Heat Transfer in glass pane windows

[Gohar Shoukat]

If the temperature of the wall is homogeneous i.e. the entire wall has the same temperature: T1 being the temperature of the left wall and T2 being the temp of the right wall, how will heat transfer take place? Can convection occur here? If yes then how will the bulk motion be set up?

I am attaching a picture of a glass pane window for clarification.

 

[MexChemE]

Assuming the left wall is the inner side (x = 0) and the right wall is the one in contact with the outside (x = 10 mm), heat conduction will occur from left to right, you can model this with Fourier's law. Then, you can model convection heat transfer from the glass to the outside air as a boundary condition for heat flux:
$$q'' |_{x=10mm} = \left. -k \frac{dT}{dx} \right|_{x=10mm} = h(T_2 - T_{\infty})$$
Where h is the heat transfer coefficient for your system and T_∞ is the temperature of the ambient air outside.

 

[Gohar Shoukat]

Assuming the left wall is the inner side (x = 0) and the right wall is the one in contact with the outside (x = 10 mm), heat conduction will occur from left to right, you can model this with Fourier's law. Then, you can model convection heat transfer from the glass to the outside air as a boundary condition for heat flux:
$$q'' |_{x=10mm} = \left. -k \frac{dT}{dx} \right|_{x=10mm} = h(T_2 - T_{\infty})$$
Where h is the heat transfer coefficient for your system and T_∞ is the temperature of the ambient air outside.

thank you for your reply. I might not have fully defined the problem, it is air in between the two walls. The question therefore is, is convection possible or is conduction the only means of heat transfer through the air in between the two walls

 

[anorlunda]

The question therefore is, is convection possible or is conduction the only means of heat transfer through the air in between the two walls

Radiation is one means of heat transfer between the walls. If there is air in the middle and the air can move, then convection can happen, yes. If there is a solid connection between the walls, or if the gas in the middle can't move, heat can flow through the solid or gas too; that would be conduction.

Does it make a difference to you if the mechanism is radiant, convection, or conduction?

 

[MexChemE]

thank you for your reply. I might not have fully defined the problem, it is air in between the two walls. The question therefore is, is convection possible or is conduction the only means of heat transfer through the air in between the two walls

Of course, free convection of air will happen in the space between the two walls, but it won't have an effect on the heat transfer model, at least not in the x direction. It will still be just conduction. That is, at least at the level of BSL. You can, however, model the movement of air inside the middle space due to free convection, the temperature profile will have an effect on the velocity profile of air. You will find what you're looking for in section 10.9 of the second edition of Transport Phenomena by BSL.

 

[Gohar Shoukat]

at least not in the x direction

How will convection be setup when the walls have the same temperature at the top and the bottom? the air next to the right wall will have the same temperature at the top and the bottom, hence , density difference is virtually non-existent. or am i missing something?

 

[MexChemE]

How will convection be setup when the walls have the same temperature at the top and the bottom? the air next to the right wall will have the same temperature at the top and the bottom, hence , density difference is virtually non-existent. or am i missing something?

As you move away from the hotter wall, density increases. This density difference will make the air start moving, and a laminar convection current will form inside the space. Both the physics and the modelling of the problem are discussed in more detail in the book I mentioned.

Sorry for the late reply. It has been a tough semester.