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

• Aug 10th 2012, 03:31 PM
math254
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)=

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))
• Aug 10th 2012, 07:26 PM
Prove It
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*}
• Aug 11th 2012, 12:14 AM
math254
Re: cooling fan, i dont know how to solve part c and d
yes that is the equation
• Aug 11th 2012, 12:22 AM
Prove It
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...