Hi. Just for illustration purposes I am trying to model the temperature in the walls of a hollow sphere. The purpose is to (very crudly) approximate the heating effects of a combustion process (running engine). It is assumed that there is gas inside of the sphere.(adsbygoogle = window.adsbygoogle || []).push({});

Assumptions:

A. Inner and Outer radii are constants - Ri and Ro, respectively.

B. The temperature outside of the sphere is constant - Tw (w stands for "water")

C. The temperature of the gas (Tg) is assumed to be uniform and either

a) Tg(t) = C (constant) or

b) Tg(t) = C1 + C2*sin(w*t)

where "t" naturally denotes time. I want to study mainly the long term solution, but for fun also the transients.

So far so good. Now to the problematic part. How to model and solve this? I understand the following:

I. Because of symmetry it can be modeled as a one-dimensional problem (T(r,t))

II. The Outer surface temperature of the sphere (T(Ro,t)) should be modeled as T(Ro,t)=Tw. Or maybe it shouldn't?

After that I am lost! Is it a good idea to model the Inner surface temperature (T(Ri,t)) of the sphere as T(Ri,t)=Tg(t)? I don't think it corresponds very well to reality, or does it? Maybe it would be better to model the flux across the surface in some way, but how?

Please help! I really would like to model and solve this in an appropriate manner.

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# Temperature hollow sphere - Temperature varying inside

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