Often around 2:00 p.m. after eating, my body falls tired. So I have to stop studying. I am myself a long term meditator, but I rarely meditate when I am tired. Is meditation a good substitute for sleep? In other words, around 2:00 p.m., if I am going to meditate mindfully for an hour instead of sleeping, will this meditation be able to replace sleep?
Often around 2:00 p.m. after eating, my body falls tired.
Might be a good idea to investigate and tackle the root cause to your tiredness first. Is it because you don't get enough sleep at night? or you usually eat a big lunch? or the workload is too stressful?...etc. It's actually not a bad idea to take a brief afternoon nap for 20-30 minutes to recharge your battery so you can come back to work all fresh and ready. Anyway, you should listen closely to your body. Try test it out/experiment with both of them, and see how your body reacts..
Meditation may result in you needing to sleep less, but it's not going to replace sleep. To give you an example, at sesshin, we'll meditate for 10-15 hours a day. By about the third day, not only am I well rested after about four hours of sleep, but I actually have trouble sleeping due to an increase in energy. In fact, one guy in our sangha spends his nights knitting; sleep for him becomes pretty much optional.
In normal, non-retreat life, if you're sitting 2-3 hours a day, you might be able to get away with an hour or so less sleep per night. What meditation won't do, however, is combat grogginess or those deep, thick, syrupy sleepy feelings that one has after a heavy meal. When those come, if you try to sit, you're just going to fall asleep on the cushion. You're much better off taking a quick nap.
Venerable Mahāmoggallāna struggled with drowsiness and the Buddha provided a list of suggestions laid out in AN7.61:
AN7.61:1.3: Now at that time, in the land of the Magadhans near Kallavāḷamutta Village, Venerable Mahāmoggallāna was nodding off while meditating. ...
AN7.61:2.3: “So, Moggallāna, don’t focus on or cultivate the perception that you were meditating on when you fell drowsy. ...
Many suggestions later, the last suggestion is to essentially take a nap.
AN7.61:9.1: But what if that doesn’t work? Then lie down in the lion’s posture—on the right side, placing one foot on top of the other—mindful and aware, and focused on the time of getting up.
In my own exploration of the escape from drowsiness, I've observed that physical activity (i.e., rousing energy) works remarkably well. Gentle chores such as housework and gardening alleviate mental burden while promoting circulation while also allowing digestion to proceed without competing with the brain for energy. Non-repetitive physical activity is best right after a meal, since stillness and repetitive activity lead to sleepiness.