How does the area of an open window affect airflow? This question stems from a disagreement between me and my girlfriend. During the hot summer months, we like to open up the windows during the early morning to cool down our flat a bit.
One of us thinks that every window should be opened fully, since that will ensure maximum airflow, the oter swears that the actual area of open window is not a huge factor. We both agree though, that at least in most situations, opening the windows fully is the best option; the question is rather.
All other things being equal, how will doubling the area of one open window affect the airflow in a flat?
If it helps at all, we typically also have a fan or two running in the flat and we have windows at opposite ends of the flat, which are all open.
 A: If the window is open just a crack, and then you open it wider, you expect this to make a difference.
As the window gets larger the difference becomes less significant - and depends on whether it is diffusion or convection that is cause the cooling of air.
Diffusion (no wind) depends directly on surface area: twice the area, twice the diffusion. For convection, the resistance to air flow of an orifice scales roughly with circumference divided by area - so the bigger window will still be better.
Anything you can do to improve airflow will help - make sure the fans are working with the wind, not against it.
A: First of all, put the fan in one window, set to force air to exit.  This is by far the most efficient way to enhance airflow.  (if there's a breeze already, make sure the fan's in the window the breeze is blowing outwards :-) ).
If there's no wind outside and  no fans running, then the size of the window opening is relatively unimportant, as only some convection due to temperature differences takes place.  It should be obvious that, with a fan in the window,  a larger fan will have a greater CFM (cubic feet/minute, or the equivalent in metric units) flow rating.
A: Nice argument, 
Why does opening windows in early morning reduce temperature? 
Every human body needs energy to survive. That energy is covered into heat while doing work or for the operation of internal organs. For example carbohydrates in our body burn with oxygen and give heat and carbon dioxide. If we do not open the windows, that heat will stagnate inside the room, because room walls are good insulators. We know that heat always flows from high temperature to low temperature. Since during night or early morning sun is not heating the atmosphere, the temperature starts decreasing. But in the room, we are acting as a heat source, so we feel hotness inside the room and feel chillness outside the room. 
Three major kinds of heat transfer are conduction, convection, and radiation. Among them, convection heat transfer dominates in this process. The equation for convection heat transfer is:
$$q = h_c A dT $$
where
$q$ = heat transferred per unit time 
$A$ = heat transfer area of the surface 
$h_c$= convective heat transfer coefficient of the process 
$dT$ = temperature difference between the surface and the bulk fluid 
This convection heat transfer will be more if there is relative motion between body and fluid. (This is because of velocity $\propto$ Reynolds number, Reynolds number $\propto$ square of the Nusselt number and Nusselt number $\propto  h_c$ )
If we open the windows because of air current velocity and turbulence of air inside the room will increase and lead to high heat transfer rate. Please note that the same principle can be applied to fan also.
From the above discussion, we know that heat transfer rate increases with increases with increase in velocity, increase in turbulence, increase in surface area and mass flow rate etc.
Will doubling the windows size will increase heat transfer rate?
The velocity of air in windows most of the time equal to or less than the velocity atmospheric wind velocity, because of losses in kinetic energy of air due to rectangle like "cut" design of windows. If we make smooth diverging  or converging windows like wind-tunnel velocity will decrease or increase. For the shake lets assume velocity of air next to windows in same as wind outside. If we increase the area this wind velocity will not affect much because these windows are not designed like rocket nozzles!, but affect mass flow rate. Because mass flow rate increases when area is increased. Mass flow rate is calculated from $\dot m = \rho A V$ Here $\rho$ is density $A$ is area of window normal to velocity and $V$ is velocity of air. As already we discussed the heat transfer rate will increase with increase in mass flow rate and mass flow rate increase with increase with increase in area so doubling windows size will increase heat transfer rate. Please note that heat transfer will cool the body if external temperature is less than the body temperature and vice verse. Now you may ask one question, why even during summer we are using fan to reduce our body temperature? Is this concept violates second law (direction of flow of heat)?. I think we need one separate post to discuss those things.Because that involves more physics and little mathematics, already this answer is too big for this question ! 
