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Transiet thermal stresses

  1. Jul 2, 2013 #1

    rock.freak667

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    1. The problem statement, all variables and given/known data
    Problem is described as follows, I have a pressure vessel which basically consists of a hollow cylindrical body with two hemispherical shells attached to both ends. Within the vessel, there is a gas flowing from top to bottom. Over a period of one week, the vessel was subjected to changes in both temperatures and pressures (inlet and outlet).

    I need to get how the stresses varied within the vessel (due to pressure and temp).


    2. Relevant equations
    Hoop stress
    3-D heat conduction equation


    3. The attempt at a solution

    Both hemispheres and cylinders are thin, so at each time interval hence change in pressure I can calculate hoop stress using

    σ=PD/2t.

    However the thermal stress becomes a bit confusing as I am not sure how to model it/solve it.

    I am simplifying the situation by ignoring the convective element of the fluid flowing and concentrating on conduction.

    The heat equation is as follows

    [Broken]

    I can simplify my situation by converting the problem to 1-D such that my temperature function T will just be of t and r i.e. T = T(r,t).

    My main issue is determining how to get ∂T/∂t.

    Plotting my data collection against time doesn't really fit any equation trendline and just looks a bit erratic.

    or do I assume T(r,t)=X(r)Y(t) and solve the PDE using separation of variables which if I remember correctly will eventually give me a Fourier Series which might complicate my situation. Is there any way to make this easier to do by hand rather than an FEA simulation?
     
    Last edited by a moderator: May 6, 2017
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