need solution with detailes please A thin metal sheet with a length \"L\" is pla

Question

need solution with detailes please

A thin metal sheet with a length "L" is placed between two large posts as shown in the figure. The post temperature at x=0 is T1 and the post at x=L is insulated. The bottom of the metal sheet is also insulated, however, the top is open to convection heat transfer. Derive a differential equation in terms of theta = T - T infinity with its boundary conditions from which steady state temperature distribution in the plate can be obtained (Do not solve the equation!).

Explanation / Answer

kAd^2T/dx^2=hA1(T-Tinfinity)/dt d^2T/dx^2=d^2theta/dx^2 substitute it we get kAd^2theta/dx^2=hA1*theta/dt iam not sure abt the ares because for conductive heat transfer its area of cross section:t*something se for the areas

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