Heat Conduction in Some Standard Solids
Heat Conduction in Some Standard Solids
The dimensionless transient temperature and average temperature (τ)=(n+1)θ(ξ,τ)dξ of a plate (), cylinder (), and sphere (), described by the partial differential equation problem θ(ξ,τ)=θ(ξ,τ)+(n/ξ) θ(ξ,τ), θ(0,τ)=0, , , are plotted (transient in orange, average in blue) as a function of dimensionless time . The numerical values for transient and average temperatures can be computed for any dimensionless coordinate and time .
θ(ξ,τ)
θ
1
∫
0
n
ξ
n=0
n=1
n=2
∂
τ
∂
ξ,ξ
∂
ξ
∂
ξ
θ(1,τ)=1
θ(ξ,0)=0
τ
ξ
τ