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Heat transfer through a hollow cone 4
- Thread starter mprice
- Start date
sailoday28
Mechanical
prex (Structural)
Please disregard my last post. I believe by constant isothermal flow you mean constant q (BTU/hr, etc).
And since you specify a frustum of a cone, there is no need for x=0. X can be a reference, ie at boundaries x=x1 and x=x2 etc.
In that case, yes, integration of the equations will be in terms of a temperature difference.
Please disregard my last post. I believe by constant isothermal flow you mean constant q (BTU/hr, etc).
And since you specify a frustum of a cone, there is no need for x=0. X can be a reference, ie at boundaries x=x1 and x=x2 etc.
In that case, yes, integration of the equations will be in terms of a temperature difference.
mprice,
Sorry, I gave a false "OK" to your re-arrangement which explains your problem with substituting numbers since. The correct re-arrangement of my equation is
dT = [Q.L.ln(Xh/L)]/kpZD
If you look at my worked example you'll see that's what I used to get the sensible answer of 24.92 degC. You substituted a divide between the Q and the L which is an error, and leads to the answer you correctly identify to be wrong.
Might I respectfully suggest that other respondents actually read the initial problem and contributions which make the problem clear. Heat flow is constant, entering at the small diameter and leaving by convection only at the cone's base. There is a temperature profile (which is the whole point of the question), assumed to be constant due to the initial unsteady state having died away over time.
Regards,
Stuart
Sorry, I gave a false "OK" to your re-arrangement which explains your problem with substituting numbers since. The correct re-arrangement of my equation is
dT = [Q.L.ln(Xh/L)]/kpZD
If you look at my worked example you'll see that's what I used to get the sensible answer of 24.92 degC. You substituted a divide between the Q and the L which is an error, and leads to the answer you correctly identify to be wrong.
Might I respectfully suggest that other respondents actually read the initial problem and contributions which make the problem clear. Heat flow is constant, entering at the small diameter and leaving by convection only at the cone's base. There is a temperature profile (which is the whole point of the question), assumed to be constant due to the initial unsteady state having died away over time.
Regards,
Stuart
c2sco,
you assumed in your calculations that the length of the cone from the base to the apex is 15.5 mm, whilst from mprice's data it is clear that this the height of the truncated cone (from major base to minor base). That's why our results are different.
To check our results we may simply replace the cone with a cylinder of the same length or height, that I'll call L as above.
In this case the result is straightforwardly calculated as:
[Δ]T=QL/([π]ktD)
If we now take for D the major diameter of the cone, we obviously will get a [Δ]T lower than the actual one, a bigger value with the minor diameter, and an hopefully close approximation with the average diameter.
So:
-with the major diameter [Δ]T=21°C
-with the minor diameter [Δ]T=69°C
-with the avg. diameter [Δ]T=32°C
The last value is not so close, but is anyway the closest one to my formerly calculated value of 36°C.
prex
: Online tools for structural design
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you assumed in your calculations that the length of the cone from the base to the apex is 15.5 mm, whilst from mprice's data it is clear that this the height of the truncated cone (from major base to minor base). That's why our results are different.
To check our results we may simply replace the cone with a cylinder of the same length or height, that I'll call L as above.
In this case the result is straightforwardly calculated as:
[Δ]T=QL/([π]ktD)
If we now take for D the major diameter of the cone, we obviously will get a [Δ]T lower than the actual one, a bigger value with the minor diameter, and an hopefully close approximation with the average diameter.
So:
-with the major diameter [Δ]T=21°C
-with the minor diameter [Δ]T=69°C
-with the avg. diameter [Δ]T=32°C
The last value is not so close, but is anyway the closest one to my formerly calculated value of 36°C.
prex
: Online tools for structural design
: Magnetic brakes for fun rides
: Air bearing pads
- Thread starter
- #24
c2sco, thanks for sorting that out - all is clear.
prex , thanks for the further anaylsis. Using the corrected height of the truncated cone I now get the same result with your formula and the formula developed by c2sco. That is DT=36°C.
Many thanks for your inputs
Matt
prex , thanks for the further anaylsis. Using the corrected height of the truncated cone I now get the same result with your formula and the formula developed by c2sco. That is DT=36°C.
Many thanks for your inputs
Matt
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