5 replies to this topic

Hi all,

 

I need to find out the time required to heat a sphere to 70°C within a water bath at 80°C and also to find temperatures of different radii within the sphere at certain times.

 

The thermal conductivity varies from 0.55-0.65 but i used a constant k=0.6W/mK

Cp=3.43J/gK

Initial temperature=20°C

Diameter=60mm

h=50W/m²K

Density=1100kg/m³

 

I had the equation 1/r² d(r² k dT/dr)/dr=(rho)Cp(dT/dt)

 

But just can't get my head around it at all!!

 

Any help would be really appreciated

 

Thanks

 

N

[thorium90]

Firstly, it does not appear your energy conservation equation for spherical coordinates is completely correct.
The mathematical methods needed to simplify and integrate this 2nd order partial differential equations might be beyond your level. Nevertheless, you would still need 2 boundary and 1 initial conditions. I would suggest numerical methods instead as it would be relatively simpler.

Edited by thorium90, 24 April 2014 - 07:56 PM.

[aroon]

Below link might be useful for you:

 

https://www.google.c...7938,bs.1,d.aWw

[Art Montemayor]

This is a classic unsteady state heat transfer problem that is found in various websites around the internet.  aroon has identified one site; there are more. But the basic topic here is Unsteady State Heat Transfer.

[PingPong]

I always find the book Heat Transfer, A Practical Approach by Yunus A. Cengel very clear on this kind of subjects.

 

As it happens, one can download Chapter 4 on Transient Heat Conduction from that book at the McGraw-Hill website:

http://highered.mcgr...n29305_ch04.pdf

 

[Art Montemayor]

Thank you for the reference PingPong.  It certainly is well illustrated and pleasantly easy to read and understand.  The derivations are condensed, but one can't have it all.

 

With this reference to study, students have no excuses for the headaches and mental concentration demanded by unsteady (transient) heat transfer.  That it isn't an easy subject, no one will debate; however, it is all around us.