Coefficient of molecular diffusivity for hot air within room temperature air

[Stephen1234]

Hi,

I have to calculate the Peclet number for a room. This room can be assumed to be at room temperature, and has a heat source within it which causes a temperature difference between the air near it, and the general room temperature. I have been unable to find an equation which will allow me to calculate the coefficient of molecular diffusivity for this scenario - Where the gases are the same, but the temperature is different.

I would really appreciate any help anyone could offer!

Many thanks in advance,

Stephen

Edit:

I have realized that i have not shown what work i have done to validate any help. I have found several equations which calculate the coefficient of diffusion, but none of these allow for a change in temperature between the two fluids.

I have used the Wilke-Chang equation to calculate the coefficient diffusivity for brine and water, and have calculated the Peclet number for this. To enable a 'simulation', i have to match the peclet numbers of the brine and water experiment, with room temperature air and hot air in a room.

The Wilke-Chang equation will not allow for a change in temperature:
k = 7.4 E^-8 * [ ((x * M)^0.5) * T] / [rho * V ^0.6]

where x = effective molecular weight of solvent
M = solvent molecular weight
T = System temp
V = Solute molal volume
rho = solvent dynamic viscosity

other equations include the Chapman - Enskog theory, Ficks law, however like the Wilke-Chang equation, it does not allow for different temperatures. This is my first post on physicsforums, and i apologise if my post is not to the standard that is acceptable. If any of you have suggestions on how i could improve the post, please let me know for the future.

At this point, i think its important to point out that this is not a homework assignment as such, I am 6 weeks in on a PhD, and have had no success in finding an equation which could do what i need.

I would really appreciate any help at all,

Many thanks,

Stephen

 

[KataKoniK]

Hi Stephen,

Calculating the Peclet number for a room with a heat source can be a bit tricky since the temperature difference is not constant throughout the room. However, there are a few equations that you can use to estimate the coefficient of molecular diffusivity for this scenario. One approach is to use the Lewis number, which is the ratio of thermal diffusivity to molecular diffusivity. The Lewis number can be calculated using the following equation:

Le = α/ D

where α is the thermal diffusivity and D is the molecular diffusivity. The thermal diffusivity can be estimated using the following equation:

α = k / (ρ * Cp)

where k is the thermal conductivity, ρ is the density, and Cp is the specific heat capacity.

Once you have the Lewis number, you can use it to estimate the molecular diffusivity using the following equation:

D = α / Le

This will give you an estimated value for the coefficient of molecular diffusivity for your scenario. Keep in mind that this is just an estimation and may not be completely accurate. Other factors such as air flow and turbulence may also affect the Peclet number in your room.

I hope this helps and good luck with your research! Let me know if you have any other questions or if this approach works for you.