to T_{n})
r_{i} = Outer radius of the layer i , (Meters)
r_{i1} = Inner
radius of the layer i, (Meters)
k_{i} = Thermal conductivity
of layer i, (W/m^{o}C)
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 T_{0} being
hotter than T_{n}. Negative values of heat (q) result in T_{0}
being cooler than T_{n}.
