Convection and Radiation Heat Transfer
Convection and Radiation Heat Transfer
(OP)
I am trying to calculate the inner surface temperature of a pipe in which a heating element is used to heat up natural gas. There is convective heat transfer from the element to natural gas and also radiation heat transfer from element to the pipe. I am given the temperature of the gas at which it is heated and also the element's temperature.
Qrad = e*σ*(Area of the element)*(Telement^4 - T_pipe^4)
Qconv = h*(Area of the pipe)*(T_pipe - Tgas)
I have 2 equations and 3 unknowns (Qrad, Qconv and T_pipe). How can I solve this? I am sure I need to use iterations.
Qrad = e*σ*(Area of the element)*(Telement^4 - T_pipe^4)
Qconv = h*(Area of the pipe)*(T_pipe - Tgas)
I have 2 equations and 3 unknowns (Qrad, Qconv and T_pipe). How can I solve this? I am sure I need to use iterations.





RE: Convection and Radiation Heat Transfer
Qinput from heating element = Energy increase of gas + Qloss thru pipe wall(=convective inside and outside pipe+ conductive heat transfer thru pipe which is probably negligble + radiant heat transfer inside and outside pipe).
RE: Convection and Radiation Heat Transfer
Your unknowns are not necessarily correct. You presumably know the amount of power supplied to the element. THAT power MUST equal all the heat transferred from the element, so Qrad+Qconv = Heater power.
TTFN
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RE: Convection and Radiation Heat Transfer
RE: Convection and Radiation Heat Transfer
RE: Convection and Radiation Heat Transfer
RE: Convection and Radiation Heat Transfer
2) What else haven't we been told?
3) How perfect is the insulation -- if it's a real-life problem, then how thick is it and what is it made of?
4) Are there any timers/ thermostats/ feedback mechanisms on the heating element that turns it off?
5) Are you trying to do a time-dependent study?
Patricia Lougheed
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RE: Convection and Radiation Heat Transfer
There is also heat transferred from the hot outer pipe to the gas, and there is also heat absorbed by the gas due to its radiative absorptivity
RE: Convection and Radiation Heat Transfer
RE: Convection and Radiation Heat Transfer
Please don't give you point problem, as it may have nothing to do with what you are actually trying to do.
TTFN
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RE: Convection and Radiation Heat Transfer
RE: Convection and Radiation Heat Transfer
If the pipe, heater and gas is a closed system and the pipe is perfectly insulated (which is unrealistic) then the heat added by the heater has nowhere to go except into the gas and pipe. However, I don't know if it's a closed system, because that hasn't been stated.
I don't know that we can assume that there is a "long length of pipe" as that wasn't stated. Conversely, if there is a "long length of pipe," the OP hasn't stated at what point he/she wants to measure the temperature (as davefitz points out the pipe temperature will be dependent on the distance from the heater.)
I don't know whether the OP is looking at solving a transient problem or not. Although I previously asked that question, it wasn't answered.
How can the OP expect to get a serious answer to "how can I solve this?" when there is so much information missing?
Which leads me back to suspecting that this is some sort of a school problem where the OP has been given certain parameters and told to solve a problem.
Patricia Lougheed
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