Heat Radiation: Is Balance Fastest
Heat Radiation: Is Balance Fastest
(OP)
Given two identical bodies with identical amounts of heat energy, both in a vacuum, radiating their heat away.
Body #1 is of non-uniform temperature (let's presume it's hot mostly on one side and cooler on the opposite side)
Body #2 is of uniform temperature.
Which one will radiate its heat away fastest and why? Does the Stefan-Boltzmann Law explain this?
Body #1 is of non-uniform temperature (let's presume it's hot mostly on one side and cooler on the opposite side)
Body #2 is of uniform temperature.
Which one will radiate its heat away fastest and why? Does the Stefan-Boltzmann Law explain this?





RE: Heat Radiation: Is Balance Fastest
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RE: Heat Radiation: Is Balance Fastest
Do you know the answer? Do you know of an easy way to find out the answer?
RE: Heat Radiation: Is Balance Fastest
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RE: Heat Radiation: Is Balance Fastest
RE: Heat Radiation: Is Balance Fastest
This is a tricky unsteady state heat transfer situation, in which temperature is a function of both space and time.
A basic assumption would be that the heat content to be lost by both bodies is equal and radiates towards a black body absorbing all the incoming radiation.
It is generally assumed that a hot body cools down to a certain heat content level in a longer time period that the same body starting at a lower temperature.
Considering the unequally heated body, part of the heat of the hotter side would most probably be internally transmitted by conduction to its colder part.
I may be wrong, but it seems to me that when the hotter surface cools down to a certain temperature level, the total cooling effect by radiation from both of its surfaces may slow down to a pace similar to that of the original homogeneously heated body.
Thus, qualitatively speaking, the answer to PentagonJohn's question seems to be that the unequally heated body may take equal or longer periods to cool down to a given heat content level.
Please correct me if I'm wrong.
RE: Heat Radiation: Is Balance Fastest
As noted by Bribyk, body 1 will have a higher radiant heat loss per unit area of its hot portions than body 2. So what are the respective areas? How hot are they wrt each other and the surrounding environment?
Both bodies will transfer heat internally by conduction. How fast is conduction compared to the radiant loss? How big are the bodies?
So without knowing the initial conditions, the question can't be answered.
RE: Heat Radiation: Is Balance Fastest
RE: Heat Radiation: Is Balance Fastest
RE: Heat Radiation: Is Balance Fastest
For clarification, I was simply interested in heat radiating away from bodies #1 and #2.
Which one would radiate all its heat away first, as in heat bleeding off into space, or into the vacuum.
Assuming no other heat generation. The bodies start with the same amount of heat energy (one with the heat perfectly evenly distributed and everything the exact same temperature, the other with the heat unevenly distrbuted)
Assume the bodies are spherical, like planets, or soccer balls, or does it even make a difference?
I just want to know if the evenness of the distribution of the heat energy will affect the loss of heat radiated into space overall such that one radiates all its heat faster than the other.
RE: Heat Radiation: Is Balance Fastest
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RE: Heat Radiation: Is Balance Fastest
Please correct me if I'm wrong.
thanks
RE: Heat Radiation: Is Balance Fastest
RE: Heat Radiation: Is Balance Fastest
The bodies are NOT together.
Which case (case 1 or case 2) will radiate away all its heat first?
I realize the case 1 (nonuniform heat distribution) will have points that radiate heat at the fastest rate (the warmer points) but it will also have points that radiate heat away very slowly.
I'm wondering if the uniform heat distribution will lose all its heat BEFORE any non-uniformly distributed case, or if it will lose all its heat AFTER those non-uniformly distributions.
- JCP
RE: Heat Radiation: Is Balance Fastest
Analytically, the rate expression is proportional to:
{(heat - delta)4 + (heat + delta)4}/2
compared with just heat4
When you do the expansions, the terms with even powers of delta will all be positive, so the overall rate for the unbalanced case is always higher.
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RE: Heat Radiation: Is Balance Fastest
I remember having read in this forum some time ago about the comparison of cooling times between a hot cup of tea and a less hot one, both equal in all other respects.
Discarding any natural air convection effect, it seems the warmer one takes longer to cool because along the way it has to reach the temperature level of the cooler analog whose cooling time should then be added.
Any comment ?
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RE: Heat Radiation: Is Balance Fastest
QED.
RE: Heat Radiation: Is Balance Fastest
- Steve
RE: Heat Radiation: Is Balance Fastest
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RE: Heat Radiation: Is Balance Fastest
I understand that the warmest sections of the uneven distribution will, at first, be radiating at a faster *RATE* than at any point on the completely evenly distributed case, but only for as long as it takes to cool to that initial temperature of the evenly distributed case, at which point it will be that much time *BEHIND*.
We could then focus on the *COOLEST* sections of the unevenly distributed case and say that they are "ahead" in the sense of losing their heat (while admitting that they are radiating at the SLOWEST rate of all).
It would seem to me that the coolest areas of the uneven distribution would ultimately lose all their heat first, followed by the entirety of the even distribution case, followed lastly by the originally warmest sections of the uneven distribution case.
Conclusion, the even distribution case loses its all its heat within a shorter time period than that of the uneven distribution case.
Am I missing anything?
RE: Heat Radiation: Is Balance Fastest
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RE: Heat Radiation: Is Balance Fastest
RE: Heat Radiation: Is Balance Fastest
Let's say we have one copper cylinder at 50C uniform temperautre.
The other copper cylinder has non-uniform temperautre at 50C + 10C * cos(theta).
The above conditions are t=0. Clearly at t=0 the non-uniform cylinder radiates more total heat for reasons stated by Bribyk (I assume we are limited to radiation and convection is not relevant).
That is t=0. The temperature distributions will evolve in a complex manner after that but the non-uniform distribution initially has an advantage in heat radiation and I suspect it would be hard to contrive a scenario where it wouldn't win the race.
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RE: Heat Radiation: Is Balance Fastest
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