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Old Sep 26th 2018, 03:06 AM   #1
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Heat loss within a control volume

Hello,

I have the following problem:
I got an electrical component within a chamber and the chamber has an opening, where air can be supplied from and an outlet. Attached you can see an illustration of the problem.
  • The electrical component has a heat loss of 150 W
  • The temperature at the Inlet is known, to be lets say $\displaystyle T_1 = 30°C / 303 K $
  • The volume of the chamber is $\displaystyle V =0.014 m³$
  • The surface area of the eletctrical component is $\displaystyle A = 0.37 m² $

What I want to know is:
  • What is the temperature inside the chamber?
  • Also, what is the temperature at the outlet? Can it be assumed, that it has the same temperature as the chamber?
  • At the end I would like to determine, which mass flow I need, to keep the temperature in the chamber below 70 °C

The first thing I attempted by calculating the mass flow with the use of
$\displaystyle Q = \alpha A (T_{surface} - T_1 ) $
where I can rewrite the equation to the mass flow by rewriting the heat transfer coefficient alpha with the Nusselt correlation. Furthermore, in order to solve for the mass flow rate I assumed the surface temperature to be 70°C as this is my maximum.

Is this the correct way to solve it or do I have to consider something else as well?

I also had an attempt to set up the energy balance by
$\displaystyle E_{in} = E_{out}$
$\displaystyle W_{in, electrical} + m h_1 = \alpha A (T_2 - T_1) + m h_2$
thus, $\displaystyle T_2 = W_{in, electrical} / (\alpha A + m c_p) + T_1 $
which I can calculate for different mass flow rates. I assumed to be the surface temperature equal to $\displaystyle T_2$
I think, that there is a mistake in this equation but do not know exactly how to set it up differently.

*The Q, W and m are all rate thus they should be seen with a point above them (don´t know how to insert it)

I have also made the assumption to keep it simple at first to just consider convection - can that assumption be made?


I hope it is clear.
Thanks for the help in advance!
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Heat loss within a control volume-schematic.png  
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Old Sep 27th 2018, 04:55 AM   #2
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let's assume isolated walls e a VC surrounding all the chamber:

For steady state and using the lumped formulation of 1st law of thermodynamics:

$\displaystyle 0=\dot{Q}_{gen}+\dot{m}_{in}h_{in}-\dot{m}_{out}h_{out}$

For $\displaystyle \dot{m}_{in}=\dot{m}_{out}$

$\displaystyle \dot{Q}_{gen}=\dot{m}\Delta h$

$\displaystyle \dot{Q}_{gen}=\dot{m}\Delta h$

Assuming constant pressure:

$\displaystyle \dot{Q}_{gen}=\dot{m}c_p\Delta T$

and now you can calculate $\displaystyle T_{out}$

In this problem, in general, its temperature profile is in the form T (t, x, y). I'm not sure how deep is this problem, but it's possible to assume $\displaystyle T_{chamber}=T_{out}$

You could calculate Prandt and Reynolds to find Nusselt and use external flow approach but i don't how deep is your problem
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Last edited by mscfd; Sep 27th 2018 at 10:12 AM.
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Old Sep 27th 2018, 07:40 AM   #3
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We have heat output 150W .... input air temp 30C ... what will be the air output temp at different flow rates???

specific heat of air is close to 1 J/gmC

so for an output temp of 50C ... 150/20 = 7.5 liters /sec

............ output temp of 40C ......... 15 liters /sec

These are quiet modest air flow rates ........... you haven't given the diameters of the inlet and outlet holes ...

I would just buy a computer fan to suit the hole size ... measure the outlet temp .. the flow will be so fast it won't be above 50C and will keep your component plenty cool ..



this one costs $1 inc delivery , eBay ... will suit a hole 35mm dia
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Old Oct 8th 2018, 03:45 AM   #4
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Thanks for the answers!
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