Temp change through a wall
Temp change through a wall
(OP)
Help please, I am a ChemE, and I know I should remember this, but i guess it's just been too long.
I have a known temperature on one side of a wall of known thickness and thermal conductivity. How do I calculate the temp on the outside of the wall?
I have a known temperature on one side of a wall of known thickness and thermal conductivity. How do I calculate the temp on the outside of the wall?





RE: Temp change through a wall
RE: Temp change through a wall
RE: Temp change through a wall
Q = -kA(dT/dx)
Generally speaking the temperature change from one side to the other of a wall of thickness x and surface A (perpendicular to heat flow), with a thermal conductivity k, depends on these and on the heat flow Q:
T2-T1=(Q/A)(x/k)
x/k is known as thermal resistance.
Please note that T drops in the direction of heat flow.
For cylinders as in thick-walled pipes or vessels with inner radius r1, outer radius r2, and length L, with heat Q flowing outwards,
T1-T2= Q*ln(r2/r1)/(2*pi*L*k)
One always has to keep in mind the consistency of the units used.
RE: Temp change through a wall
Usually in heat transfer (for pipes) you consider:
1) Inside heat transfer from medium to solid
2) conduction through solid
3) Transfer from outside wall to outside medium
Usually either 1) or 3) will be much larger than 2) and also 1)>>3) or 3)>>1)
If you have a liquid flow in a pipe and air on the outside you will find that 1)>>3) so that the bulk of "resistance" will be from outside wall and to outside medium-
Therefore the outside wall temperature will be quite close to the inside medium temperature.
Best regards
Morten
RE: Temp change through a wall
RE: Temp change through a wall
TTFN
RE: Temp change through a wall
RE: Temp change through a wall
Could you give us an idea of the temperatures and materials you are using (even wall thickness would help). If you have steam running through a thin steel pipe, the outside temperature is going to be less than a degree different from the steam temperature.... even if you're in the artic.
If you want to get a close outside wall temp. estimate, you need to know the external wall conditions (e.g. air temperature, wind speed). For a conservative number (highest wall temp) you can use the average high temperature of the area with no wind (natural convection).
Let us know some more specific info and we can try to help you out.
Regards,
jproj
RE: Temp change through a wall
RE: Temp change through a wall
T=75*(20-648)/(75+0.0006/h)+648 where h is the heat transfer coefficient to an ambient temperature of 20C. h is usually about 10 W/m^2 C so your outside temperature is about 300 C.
I would guess that your silica is surrounded by a steel shell but the conductivity of steel is relatively high not to affect the sums.
RE: Temp change through a wall
3" of refractory in such a furnace does not offer much resistance to heat flow and is one reason why it is rarely used alone.
good luck with your design...
RE: Temp change through a wall
Q=(T-t)(A)(0.6/0.075)=(t-25)(15)(A)
(649-t)(0.6/0.075)=(t-25)(15)
This results in: t=242oC.
As one can see the resulting external wall temperature also depends on the outside htc, corus took 10, I used 15 W/(m2*K). There are graphs that help in estimating the outside htc w/o many iterations.