Apply for a cluster for scientific computing from a developing country for academic use?
This doesn't quite answer the question, but in case you have some funds available (but not enough to buy a cluster): Various cloud services - Amazon in particular but probably others - will let you "spin up" a temporary compute cluster on their servers. You pay for this by the minute, or sometimes by more complicated systems where the price is according to demand.

For small projects this approach can be quite economical, and so may be feasible in some circumstances where access to a dedicated system is unaffordable.