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# time needed fto reach thermal equilibrium

## time needed fto reach thermal equilibrium

(OP)
How do I calculate the time needed for a metal block to reach its equilibrium in a thermal chamber?

### RE: time needed fto reach thermal equilibrium

You are looking for the time it will take to warm the block up approximately to the environmental chamber temperature?

Remember Newton's law of cooling?  The rate of cooling (or heating) is proportional to the temeperature difference.

Do you have the density, thermal conductivity, specific heat and the thermal diffusivity of the metal?  Also need to know the dimensions so that you can find the Biot number.

### RE: time needed fto reach thermal equilibrium

(OP)
The block I preferred to was actually a quad hybrid. It was left in a thermal chamber from -55 deg to +85 deg thru thermal cycling for 15 minutes. I want to know if in that 15 minutes, the quad will reach its equilibrium. Can you please explain more? Thank you.

### RE: time needed fto reach thermal equilibrium

Excuse my ignorance, but what is a "quad hybrid" and how big is it?  And what do you consider the equilibrium temperature?

But with no more information, I'd make the rash statement that it's doubtful anything would reach equilibrium when the temperature changed by 140° in 15 minutes.

Patricia Lougheed

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### RE: time needed fto reach thermal equilibrium

You've already got the oven, and material. Did you insert a thermocouple in the block?  The most accurate way to determine how long until the block reaches thermal equilibrium would be to measure the time experimentally.

### RE: time needed fto reach thermal equilibrium

(OP)
It's quadrature hybrids (a microwave component)
No, I can't stick anything into the part. I have to calculate the time to prove that it reaches equilibrium in that 15 mins.

### RE: time needed fto reach thermal equilibrium

How are you going to "prove" that your calculations are correct?

### RE: time needed fto reach thermal equilibrium

Is this an electronic component of a microwave oven? Please give some details especially why you are being asked to make this calculation.  I agree with dvd that empirical data will be far superior to engineering calculations in this instance.  Perhaps you could make a mock-up of similar size and properties using that to measure temperature.

### RE: time needed fto reach thermal equilibrium

Refer to heat transfer texts to find the best relationship you can for heat transfer by natural convection for the situation- treat it as a plate or sphere or whatever is close.  Then assume your widget is all at the same temperature.  You can then equate the time rate of change of temperature to the difference in temperature between the widget and the surroundings.  This lets you solve for temperature as a function of time.

We did this way back in an ME lab to ascertain how long a thermocouple needed to remain in the surroundings before it read the "right" temperature.  This is not expected to be an accurate method, but a ballpark method, with the uncertainties in the convective heat transfer being the biggest problem.

If you go through this process and it shows you reach equibrium in 10 minutes or in 20 minutes, it may not be too meaningful, as the inaccuracies could be too great.  But if it shows that the equilibrum is reached in 30 seconds or takes 4 hours, that would be more meaningful.

### RE: time needed fto reach thermal equilibrium

Much of that depends on the amount of air flow(surprise!).  Most time critical testing of components used to be done with a widget that specifically pumped the correct temperature air directly on the component and nothing else.

As for calculations, you could assume a worst-case thermal mass located in the center of the component, and the serial thermal resistances to the ambient air.  It'll look like an RC-time constant problem from electronics.  But, it's something that could be approximated in an Excel spreadsheet.

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