I am having a difficulty understanding some mechanism regarding heat generation from an electronic PCB (Printed Circuit Board) and its effect on atmospheric temperature.
I don't know if this question is related to This forum or its related to Physics, but I am going to post it here as my concern is regarding Electronic PCB.
Please bear with me on this long question.
A PCB with specifications:
- Surface mount-multi layered with few through-hole components (capacitor, LCD etc).
- The circuit designed on it consists of Capacitors, Resistors, EEPROM, 3.3 V regulators, RC Power Supply circuit, LCD, MCU etc.
- Area = 66 cm^2 Power Dissipation in the circuit on PCB = 0.44 W to 1.0 W, typically 0.5 W
- No heat sink, or specific heat generating components.
- The circuit is operated on 3.3Vdc
- Enclosed in a Box of volume 1007.8 cm^3.
- The box has holes (where wires are passed to PCB) that can accommodate air flow easily.
I want to find:
- The temperature rise of PCB when it consumes 0.5 W power.
- The temperature rise of air inside the box because of heat transfer from PCB and time.
- Time to reach equilibrium when PCB surface and air inside the box are at the same temperature.
Note: I don't want to go into details or very deep into the design (as I have seen some designer do the very complex and detailed calculation for these purposes). I only need to find the general idea about the heat transfer of this topology. For that, if it's easy, you can assume that PCB is just a heat generating surface (amount of heat can be calculated from power).
Now, I came this far,(this work was done by someone else on this forum)
- The copper side with the traces is modeled as a sheet of copper rather than traces.
- The body is thin enough that thermal conductivity within the body is unimportant, and the entire device is considered to be at a uniform temperature.
- Only the two broad surfaces contribute to the heat loss, the sides are neglected.
- The surroundings, including the air and radiative syncs, are at a uniform temperature Ts
- Thermal coefficients: ϵcu=0.78, ϵpcb=0.50, hup=7.25 W/m2K, hdown=3.63 W/m2K Under these assumptions, we can estimate the temperature of the board by simply equating heat flows.
The heat coming in per unit time is from Joule heating from the current running through the copper and is given by qin=I2R = Power Dissipated
The heat flowing out has two escape mechanisms; radiative heat transfer to the surroundings which is given by
qrad=ϵσA(T^4 − T^4 * s) Here, ϵ = ϵcu +ϵpcb
and convective heat transfer to the air which is given by
qconv=hA(T−Ts) Here, h = hup + hdown
Now we just equate the heat flows
we can rearrange this to look like a quartic equation
σ(ϵcu+ϵpcb)T^4 +(hu+hd)T−[I2RA+σ(ϵcu+ϵpcb)T^4 *s+(hu+hd)Ts]=0
From here, I calculated the temperature of the PCB surface to be 28.9 degrees Celcius, assuming the temperature of the air inside the box to be 25 degree Celsius.
- Have I done it correctly? if not please tell me the reason (cause I am not confident about this).
- If its ok, how do I find the temperature rise of inside the box and the time it will take to raise that temperature?
- Will air inside the box and PCB surface ever be at equilibrium and at what temperature and what time will it take to reach that state?
I know this is a mess, but I can't find any help regarding this specific problem, I tried other methods and tricks but the results are far too much wrong that even I know they are not right (one such example; temperature cam out to be 300-degree Celsius).
Please give me the directions to how to approach this (as I am fresh electrical engineer and don't know about heating, thermodynamics of this level).