e.g. why do we feel sleepy on our way back home in the car after dinner at grandma’s?
First, when you eat, blood in your body focuses near your digestive system, and those organs are currently working digesting the food you just ate. Due to the lack of blood flow to other parts of your body, you get that fatigued feeling. This feeling is accelerated by the fact that us sitting also screws with our blood flow, making us feel more tired. This is also why a lot of students fall asleep during the class after lunch.
For your example, you reference grandma’s house. Personally when I think of dinner at my grandmother’s house, I think of glutinously devouring food in larger quantities than I am accustomed. This increased quantity of meal signals to the brain that “hey I’ve eaten a very large meal” which triggers the digestive processes via the “rest-and-digest” part of the nervous system and the fullness part of the brain. Because this signal to the brain can be scaled with bigger meals, the input from this part of the brain is larger as well. As a result, a massive increase in blood flow and activity of the digestive system ensues. This diverts blood from other areas and promotes that sense of fatigue. In general, the “rest-and-digest” part of the nervous system dampens alertness and promotes these types of house keeping functions. While we know that the “fight-or-flight” nervous system, increases alertness and moves blood to your muscles. The “r-and-d” nervous system levels are greater than the “f-or-f” levels after a meal and thus, sleep is promoted.
TLDR; If you travel for a meal, it is generally going to be “special” and eaten in larger quantities than normal. Increased meal = increased fullness and “rest-and-digest” nervous system activation. Increased blood flow to gut promotes sleepiness and the main function your body is worried about is digesting the meal and getting all the nutrients out of it
when you’re sitting in a vehicle, you use muscles to hold yourself in a seated position, plus it’s warm so it makes it easier to fall asleep