I have build an LED array consisting of 75leds, 5 connected in series with a 39ohm-1/4watt resistor and 15 such series connected in parallel to the rectifier circuit having 2-IN5408 diodes and 1- 25V_4700µF capacitor. The transformer is 12-0-12v_3A. The leds forward voltage is 3.3v-3.4v and forward current is 60mA. As the whole fixture is for an aquarium i have to run it continously for 6 hrs and the transformer gets quite hot (cannot touch it for more than 5 secs)? Is the rectifier circuit and the transformer not adequate for running the leds?
That is not too hot. You may be able to reduce the heat with an improved rectifier, by reducing current, or using a more efficient number of LEDs in the strings.
Efficiency is mostly a function of how close the supply voltage is to the LED string's forward voltage.
You measure the DC forward voltage of the LED strings and the supply voltage.
Then select a current that gives you the desired LED intensity.
This online calculator will give you the efficiency based on the measured values.