If I understand correctly it is like an interior courtyard. I don’t see how you can add it to a house unless you build more house around a central open space. Easier to build a covered patio and add shades to block sun. My shades come down ¾ so air still travels through below the shades.
North side of the house would usually be the coolest. My current patio is southwest, but mostly west, so it is horribly hot in the early evening, but the shades work really well to reduce the heat. On the southern side I only have a small area and I put solar screen on the upper part, which works great to block a good portion of the heat of the sun. The entire patio is screened.