How should a passenger on an airplane do wudoo’ if there is no water?

In the cases that you describe, wudoo’ is not possible or is difficult. Allaah says (interpretation of the meaning):

“and has not laid upon you in religion any hardship” [al-Hajj 22:78]

So the passenger should do tayammum using the chairs of the airplane, if there is dust there. If there is no dust, then he should pray even if he is not taahir, because he is unable to purify himself. Allaah says (interpretation of the meaning):

“So keep your duty to Allaah and fear Him as much as you can” [al-Taghaabun 64:16]  

But if it is possible that you will land in the airport before the end of the time of the second of two prayers that may be joined together, then he should delay it, i.e., he should have the intention of joining the prayers and praying at the later time. Then he should pray both prayers when he lands at the airport. But if that is not possible, e.g. it is already the time for the latter of two prayers that may be joined, or it is a prayer which cannot be joined to the following prayer – such as ‘Asr and Maghrib, or ‘Ishaa’ and Fajr, or Fajr and Zuhr – then he should pray that according to his circumstances.