How does the Eco-Cooler air conditioner really work?

Here is a simple experimentalist's answer:

a) Tin huts in the sun get extremely hot, as anybody who has left a car in the sun will know, much hotter than the outside temperature.

b) People in Bangladesh will have about the same IQ as people in other countries, therefore these tin huts will have at least two windows for a cross current in an effor to lower the inside temperature drawing the outside air in. ( I was thinking of chimneys, but these are for cooler countries). Leaving windows open is what one does to keep a car cooler in the sun.

The smart thing is to have the windows north/south, because even on windless days the south side outside the house heats more than the north, and more than inside the house : a natural convection happens between the two windows: hot air rising on the south pulling cooler air from inside the house, and the air replaced by the north window, with the cooler air of the shadow of the house.

If you watch the video there is no sun on the window used, so it must be the north side window.

This natural circulation brings the tin hut to a lower temperature but still not equal to the ambient outside air in the shadow.

The cooler, replaces the north window. What happens is that the air pulled in because of the open south window goes through the smaller openings and acts as a fan . I.e. instead of an electric fan, and everybody knows that it does not lower the room temperature, this is a passive fan, as explained in other answers.

The room as a whole will reach the same temperature as before the installation, but the people next to the cooler have the same feeling as sitting in front of a fan or using a hand fan. The video shows them next to it. In addition, the temperature next to the cooler will be the outside temperature in shadow, which is certainly lower than the one in a tin hut.

In the video they also say that how well it works depends on the wind. On a windy day convection wind currents are much stronger.

I can't rule out the possibility that it gets more comfortable inside with the "eco cooler" installed, but the explanation that they give is utter nonsense. They show a thermometer "before" and "after", but they don't tell what the "before" condition was: open window? glass panel? wooden shutter?

CuriousOne already hypothesized that it works by blocking sunlight and still admitting air. Could be. We can't tell from the video clip or article.

They offer two "explanations", which I paraphrase:

(1) "When you blow a jet of body-temperature humid air on your skin, it feels cooler than the same air volume at low speed"; (2) "As hot air passes through, the bottle neck compresses and cools the air".

The explanation for the effect in #1 is that the jet will drag dry air with it, thereby amplifying the air volume, and the high speed will lead to better evaporative cooling from the skin.

The "explanation" in #2 has several problems. First, terminology. In physics, the term "compress" refers to reducing the volume of a fixed amount of matter. If you compress a given amount of air, it will generally increase in temperature. Here, they seem to mean that the cross section of the air stream decreases along the line of the flow.

Bernoulli's principle will tell you that the accompanying velocity increase must lead to a drop in pressure, compared to the pressure in the wide part of the bottle. The pressure drop may even lead to a temperature decrease of a fraction of a centigrade. However, when the air slows down as it mixes with the indoor air, the pressure will increase again and the temperature will increase again (also by $\ll 1$ °C) as you follow the air-flow path.

How much is $\ll 1$ °C? Let's say that the highest velocity involved is $v=5$ m/s (that's a nice breeze). Bernoulli: pressure difference is $\Delta p=\rho v^2/2=16$ Pa. Adiabatic expansion of gas: $pV^\gamma=\mathrm{constant}$, with $\gamma=1.4$ a property of air. With the universal gas law ($pV=nRT$) and a first-order approximation, we can derive that the temperature drop in at the highest velocity point is $$\Delta T \approx T\frac{\Delta p}{p} \left(1 - \frac{1}{\gamma}\right).$$ With $p=10^5$ Pa as the atmospheric pressure and $T=300$ K as the absolute temperature, we get $\Delta T\approx 0.014$ K. (And even then, heat exchange between a stationary object and a high-speed gas that has a lowered temperature due to its high velocity is a difficult topic that could actually to heat transfer in the opposite direction of what you'd expect, in some cases.)

Another misconception here is the implicit assumption that the volume of air (per time unit) passing through this device is the same as if there had just been an open window. If you blow with your mouth open, your lungs need to produce less pressure than if you blow the same volume flow rate with your lips pursed. But with the wind, the available pressure is a given; placing a flow restriction in the wind can only reduce the flow rate, not increase. In the bottle necks, the air flow velocity may be slightly higher than if you had had an entirely open window, but the total volume rate of air passing through will be much smaller. How much, that depends on how the air leaves the building and of course the direction of the wind outside.