# Heat Transfer between 2 control Volumes

#### DallasSE

Hey I'm new to the forums, but I could really use some help with a problem. My school does a senior design project where we design and build some prototype system. My team has a client that wants an internal cooling device through inhalation. I'm the only team member who has had experience with thermodynamics.

So I made a few assumptions to actually be able to do this:
1. Heat generated by metabolism is equal to heat lost to atmosphere.( Qmetabolism and Qloss through skin)
2. change in energy over change in time is constant (dE/dt = deltaE/delta t)

Our client wanted us to have 2 control volumes.
The lungs are control volume I and is an open system.
The body is control volume II and is a closed system.

I'm unsure about how to use Conservation of energy to find this relationship. I know what I am probably messing up is the difference in the closed and open system.

I can also give values and constants if necessary although I would prefer to do everything in symbol form first.

Any help would be greatly appreciated!

#### studiot

You don't get to arbitrarily choose the system description and thereby the control volumes in Thermodynamics.

Failure to properly include all that is going on and then specify the resulting system model is the cause of many upsets in Thermodynamics.

#### Woody

Two points spring to mind

1) The temperature difference will be important.
Body temp is pretty well fixed, Outside air temp is more variable, are you going to assume "standard" temp?

2) The majority of heat transfer from breathing is down to evaporation, are you going to include this in your model?

#### studiot

2) The majority of heat transfer from breathing is down to evaporation, are you going to include this in your model?
Have you taken into account the heat changes due to oxygen in - carbon dioxide out?

#### Woody

My guess is that it would be a small effect compared to the others,
but is it negligible?

#### studiot

Why would it be small?

You are breaking oxygen-oxygen bonds to burn a carbon compound in the body and form carbon to oxygen bonds and then adding the latent heat to turn it into a gas for exhalation.

So you are adding enthalpy with the oxygen and subtracting it with the exhalation.

The thermodynamics of biochemistry is not my scene, but I would be suprised if it were small. The power output of a human is a few hundred watts, all powered by this fire.

#### Woody

The original post related to heat transfer in the lungs,
The CO2 / O2 transfer in the lungs is from Haemoglobin "swapping" CO2 for O2.
The breaking/making of Carbon-Oxygen and Oxygen-Oxygen bonds occurs within the cells of the body, not in the lungs (any more than in any other part of the body).

#### studiot

The original post related to heat transfer in the lungs,
The CO2 / O2 transfer in the lungs is from Haemoglobin "swapping" CO2 for O2.
The breaking/making of Carbon-Oxygen and Oxygen-Oxygen bonds occurs within the cells of the body, not in the lungs (any more than in any other part of the body).
Yes, but the oxygen enters (and leaves) the body through the lungs.
When it does so it carries with it the enthalpy of the bond, as well as the energy of the motion.

Thus any thermodynamic consideration of respiration must include this energy in the balance book.

#### benit13

Hey I'm new to the forums, but I could really use some help with a problem. My school does a senior design project where we design and build some prototype system. My team has a client that wants an internal cooling device through inhalation. I'm the only team member who has had experience with thermodynamics.

So I made a few assumptions to actually be able to do this:
1. Heat generated by metabolism is equal to heat lost to atmosphere.( Qmetabolism and Qloss through skin)
2. change in energy over change in time is constant (dE/dt = deltaE/delta t)

Our client wanted us to have 2 control volumes.
The lungs are control volume I and is an open system.
The body is control volume II and is a closed system.

I'm unsure about how to use Conservation of energy to find this relationship. I know what I am probably messing up is the difference in the closed and open system.

I can also give values and constants if necessary although I would prefer to do everything in symbol form first.

Any help would be greatly appreciated!
Whenever you have a tricky problem like this, start with something very simple and then make it more complicated later after you have some solutions.

For example, the lungs can be approximated by a container with a constant temperature equal to the ambient temperature. The rest of the body can then be approximated by another container with the typical dimensions of a humanoid, which surround the first container. Since the question requires the lungs to be an open system, you'll need to track the amount of energy entering the lungs (by mass influx) and energy leaving the lungs (through mass outflux). You can make some assumptions to begin with about the inhalation and exhalation, such as, for example, constant, time-independent, net energy outflux. For the body, since it is a closed system, you can consider it as adiabatic to the outside air (no heat loss through the skin) so the only temperature exchange is between the lungs and the body. You can also assume thermal equilibrium.

Then, for the lungs, you'll have something like this:

$$\displaystyle E_{exhale} = E_{conv}$$
$$\displaystyle E_{exhale} = hA(T_{body} - T_{amb})$$

and for the body

$$\displaystyle E_{metabolism} = E_{exhale}$$

This will allow you to calculate the metabolism required to equal the net energy loss. Later, if you want, you can consider time-dependent terms and other heat transfer mechanisms (like conduction using Fourier's law).