# Environment-resistor temperature

• posted

Hello to everybody, first of all sorry for my English (I'm Italian).

I have a circuit, enclosed in a plastic box, where there is power resistor 1K, 50W and Tmax=200 degrees centigrade. On the resistor is not present any heat sink.

After few hours that the circuit is working, the temperature measured on the case of the resistor (Tr) reaches 110 degrees, in a environmental temperature (Te) of 20 degrees.

My boss says that if Te increases50 degrees (Te = 20+50 =70 degrees), Tr will increase the same value (Tr = 110+50 = 160 degrees).

I would say that Tr will increase, but not so much, just a little bit. In my opinion it will be reduced the time for the resistor of reaching the maximum value.

Is my boss right? Am I right? Are we both wrong?

Massimo

• posted

well... to be honest he is not an engineer, I'm an engineer.. I am deeply ashamed...

• posted

distrust an engineer so easily, (that's what I

I suspect that the approximation attributed to Massimo's boss is the most useful one to be made. However, it must be recognized as nothing more than an approximation. The heat loss mechanisms do not have an inherently linear relationship between heat flow and temperature differences. For example, convection loss partially depends on radiation which varies with the 4th power of absolute temperature. Chimney effect can cause more air flow and thinner boundary layers through which the heat must flow for convection cooling.

```--
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com```
• posted

distrust an engineer so easily, (that's what I

Should be: total heat loss partially depends on radiation which

```--
--Larry Brasfield
email: donotspam_larry_brasfield@hotmail.com```
• posted

About the most I can say is that Tr will not rise more than Te does, though it is possible that Tr will rise almost as much as Te does. At low temperatures (low not being defined) heat is transferred primarily by by conduction and convection. Conduction is a fairly linear process that passes energy with a temperature rise about proportional to the energy flow. Convection is also fairly linear. But in parallel with these two mechanisms is radiation, and it is decidedly nonlinear. Radiation passes energy in proportion to the 4th power of absolute temperature difference. So as the temperature of box and resistor rise, there is some absolute temperature at which radiation will overtake both conduction and convection as the dominate transfer mechanism. I don't know if that temperature is any where near the temperatures you are talking about, however.

So your is correct, in the limit for low temperatures, and you are right above some particular temperature. An experiment is the best way to settle this argument.

• posted

Massimo, your boss is right, what counts is the temperature difference. You shouldn't distrust an engineer so easily, (that's what I suppose he is). :-))

```--
ciao Ban
Bordighera, Italy```
• posted

Unfortunately you cannot rely on the radiation, it will be a miniscule amount compared to the convection, because he says the box is closed, so radiation can only be from the outer surface, which he didn't report. I presume it will be half way between inside and outside, if the surface is

0.1mq and e=0.8, then with 338K 0.55W is radiated and with 408K 1W is radiated, hardly much in comparison to the total power, but it makes a good excuse to the boss. THX to Larry The formula to impress the boss: surfaceArea(m^2) * e(0.5...1) * constant 5.67e-8(W/(m^4 * K^4)) * (emitterK^4 - ambientK^4)/(emitterK - ambientK)
```--
ciao Ban
Bordighera, Italy```
• posted

Yesterday I've tried to test Tr with Te variable (from 20 degrees to 35 degrees). I can say that, with a tollerance of one degree, approximately the variation of Te is the same of the variation of Tr.

Thanks to everybody, Massimo

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