I need an equation or an answer....

[tylerdustin2008]

I would post this in the cooling area, but I post there quite a bit and i dont think anyone will know.... Plus i need a formula....

Heres the situation.

We have 6 gallons on mineral oil, in a tank with a computer submerged. The computer puts out a total of 275watts of power. The temp in side the tank before the computer starts is 21.1c.

How long will it take for it to hit 90c.


Thanks.

Tyler

 

[tylerdustin2008]

Hmmmm no one..

 

[Schfifty Five]

Is that all the info you have? I would think at the least you would need to know the rate at which the computer will rise in temp whiel submerged.

 

[tylerdustin2008]

Well thats why I gave the wattage. A constant of 275watts. The rate is also what i am asking, If i knew the rate I would not have posted....

 

[dighn]

is this a "real-world" problem? i.e. the system is not closed? then it can get a bit complicated because in addition to the specific heat capacity of the mineral oil, we also need to know how well the heat dissipates which can be quite complex to calculate as it depends on many factors such as the container dimensions, the thickness/material of the container, the ambient temperature etc.

 

[Cuda1447]

Its a trick question. See the 275watt output would not be possible, assuming we are on Earth. With the current gravitational pull the mineral oil would be obversely affected by the cumbersome amount of wattage. If so facto, the watts will decrease until they are ohms, which will cause a decrease in mineral capabilities. As a result you will no longer have a functional rock with a temperature, but rather a gasesous state of affairs.

 

[Idontcare]

Well you have some info that can be used, but not all the info needed to answer all questions.

10 gallons - OK so we know the mass.

275W - OK so we know the heat input.

Based on this we can calculate the time it would take to pump in enough watts to raise the temp from 21.1C to 90C provided we can find the heat capacity for your mineral oil.

What this will not answer though is the question most folks are thinking when they read a question as you wrote it. In other words this will not address heat loss to the environment.

hile the mineral oil is heating up it is also transfering heat to the air and the surroundings. Because of this the time to heat 10 gallons of mineral oil from 21C to 90C will be much much longer than the heat-capacity based calculation would lead you to beleive.

In fact depending on the configuration of the mineral oil tank (surface area versus volume) and the dynamics of the airflow (and humidity) of the air in the room the mineral oil may actually never reach 90C...it could very well stabilize at some temperature below 90C at which point it is transfering heat to the environment just as quickly as it is being heated by the computer.

This is the basis of all heat-exchange techniques, including heatsink/fan combos, which is why the temperature of a CPU varies as a function of the heatsink or cooling solution used to remove heat from the CPU. Its all the same physics of heat transfer.

So to answer the question you asked, you need the heat capacity for mineral oil before you can go any further. But to answer the question you probably intended to ask, you need to capture the heat loss to the environment portion of the system and that is very very difficult to do by theory alone my friend.

 

[tylerdustin2008]

Ok i can help with those.

16"W x 7.5" Dx14.5" H"

1/4" plexiglas

That will hold 6 gallons of store bought mineral oil. Ambient temp would be 21.2c, or 70f.

Tyler

 

[DrPizza]

It depends on the temperature in the room that the tank is in. If the room is 40 below zero, I doubt the tank would ever reach that temperature. The problem can be solved, but it'd be a major pain in the neck to do so.

 

[tylerdustin2008]

Originally posted by: Idontcare


So to answer the question you asked, you need the heat capacity for mineral oil before you can go any further. But to answer the question you probably intended to ask, you need to capture the heat loss to the environment portion of the system and that is very very difficult to do by theory alone my friend.

Nothing exact just a rough estimate is all I would need.

 

[dighn]

it's actually a pretty difficult problem to solve because there are so many variables. internal convection, air convenction etc.. the oil itself will have a temperature gradient. if we assume the thermal conductivity of the mineral oil is much greater than the plexiglass, then we can assume the gradient is much less than the gradient across the plexiglass. by my estimate, it shouldn't even reach 90 degrees:
area of the 5 panels of the box is about 0.51 square metre
thickness is 0.00635 metre
thermal conductivity of plexiglass seems to be k = 0.2 W/(m*k)
this means that by the conductive heat dissipation of the 5 panels alone, the equilibrium temperature inside the tank just at the edge is around
T = (275*thickness)/(k*area) + ambientT = 38c

obviously that is grossly simplified, but looks like it should settle into equilibrium before it reaches 90 degrees.

 

[Idontcare]

Originally posted by: tylerdustin2008
Ok i can help with those.

16"W x 7.5" Dx14.5" H"

1/4" plexiglas

That will hold 6 gallons of store bought mineral oil. Ambient temp would be 21.2c, or 70f.

Tyler

Some leisure reading: http://en.wikipedia.org/wiki/H...capacity#Heat_capacity

Let's assume you are using this mineral oil: http://www.multitherm.com/multitherm-pg-1.html

It is 7.30 lb/gal so your 6 gallons would be 43.8 lbs...converting to metric that comes out to be 19.9 kg of mineral oil.

Specific heat is 2023 J/(kg-°K) at 80C...now 1 watt-hour = 3600 J

So you need 2023 J/(kg-°K) x 19.9 kg = 40,258 Joules to raise the mineral oil one degree Celsius.

At 275W heat input, you are pumping out 275*3600 = 990,000 Joules per hour. So in one hour, assuming the mineral oil tank is vacuum insulated from the environment and is losing zero heat to its surroundings, the mineral oil heats up approximately 990000/40258 = 24.6°C

Your budget is 90°C - 21.1°C = 68.9°C...

68.9/24.6 = 2.8 hours.

In 2.8 hours the 6 gallons of mineral oil will have absorbed enough heat to rise from 21.1C to 90C. Whether it gets there or not depends on how much heat is lost thru the surface area of the tank's sidewalls and the environment.

 

[DrPizza]

I don't think we can even give you a rough estimate... as was already explained in this thread, there are too many variables. However, for starters, you could heat the tank of mineral oil up to some known temperature warmer than room temperature. Take a very accurate measurement of the temperature of the oil in the tank. Wait 30 minutes, take another very accurate temperature.

Use Newton's law of cooling - the rate of temperature change is proportional to the difference between the temperature of (the tank) and the surrounding room.

After you solved for the constant in that equation (simple calculus or differential equations to solve for k) I think you can use it to do a simple mixing problem (again, more differential equations and/or calculus.) Figure out the specific heat of your mineral oil, and how much energy in Joules would be present for 90C. Solve the differential equation, then solve for t when the energy reaches that 90C value.

Rate of change of temperature = (rate in) minus (rate out.)

Let's put it another way: My car has 3 gallons of a 50/50 water/ethylene glycol mix in it. My engine puts out a heck of a lot more energy than 325 watts. How long will it take for the antifreeze mix to his 120 degrees C? It won't, because it hits equilibrium at a lower temperature. No matter how hard my car tries, it's not going to be able to keep the temperature at, say, 30C. But, there is a temperature at which it radiates heat at the same rate that the engine produces heat.

 

[tylerdustin2008]

Originally posted by: Idontcare

Originally posted by: tylerdustin2008
Ok i can help with those.

16"W x 7.5" Dx14.5" H"

1/4" plexiglas

That will hold 6 gallons of store bought mineral oil. Ambient temp would be 21.2c, or 70f.

Tyler

Some leisure reading: http://en.wikipedia.org/wiki/H...capacity#Heat_capacity

Let's assume you are using this mineral oil: http://www.multitherm.com/multitherm-pg-1.html

It is 7.30 lb/gal so your 6 gallons would be 43.8 lbs...converting to metric that comes out to be 19.9 kg of mineral oil.

Specific heat is 2023 J/(kg-°K) at 80C...now 1 watt-hour = 3600 J

So you need 2023 J/(kg-°K) x 19.9 kg = 40,258 Joules to raise the mineral oil one degree Celsius.

At 275W heat input, you are pumping out 275*3600 = 990,000 Joules per hour. So in one hour, assuming the mineral oil tank is vacuum insulated from the environment and is losing zero heat to its surroundings, the mineral oil heats up approximately 990000/40258 = 24.6°C

Your budget is 90°C - 21.1°C = 68.9°C...

68.9/24.6 = 2.8 hours.

In 2.8 hours the 6 gallons of mineral oil will have absorbed enough heat to rise from 21.1C to 90C. Whether it gets there or not depends on how much heat is lost thru the surface area of the tank's sidewalls and the environment.

Thanks allot "Idontcare".

And thanks all of you for the help.