Why do the humans become sleepy after meals?
The name used frequently for this phenomenon is "Post-lunch dip".

"The post-lunch dip is a real phenomenon that can occur even when the individual has had no lunch and is unaware of the time of day. This dip has its roots in human biology, and may be linked to the size of the 12-hour harmonic in the circadian system. It is certainly exacerbated by a high-carbohydrate lunch, and may be more likely to occur in extreme morning-type individuals."

PubMed Source

Another PubMed source
"The 'post-lunch' dip is a bi-circadian phenomenon, largely unrelated to lunch, and worsened by a disturbed prior night's sleep. Despite anecdotal claims of adverse effects of larger lunches on afternoon driving ability, there is little actual driving data to support this belief."

For other reading and research...