Hi,
UART can only send or receive one byte of data at a time
indeed just one single bit a time.
"Integer value" depends on microcontroller. It may be 8bit, 16 bit or 32 bit, maybe even 24 or 64 bits.
So let it be 32 bits. Signed or unsigned? Do you need the full range ?
So basically when you want to send more bytes .. you need some kind of frame .. and some kind of frame sync.
Frame sync may be bit_coded, byte_coded, or timing controlled, or you use an extra bit in the UART ( for example 9N1), or any other method.
.
Timing: send 4 bytes in a row, then wait minimum time (let´s say 50ms).
This is good when you expect a low average data rate.
For a high data rate you may use a bigger frame, maybe 64 x 4 bytes in one frame.
As said: you need frames everywhere you send more than 1 byte. And this is the usual way, thus you will find frames in almost any communcation: USB, Profibus, ModBus, Ethernet, Bluetooth, Morse, SPI, I2C, WiFi, IR remote control, every digital audio format, TV analog & digital ... you can find it everywhere.
Even this text uses spaces as "frame_sync" for words. Dots as frame sync for sentences.
New_lines for sections...
If you do an internet seach you will get many millions hits.
Klaus