I doubt the 3.3V powered processor can produce exactly 3.3V when loaded by the transistor's base current. The calculation for the series base resistor must allow for the voltage drop.

The ESP32 output drive is pretty good and well above 3v when driving a 15mA load.

 

I could be calculating the base current based on the amount of current that would flow through the B-E diode at Vbe(sat), and that the base current depends only on the base-emitter diode, and the collector current depends on the base-emitter voltage.

You are still missing my point.
You don't need to calculate the resistor value needed to give a particular base current unless you are using the current-controlled model.
The voltage-control model would require only that you calculate the base-emitter voltage.

 

Greetings everyone, I have updated my schematics design and here the latest design. After listen to the advice from previous reply, I have added a flyback diode, and changes the resistor values. The question I am having now is that when calculating the resistor value for the LED, should I take into account of the voltage drop across the collector and emitter? If so what value should I take ? (Vce = 1V or Vce(sat) value?) For the calculation for the voltage across the resistor R1, the value I used is :

12V(source) - 2.5V(Voltage across the LED) - 1V ( Vce = 1V from datasheet )= 8.5V (voltage across the resistor R1)

Is there anything wrong with the calculation above? and also do I need to change/add anything for the above design?

Thanks again for people trying to teach me this newbie on the design above ! Thank you very very much!!!

 

Is there anything wrong with the calculation above? and also do I need to change/add anything for the above design?

Why are you splitting hairs and trying to have the base current be so close to a tenth of the required collector current? If you use a 510 ohm resistor, you'll have a little buffer for base current and only need one base resistor.

More base current doesn't hurt anything as long as you don't go overboard.

You could also go with a logic level N channel MOSFET instead and eliminate the base resistor. Though a conservative design might add a gate resistor (like 10k) to ground. So the MOSFET can't turn on if the ESP32 isn't driving the gate and the 12V supply is on.

 

Why three resistors at the base?
Use a single 470Ω resistor.

 

You are using the transistor as a saturated switch, not as a linear audio amplifier. Then the hFE and fairly high Vce voltage are not used with a saturated switch. Use a base current that is 1/10th the collector current and use the Vce sat voltage in your calculations.