The integro-differential equation for temperature θ(γ, t) of an infinite hollow cylinder (temperature diffusivity is
k), which is kept constant temperature
T initially and radius γ=b, and loses heat by the radiation from interior surface (γ=α) to air flow of temperature
f (
t) with transfer coefficient
h, is set up as follows:
_??_
G (γ, ξ) is Green's function belonging to the differential equation (
γy')'=0 and satisfying the next boundary conditions:[
y'-hy] a=0,
yb=0.
Let λ
n, Φ
n (γ) be eigenvalue, eigenf unction of the kernel
K (γ, ξ), the solution of above equation
V (γ,
t) is as follows:
_??_
If we put the temperature of air flow
f (
t) is equal to
Sθ(α,
t)(0<S<1),
f (
t) may determined. Its solution is much complex, but if the product
ah is large, the solution can be denoted simply.
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