## anonymous 3 years ago Find the BVM of θ(x,t): by Deriving the equation ∂φ/∂t=k/ρc (∂^2 φ)/(∂x^2 ) - (h/ρAc) φ , where φ(x,t) = (θ(x,t)- θ_0)

1. anonymous

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2. anonymous

how to prove $\theta(x,t)$ ?

3. anonymous

form this qs: Find the BVM of θ(x,t): by Deriving the equation ∂φ/∂t=k/ρc (∂^2 φ)/(∂x^2 ) - (h/ρAc) φ , where φ(x,t) = (θ(x,t)- θ_0

4. abb0t

whats BVM?

5. anonymous

Boundasy Value Mean

6. anonymous

please jsu ignore the BVM, just fint the partial derivative of (θ(x,t)

7. anonymous

The new BC at L/2 would be: ∂θ(L/2, t)/∂x = 0, which means for all time t the slope of the temperature curve versus x is zero at x = L/2, because the temperature profile is symmetric and continuous about the midpoint. To prove this is true take your heat solution equation where θ(x,t) = θ0 + Sum terms and take the partial derivative of that eqn. with respect to x.