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Sleepy and tired after eating, with food in the stomach. When food is still present in the stomach and the person overeats, overeating produces a biochemical shock on the whole organism due to factors related to heavy breathing. Falling asleep and tired after eating (usually in 20-60 minutes after eating) are frequent signs of this biochemical shock. This effect of being sleepy after eating meals is much stronger after eating junk food and especially overeating (see the second half of this page for more info about this effect).
Be aware that feeling sleepy after lunch is related to digestion. The main reason why you get sleepy after lunch is because food that you eat for lunch diverts your blood away from your brain to help with the digestion process. Your body also releases a bit of melatonin after lunch, which is a hormone that helps you fall asleep at night.