rate of heat loss from a cup of coffee?

[loic2003]

So, my sister appears to have sent me a USB hub/coffee warmer device. It's essentially a heated placemat that has a 4-port hub in it.

It's rated at 2.5W, so I was wondering what sort of rate a mug of tea/coffee loses heat. Is the 2.5W output, minus all the inefficiencies of transferring heat going to make a significant difference. It gets pretty warm, but I dunno...

Also... would you guys be concerned about plugging in a device that basically uses a short to generate heat into your motherboard?

yeah.... pure adrenaline life here, tonight....

 

[loic2003]

Bump for the bored.

 

[djheater]

It depends on the vessel, and I wouldn't be worried about plugging it in...
How do you a short? I would assume a device of that nature uses resistance to generate heat.

 

[Heisenberg]

Look up Newton's Law of Cooling.

 

[EyeMWing]

The device is perfectly safe. It doesn't use a short to generate heat (that would generate the heat in the circuitry that feeds the USB port, which would be bad) - it uses resistance - which is the same electrically speaking to any other USB-powered device.

 

[rgwalt]

The scary thing is that I should be able to do the calculations... It all depends on the material your mug is made from and on the dimensions of the mug. The main heat loss point is through the top of the mug (where the coffee is exposed to the air).

This all being said, all the coffee mug warming plates I have seen in my 2 minute google search are listed at ~20W.

Experiment: Pour yourself a piping hot mug of coffee and set it on the warmer. Don't drink it, but periodically stick your finger (or a thermometer) into it to check the temperature. See if it actually drops to the point of being tepid, or even cold.

R

 

[dullard]

This reminds me of the thread about the cooling rate of a mug. I did a lot of experiments to measure that. Can't find it at the moment though.

Assumptions:
[*]Assume mug is made of porcelain (or ceramic of similar thermal conductivity).
[*]Because I'm lazy, assume no heat loss out of the top.
[*]Assume coffee is at 140°F.
[*]Assume room is at 72°F.
[*]Assume the mug surfaces are therefore kept constant at 140°F and 72°F (a poor assumption I know, but I'm lazy).
[*]Assume mug is nearly full.
[*]Assume mug has the typical coffee mug dimensions.
[*]Because I'm lazy, assume mug is flat instead of round.

Data:
[*]Thermal conductivity of porcelain: k=1.05 W/m/K
[*]Thickness of mug: t=0.25".
[*]Mug radius: r=1.5".
[*]Mug height, 3.75", of that h=3" are full of coffee.

Calculations:
[*]Temperature difference: dT = 140°F-72°F = 68°F
[*]Mug surface area: A = pi*(2*r*h + r^2) = 0.023*m^2
[*]Heat loss: Q=k*A*dT/t = 142 W.

Those are crude calculations. The assumptions I made over estimate the amount of heat needed. But it shows a 2.5W heater will do nearly nothing. USB is rated to supply up to 2.5W for a device. So it really shouldn't harm your motherboard. But it really won't help your coffee much.

 

[loic2003]

Originally posted by: dullard
This reminds me of the thread about the cooling rate of a mug. I did a lot of experiments to measure that. Can't find it at the moment though.

Assumptions:
[*]Assume mug is made of porcelain (or ceramic of similar thermal conductivity).
[*]Because I'm lazy, assume no heat loss out of the top.
[*]Assume coffee is at 140°F.
[*]Assume room is at 72°F.
[*]Assume the mug surfaces are therefore kept constant at 140°F and 72°F (a poor assumption I know, but I'm lazy).
[*]Assume mug is nearly full.
[*]Assume mug has the typical coffee mug dimensions.
[*]Because I'm lazy, assume mug is flat instead of round.

Data:
[*]Thermal conductivity of porcelain: k=1.05 W/m/K
[*]Thickness of mug: t=0.25".
[*]Mug radius: r=1.5".
[*]Mug height, 3.75", of that h=3" are full of coffee.

Calculations:
[*]Temperature difference: dT = 140°F-72°F = 68°F
[*]Mug surface area: A = pi*(2*r*h + r^2) = 0.023*m^2
[*]Heat loss: Q=k*A*dT/t = 142 W.

Those are crude calculations. The assumptions I made over estimate the amount of heat needed. But it shows a 2.5W heater will do nearly nothing. USB is rated to supply up to 2.5W for a device. So it really shouldn't harm your motherboard. But it really won't help your coffee much.

Hey, cheers for the help!

As I thought, it's not much of a heater. The very center of the heated disk gets pretty hot, slighty too hot to touch, but I imagine someone with calloused hands (eg a bricky) would be able to hold a finger there. I think it's a gimmic, but it does add a certain extra nerd-ass quality to my rig that the chicks are sure to dig....

 

[Rubycon]

I find that a 2.5 watt laser burns a hole through the mug pretty fast.

Amazing what a little bit of power can do when concentrated.

2.5 watt is very low for a resistance heater for a coffee plate. Most are 500W and up - but that's for the whole pot. 2.5W would make an ok fanny warmer though.