Lengthwise or widthwise. Which towel will dry faster? So I was putting towels on drying rack and I had extra space. Should I hang towels lengthwise to speed up drying?
If we have a standard, rectangular towel. Say like this:

Which will dry sooner?
Lengthwise:

Or widthwise:

I am leaning towards lengthwise, since the water will have more surface to dry away from, but with widthwise maybe having higher vertical difference will cause water to accumulate at the bottom of the towel and dry sooner.
 A: In both cases the contact area of the towel with air is a² (I'm considering that the back of towel is in contact with the other back when folded).
Therefore, one can expect that the exchange of water molecules with the air happens at the same rate.
However, there is one more phenomenon that should be taken into consideration which is the liquid water moving towards the bottom edges and dropping into the floor.
In the latter case, the resistance of the water is lower (because the distance to the edge is lower) for the case when it's folded lengthwise and hence the water will reach the bottom edges faster, thus drying faster.
A: If we really want to maximise the drying rate, we need to get the water out far more than we need to worry what angle it should hang at. This is particularly important if the towel is doubled over, as large towels invariably are. 
If it is  hung outside, wind direction is important, especially if we have the ability to keep the towel aligned correctly to the breeze for as long as possible.  
Like most physics problems, it's much  more subtle than it first appears.  
It depends on how much water the towel contains.


*

*Determine how much water is squeezed out of the towel, if it is still say 50 percent wet, and you don't have the means or strength to reduce this percentage, then hang it to maximise  water seepage first. This is vital to the operation.

*If you are thinking ahead, you will have drained as much water possible out first, getting  it down to 20 percent is good, then hang it in a position to maximise breeze assisted / radiator drying.

So... when do you hang it widthwise, and when lengthwise

It's the amount of water you get out of it before hanging that is important,

You say what factors are important, but you don't apply them to the situation and arrive at a conclusion. Which direction maximizes seepage? Which direction maximizes breeze-assisted drying?

Sammy raises an important point, we also need to look at how the towel fibres are aligned for maximum drainage rate.
I would also conclude that, as Sammy has kindly pointed out, I should confirm that once the mechanical release of water has been achieved, in my opinion it does not make a significant difference which orientation we choose to facilitate breeze  or radiator drying. 
The only exception I would make to that is in the case of heavy towels with a definite pattern or fibre structure which may help as channels to remove as much water as possible.
A: I'm going to assume:


*

*I have 2 towels equally wet

*Water only moves within the towel and does not drip off (or equal amounts drip off for both towel) (I want to confine the problem to a purely evaporation standpoint)

*No wind

*Equal and constant temperature environment for both towels


I hang them as such:

I'll assert that towel A dries faster:


*

*Imagine the edge case of a very very long and narrow towel (make it infinitesimally small width or string-like):

*In orientation A, there is no room for water to redistribute, all surfaces participate in evaporation. 

*In orientation B, the water redistributes within the material (due to gravity); the bottom has more water, and at the very very very top there is no water and it does not participate in evaporation. You now have a very tiny (nonzero) decrease in area that participates in evaporation.


So, I assert that A will dry faster than B. Lengthwise dries faster than widthwise.
This answer doesn't account for other possible orientations like hanging on the diagonal since it appears the question asked specifically about lengthwise versus widthwise.
A: 
Hanging it along the diagonal will maximize the surface area, but while the corners will dry faster, the thickest area with two layers will not.
A simple way to speed up the process is to flip the towel over after some time to expose the wet insides. Or using clothespins to avoid the slow drying double layer alltogether
