Most Rishonim agree that, in principle, it is not necessary to recite the bitul ĥametz aloud. It is possible to nullify the ĥametz “in one’s heart,” i.e., to mentally regard his ĥametz as null and consider it as the dust of the earth. Preferably, however, one should express the bitul verbally, because this makes it clear and explicit. Moreover, some Rishonim maintain that the bitul must indeed be pronounced aloud (see SAH 434:7). All poskim agree that it is not necessary to pronounce the bitul in the presence of others. Nonetheless, some people enhance the mitzva by reciting the bitul in the presence of their family, to remind them that there is such a mitzva.
The bitul must be sincere. One must agree in his mind that the ĥametz is null and void forever, and that he will not use it even after Pesaĥ. If one intends to use the ĥametz after Pesaĥ, the bitul is not effective, and he violates bal yera’eh and bal yimatzei. Likewise, even if one renounces ownership of his ĥametz and places it in a completely open domain, he must not intend to reclaim it after Pesaĥ, for if he does, his bitul is not wholehearted (MB 445:18).
As mentioned above (3:4), according to the Torah, one can dispose of his ĥametz by merely nullifying it, and even if one were to keep ĥametz of great value in his possession, he may nullify it and would not transgress bal yera’eh and bal yimatzei as long as he makes a firm mental commitment that the bitul is absolute and that he will never again derive benefit from the ĥametz.
However, the Sages ordained that we not rely upon the bitul alone. Rather, one must also physically remove the ĥametz from his possession. They did this because they feared that the bitul might not be performed wholeheartedly. However, if one forgets to eliminate his ĥametz, and when Erev Pesaĥ arrives he is far from his home, he may rely on the bitul alone – but as soon as he returns home he must destroy the ĥametz. Even if he returns after Pesaĥ, he must remove the ĥametz, for if he fails to remove it, he proves that his bitul was not wholehearted (SA 448:5; MB ad loc. 25).
In principle, it is possible to nullify ĥametz through a shali’aĥs. However, preferably the owner of the ĥametz should perform the bitul himself, because some authorities maintain that only the owner of the ĥametz has the power to nullify his ĥametz (SA 434:4; MB ad loc. 15).
. Bedikat Ĥametz U-vi’uro (6:4) which cites Tur §436, Ramban, Ran, and Maharam Halawa that bitul in one’s mind is sufficient. SAH (434:7 and Kuntrus Aĥaron) explains that even though these authorities believe that nonverbal nullification suffices on a Torah level, they still maintain that on a rabbinic level preferably one should nullify the ĥametz verbally. According to Ritva and Beit Yosef, based on the Yerushalmi, one must verbalize the bitul. However, SA 437:2 states: “He nullifies it in his heart and this is sufficient.” BHL 437:2 states that there are two opinions in the matter, and Gra agreed that nullification in one’s mind is sufficient. Whatever one nullifies to himself is considered hefker, as per Tosafot’s explanation that the purpose of the nullification of ĥametz is to deem it ownerless. Even though generally if one wants to declare his property ownerless he must do so in front of three others, as per rabbinic injunction, in this case the Sages deferred to the Torah standards of hefker and allowed one to make the declaration to himself.
. See Bedikat Ĥametz U-vi’uro 6, n. 7, which cites Responsa R. Akiva Eger that if one verbalized the declaration to make his ĥametz ownerless, it becomes ownerless, even if he did not make the declaration wholeheartedly. Thus, anyone can claim his ĥametz, and the former owner is not able to claim that he did not mean what he said. Perhaps, according to MB in the name of SAH, although legally another individual can acquire the ĥametz, if the original owner did not nullify his ĥametz wholeheartedly, the ĥametz remains in his possession until someone else actually claims it (as opposed to becoming ownerless right away).