What was the story of death of Ali Akbar?

After the morning prayer on 10 October, both parties took up battle positions. Husayn appointed Zuhayr ibn Qayn to command the right flank of his army, Habib ibn Muzahir to command the left flank, and his half-brother Abbas as the standard bearer. Husayn's companions, according to most accounts, numbered thirty-two horsemen and forty infantrymen; although forty-five horsemen and one hundred foot-soldiers, or a total of a few hundred men have been reported by some sources.] Ibn Sa's army totaled 4,000. According to the Shi'a sources, however, more troops had joined Ibn Sa'd in the preceding days, swelling his army to 30,000 strong. The ditch containing wood were set alight. Hussain then delivered a speech to his opponents reminding them of his status as Muhammad's grandson and reproaching them for inviting and then abandoning him. He asked to be allowed to leave. He was told that first, he had to submit to Yazid's authority, which he refused to do. Husayn's speech moved Al-Hurr ibn Yazid Al-Tamimi to defect to his side.

The al-Abbas Mosque in Karbala

After Husayn's speech, Zuhayr ibn Qayn attempted to dissuade Ibn Sa's soldiers from killing Hussain, but in vain. Ibn Sa's army fired several volleys of arrows. This was followed by duels in which several of Husayn's companions were slain. The right-wing of the Kufans, led by Amr ibn al-Hajjaj, attacked Husayn's force, but was repulsed. Hand-to-hand fighting paused and further volleys of arrows were exchanged. Shemr, who commanded the left wing of the Umayyad army, launched an attack, but after losses on both sides,
he was repulsed. This was followed by cavalry attacks. Husayn's cavalry resisted fiercely and Ibn Sa'd brought in armored cavalry and five hundred archers. After their horses were wounded by arrows, Husayn's cavalrymen dismounted and fought on foot.

Since Umayyad forces could approach Husayn's army from the front only, Ibn Sa'd ordered the tents to be burned. All except the one which Husayn and his family were using were set on fire. Shemr wanted to burn that one too, but was prevented by his companions. The plan backfired and flames hindered the Umayyad advance for a while. After noon prayers, Husayn's companions were encircled, and almost all of them were killed. Husayn's relatives, who had not taken part in the fighting so far, joined the battle. Husayn's son Ali Akbar was killed; then Husayn's half-brothers, including Abbas, and the sons of Aqil ibn Abi Talib, Jafar ibn Abi Talib and Hasan ibn Ali were slain. The account of Abbas' death is not given in the primary sources, al-Tabari and Baladhuri, but a prominent Shi'a theologian Shaykh Al-Mufid states in his account in Kitab al-Irshad that Abbas went to the river together with Husayn but became separated, was surrounded, and killed. At some point, a young child of Hussain's, who was sitting on his lap, was hit by an arrow and died.