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!