Solution Governing Equation: PCp t (1a) Boundary Condition: x=0, OT-h(T-T.) d (1b) x=L, T=T,=310K Initial Condition: t=0,T=T,=310K (1c)
Solution ( ) p T T c k txx ρ ∂ ∂∂ = ∂∂ ∂ 0, ( ) , 310 b T x k hT T x xL TT K ∞ ∂ = =− ∂ = == Governing Equation: Boundary Condition: Initial Condition: (1a) (1b) (1c) 0, 310 b t TT K = ==
Continued Separating T(x,t)to T(x,t)=θ(x,t)+T The equations change to (1a) ∂0 x=0, x ≥hd (1b) x=L, 0=T6-T=32K t=0, 0=T-T=32K (1c)
Continued ( ) p c k txx θ θ ρ ∂ ∂∂ = ∂∂ ∂ 0, , 32 b x kh x x L TT K θ θ θ ∞ ∂ = = ∂ = =− = T xt xt T (,) (,) = + θ ∞ The equations change to : (1a) (1b) (1c) Separating T(x,t) to 0, 32 b t TT K = =− = θ ∞
Continued General Solution Particular Solution: e(x,t)=T,(x,t)+T (x)
Continued General Solution + Particular Solution: (,) (,) () n w θ x t T xt T x = +