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Math Help - cooling fan, i dont know how to solve part c and d

  1. #1
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    cooling fan, i dont know how to solve part c and d

    the temperature T of a cooling fan of finite length, L satisfies

    d2T/dx2=-K^2*(T(sub L)-T) 0<=x<=L T(0)=T0 T(L)=T(sub L) TL

    where K, T0 and TL are constant

    a) find the complimentary function Tc(x) stating your answer in terms of unknown constants c1 and c2

    answer for this part is: Tc(x)=c1cosh(xk)+c2sinh(xK)

    b) complete the following

    sinh(KL-Kx)=

    answer for it is: =[sin(kL)cos(KL)-cos(kL)sin(kx)]




    now this is where i have problems



    c) write down your starting point for the particular solution Tp(x)


    d) find Tp(x) and the coefficients c1, and c2 and hence show that the solution of the above problem is


    T(x)=Tl+(T0-TL)(sing(k(L-x))/sinh(KL))
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  2. #2
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    Re: cooling fan, i dont know how to solve part c and d

    Just so we're clear, is this your equation?

    \displaystyle \begin{align*} \frac{d^2T}{dx^2} = -k^2\left(T_L - T\right), 0 \leq x \leq L, T(0) = T_0, T(L) = T_L \end{align*}
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  3. #3
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    Re: cooling fan, i dont know how to solve part c and d

    yes that is the equation
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  4. #4
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    Re: cooling fan, i dont know how to solve part c and d

    First of all, your answer to part b) can not possibly be right, since a real hyperbolic function never equals a combination of real trigonometric functions...
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