When to Make Intention for Wudu
Question

When are we to intend for making Wudu? Is it at the beginning or while washing the face or can it be done at any time while making Wudu?
Praise be to Allah.Is intention essential for acts of worship? 
The intention (Niyyah) is essential for all acts of worship ; no act of worship – including Wudu – is valid without the intention. 
An-Nawawi (may Allah have mercy on him) said: 
“The intention is an essential condition of Wudu , Ghusl and Tayammum being valid, and there is no difference of opinion among us concerning that. This is the view of Malik, Al-Layth ibn Sa`d, Ahmad ibn Hanbal and Dawud. They quoted as evidence the words of Allah (interpretation of the meaning): 
“And they were commanded not, but that they should worship Allah, and worship none but Him Alone (abstaining from ascribing partners to Him).” [Al-Bayyinah 98:5]
Worshipping none but Allah with sincere devotion is an action of the heart; this is intention, and the command here shows that it is obligatory. 
From the Sunnah, we have the words of the Prophet (peace and blessings of Allah be upon him): “Actions are but by intentions.”  
What is meant is that the ruling on an action is based on the intention behind it. 
Another piece of evidence is the Hadith in which the Prophet (peace and blessings of Allah be upon him) said: “Every person will have but that which he intended.” If he did not intend to do Wudu then he has not done Wudu, and so on.” (Al-Majmu`, 1/356. See also Al-Mughni, 1/156)
What is the seat of the intention in Islam? 
It should be noted that the seat of the intention is the heart, and it is not prescribed to utter it out loud.
When to Make Intention for Wudu
It is better to form the intention when starting to do Wudu or shortly before, so that the intention will cover all parts of Wudu. What is obligatory is to have the intention when starting to do the obligatory parts of Wudu. 
Ibn Qudamah (may Allah have mercy on him) said in Al-Mughni, (1/159): 
“The intention must precede the entire act of purification, because it is an essential condition thereof, so it is regarded as being essential throughout. If any of the obligatory parts of the act of purification take place before the intention, they do not count. It is recommended to form the intention before washing one's hands, so that the intention will cover both the Sunnah parts of the purification and the obligatory parts. If a person washes his hands before forming the intention, he will be like one who has not washed his hand. It is permissible to form the intention shortly before purifying oneself… but if there is a long time in between, that is not sufficient.” 
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said in Ash-Sharh Al-Mumti’ (1/140): 
“The intention is either of two things: 

Either it is Sunnah, which is if it is done before a Sunnah act of purification that comes before an obligatory act’ 
Or it is required when doing the first obligatory action. End quote. 

Based on this, it is better to form the intention before starting to do Wudu, and it is obligatory to have the intention when doing the first of the obligatory actions of Wudu. The scholars differed as to which is the first obligatory action of Wudu. It was said that it is saying Bismillah , or rinsing out the mouth – which is the correct view – or washing the face. 
But if a person forms the intention with the first obligatory action of Wudu, he will not be rewarded for whatever Sunnahs of Wudu he did before that, such as saying Bismillah and washing the hands three times, as stated above in the words of Ibn Qudamah (may Allah have mercy on him).” 
Shaykh `Abd Al-`Aziz ibn Baz (may Allah have mercy on him) said: 
“It is proven from the Prophet (peace and blessings of Allah be upon him) that the first part of Wudu is to wash the hands three times, with the intention of doing Wudu, and to say Bismillah.” (Majmu` Fatawa Ash-Shaykh Ibn Baz, 10/98) 
And Allah knows best.