1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Transiet thermal stresses

  1. Jul 2, 2013 #1


    User Avatar
    Homework Helper

    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


    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


    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
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted