# Temperature drop in the interface between air and plane surface

I’ve searched a lot but I couldn’t find any answer. What is the reason behind the temperature drop between the air-surface interface? Why isn’t it just like: And what even causes this drop to be non-uniform? Is there any equation related to calculating the gradient before or after the plane surface?

It depends on the modes of heat transfer.

The glass is solid, so it experiences thermal conduction, which has a linear relationship between temperature and distance in 1D; that's why it has a straight slope for the glass.

The air is a fluid, and is able to flow, so it is modeled with convection. This is either due to forced air movement (such as wind or a fan) or natural convection due to density, temperature, and buoyancy. Convection doesn't require a linear relationship between distance and temperature, because it is a complex dynamic process, that is one reason why the line is not straight, as it is with glass.

You will also notice that right near both sides of the glass, it starts off with a different, varying slope. As Pieter mentioned in his answer, this is the boundary layer where the flow is restricted, and therefore the heat transfer through convection is restricted in the circled area. Since convective heat transfer depends on flow rate, as you get out of the boundary layer, the heat transfer becomes approximately constant again.

Where it levels off would be the "surroundings" of the problem, where they assume the air is well mixed and the effect of distance from the glass on temperature is negligible.

• So just to make sure I got it right, viscosity of the fluid changes in the boundary which in turn affects the coefficient of convection, so the temperature difference changes accordingly to keep the heat flux a constant right? – user3407319 Oct 31 '19 at 13:01
• It’s not that viscosity changes, it’s that viscosity causes the boundary layer where the airflow is to be restricted because it “sticks” to the glass. Has to do with the no-slip condition. – JMac Oct 31 '19 at 14:44
• so it’s velocity that changes? – user3407319 Oct 31 '19 at 14:53
• Yup, that’s what causes lower heat transfer there. – JMac Oct 31 '19 at 15:08

The thermal conductivity of glass is much higher than of stagnant air.

The temperature gradient is not linear because the viscosity of the air creates a boundary layer.

You will have noticed that the inside surface of a single-pane glass window in the winter has a much lower temperature than that of the air in the room.

Both the temperature and the heat flux must be continuous at the interface. If the heat flux were not continuous, energy would be rapidly accumulating or depleting without bound at the zero-mass interface, which would be impossible. Since the heat flux is continuous, the product of thermal conductivity and temperature gradient must be the same at all times on the two sides of the interface. So there has to be a temperature gradient within the air boundary layer.