Convection and Radiation Heat Transfer

[karan87]

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.

 

[chicopee]

Qconv is not quiet accurate unless your pipe diameter is very large. Check heat transfer book for proper equation.

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).

 

[IRstuff]

Your narrative does not correspond to your equations. You state that there's convection from the "element" to the gas, yet, the only equation for convection is for the pipe, and not the "element."

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

FAQ731-376
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[Compositepro]

It would be difficult for the pipe to get any hotter than the outlet temperature of the gas.

 

[karan87]

I should have mentioned that the pipe is insulated. So only radation and convection inside the pipe is considered. Thanks for all the input. Appreciated

 

[chicopee]

Nothing worse than someone introducing a belated variable.

 

[vpl]

1) Is this homework?
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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[davefitz]

If the pipe OD is insulated, then you have an "adiabatic" boundary condition, so Q to environment = 0. Therefore the first law holds, and that is your 3rd equation.

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

 

[karan87]

This is not homework. I am trying to determine the effect of radiation from the heating element to the inner surface of the shell when air is being heated up. I am assuming that the pipe is perfectly insulated. This is the worst case scenario because the shell's temperature will be maximum since it cant lose any heat to the outside environment.

 

[IRstuff]

Again, you.re not making complete sense. Why is there a concernt about radiation? If you run a certain power level into the heater, then ALL of it is going into the pipe. Just what exactly are you actually trying to do overall?

Please don't give you point problem, as it may have nothing to do with what you are actually trying to do.

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[davefitz]

The rate of heat conducted along the length of the 2 pipes will be greater than the rate transferred to the gas locally- so the problem needs to be simulated on a computer model, over a long length of the pipe- it will be hottest at the element, and progressively cooler the further from the pipe .

 

[vpl]

I agree with IRStuff that the problem doesn't make sense.

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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