I am looking for a way to mount a window fan like this one in my apartment. The only windows my unit has measure 70" x 58" (H x W) with 29" wide slider panel which opens horizontally. This is too tall to mount most window fans as the extenders don't usually stretch past 3-4'.
Window fans and window air conditioners seem to be almost universally designed to work with single-hung or double-hung windows -- that is, windows in which a sliding sash moves up and down rather than sideways. Installing one of these in a horizontal window will be a fight from the moment you open the box.
The first thing is to prevent the sash sliding sideways (opening) any further than needed to accommodate the fan. The same techniques that prevent a burglar forcing entry by sliding the window work here: a wood dowel in the sliding track, a clamp to the window frame, etc.
Assuming the fan rests at the bottom of the opening, the second thing is to block the space above the fan. Depending on your requirements for security, aesthetics, air sealing, and weather resistance you might choose acrylic or polycarbonate sheet, plywood, or even cardboard. A foam gasket around the sheet can improve the weather seal. Whatever the material it'll need to be trimmed to fit. Shims or a narrow block of wood on the fixed side and top of the frame can help to hold the sheet in place. The side that interfaces with the window sash is difficult: a person could make or find some kind of U- or H-profile channel that fits nicely around the edge of the sash, but it might just be too much trouble.