Ruling on reciting al-Faatihah out loud then reciting the surah that comes after it quietly, in the same rak‘ah

Firstly: 

It is prescribed for the worshipper to recite al-Faatihah quietly in prayers where it is to be recited quietly, and to recite it out loud in prayers where it is to be recited out loud. 

Al-Bukhaari (772) and Muslim (396) narrated that Abu Hurayrah (may Allah be pleased with him) said: In every prayer you should recite. What the Messenger of Allah (blessings and peace of Allah be upon him) made us hear we make you hear, and what he recited quietly we recite quietly. 

So if a person prays and recites quietly where recitation is to be done quietly and he recites out loud where recitation is to be done out loud, then he has complied with the Sunnah. If he recites quietly in places where recitation is to be done out loud, or he recites out loud in places where recitation is to be done quietly, if that was done for a valid reason, then there is nothing wrong with it. But if he did that deliberately with no need for it, then he has gone against the Sunnah, although his prayer is still valid. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: 

Is it stipulated that recitation should be done out loud in all the prayers where it is to be done out loud? What is the ruling if a person recites out loud in the first rak‘ah and recites quietly in the second? 

Reciting quietly when prescribed to do so and reciting out loud when it is prescribed to do so in the prayer is Sunnah, and is not obligatory. Rather what is obligatory is to recite, because the Prophet (blessings and peace of Allah be upon him) said: “There is no prayer for the one who does not recite the Essence of the Book (i.e., al-Faatihah).” 

So if a person recites out loud in places where recitation should be done quietly, or he recites quietly in places where recitation should be done out loud:

if his intention was to go against the Sunnah, then undoubtedly this is haraam and very serious. 

But if it was for some other reason that required reciting quietly or out loud – and we cannot list all the circumstances in which that may be required – then there is nothing wrong with that. 

in fact if he deliberately did not recite quietly in places where recitation is to be done quietly, or he did not recite out loud in places where recitation is to be done out loud, and his intention was not to turn away from the Sunnah or forsake it, then he is not sinning, but he has missed out on the reward. 

End quote from Fataawa Noor ‘ala ad-Darb (8/2) 

It makes no difference in that regard if he recites out loud in one rak‘ah and recites quietly in another, as mentioned in the question, or if he combines reciting out loud and quietly in a single rak‘ah. 

However he should not do that all the time, or do it a great deal. Rather what he should do is pray as the Messenger of Allah (blessings and peace of Allah be upon him) prayed, in general terms. But if he does that sometimes, there is nothing wrong with it, in sha Allah, as stated above. 

Please see the answer to question no. 174660 

Secondly: 

If the worshipper is praying behind an imam, then he should not recite out loud so as not to disturb other worshippers with his loud recitation. Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

With regard to those who are praying behind an imam, they should not recite out loud because that will disturb others. The Prophet (blessings and peace of Allah be upon him) came out to his companions when they were reciting out loud, and he (blessings and peace of Allah be upon him) said: “Do not recite the Qur’an out loud, drowning out one another’s voices.” Because reciting out loud disturbs others, he told them not to do that.

End quote from Fataawa Noor ‘ala ad-Darb (8/2) 

For more information, please see also the answer to question no. 67672.

And Allah knows best.