Most Rishonim agree that, in principle, it is not necessary to recite the bitul ḥametz aloud. It is possible to nullify the ḥametz “in one’s heart,” i.e., to mentally regard his ḥametz 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. All poskim agree that it is not necessary to pronounce the bitul in the presence of others. Nonetheless, some people are meticulous about reciting the bitul in the presence of their family, to remind them of the mitzva.
The bitul must be sincere. One must agree in his mind that the ḥametz is null and void forever, and that he will not use it even after Pesaḥ. If one intends to use the ḥametz after Pesaḥ, the bitul is not effective, and he violates bal yera’eh and bal yimatzei. Even if he renounces ownership of his ḥametz and places it in a completely open domain, he must not intend to reclaim it after Pesaḥ, for if he does, his renunciation is not wholehearted (MB 445:18).
As mentioned above (3:4), according to the Torah, one can dispose of his ḥametz by merely nullifying it, and even if one were to keep ḥametz 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 ḥametz. However, the Sages were concerned that the bitul might not be wholehearted, so they ordained that we physically eliminate the ḥametz from the home. Be-di’avad, however, if one forgets to eliminate his ḥametz, and when Erev Pesaḥ 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 ḥametz. Even if he returns after Pesaḥ, he must remove the ḥametz, 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 ḥametz through a shali’aḥs. However, preferably the owner of the ḥametz should perform the bitul himself, as some authorities maintain that only the owner of the ḥametz has the power to nullify his ḥametz (SA 434:4; MB ad loc. 15).
. See Bedikat Ḥametz U-vi’uro 6, n. 7, which cites Responsa R. Akiva Eger that if one verbalized the declaration to make his ḥametz ownerless, it becomes ownerless, even if he did not make the declaration wholeheartedly. Thus, anyone can claim his ḥametz, and the former owner is not able to claim that he did not mean what he said. Perhaps, according to MB 445:1, in the name of SAH, although legally another individual can acquire the ḥametz, if the original owner did not nullify his ḥametz wholeheartedly, the ḥametz remains in his possession until someone else actually claims it (as opposed to becoming ownerless right away).