Working out the rate of heat loss from a radiator

[Bolter]

Homework Statement

Working out rate of heat loss from radiator

Relevant Equations

Power = energy/time

Here is the Q below

This is what I have tried so far. I ended up getting a value of 1772.4 watts

Is this the correct way of doing this problem?

 

[Chestermiller]

Not even close. What is the equation for the rate of radiant heat transfer? There is also going to be natural connective heat transfer from the radiator.

 

[Bolter]

Not even close. What is the equation for the rate of radiant heat transfer? There is also going to be natural connective heat transfer from the radiator.

Sorry I'm a bit unsure to which equation I need to use for radiant heat transfer? Is it Stefan's law?

 

[Chestermiller]

Sorry I'm a bit unsure to which equation I need to use for radiant heat transfer? Is it Stefan's law?

Yes, but don’t forget to include the amount radiated back from the room, to get the net rate of heat transfer.

 

[Bolter]

Yes, but don’t forget to include the amount radiated back from the room, to get the net rate of heat transfer.

This was all I was able to think of but I don't know how to proceed further from this?

Also how I would I work out the surface area (i.e. surface area of sphere) if I am not given a radius?

 

[TSny]

It seems to me that @Bolter has the correct answer. For steady-state conditions, the rate of heat loss by the radiator must equal the rate that heat is transferred to the radiator by the circulating water. It is not necessary to worry about the various ways in which the radiator loses heat (such as radiation, convection, etc.).

 

[Bolter]

It seems to me that @Bolter has the correct answer. For steady-state conditions, the rate of heat loss by the radiator must equal the rate that heat is transferred to the radiator by the circulating water. It is not necessary to worry about the various ways in which the radiator loses heat (such as radiation, convections, etc.).

So 1772.4 watts would be an acceptable ans?

 

[TSny]

So 1772.4 watts would be an acceptable ans?

I believe so. But @Chestermiller is an expert in thermodynamics. So, I don't feel comfortable without his blessing

Also, if your instructor cares about significant figures, then you might want to round off your answer to an appropriate number of significant figures.

 

[Bolter]

I believe so. But @Chestermiller is an expert in thermodynamics. So, I don't feel comfortable without his blessing

Also, if your instructor cares about significant figures, then you might want to round off your answer to an appropriate number of significant figures.

I think my instructor is possibly looking for this answer as I haven't yet covered heat loss through radiation, convection etc.

I'll just keep it into a minimum of 3 sig figs so 1770 watts

 

[TSny]

I'll just keep it into a minimum of 3 sig figs so 1770 watts

OK. The volume flow rate is only given with one significant figure. If you use the rough rules of thumb for significant figures that are given in many introductory courses, then the answer should have only one significant figure: 2000 W. But, I suspect that your answer of 1770 W is fine.

 

[Chestermiller]

It seems to me that @Bolter has the correct answer. For steady-state conditions, the rate of heat loss by the radiator must equal the rate that heat is transferred to the radiator by the circulating water. It is not necessary to worry about the various ways in which the radiator loses heat (such as radiation, convection, etc.).

Maybe I am mistaken, but I was assuming that the radiator is already operating at temperature, and he was not looking at the amount of heat necessary to bring the radiator up to temperature (and certainly not in 1 second). He was interested in the rate of heat transfer to the room.

 

[Chestermiller]

So 1772.4 watts would be an acceptable ans?

I totally disagree. See my previous post.

 

[Chestermiller]

This was all I was able to think of but I don't know how to proceed further from this?

View attachment 253758
Also how I would I work out the surface area (i.e. surface area of sphere) if I am not given a radius?

Yes, this is correct, except that you should be using absolute temperature rather than centigrade temperatures. You get the area just by looking at the surface geometry of the radiator. Just estimate it roughly from what you see.

 

[TSny]

Maybe I am mistaken, but I was assuming that the radiator is already operating at temperature...

Yes, the radiator has already reached a steady average temperature. So, the internal energy of the radiator itself is not changing. Thus the rate at which heat is transferred to the radiator from the water equals the rate at which the radiator transfers heat to the room.

 

[Chestermiller]

Yes, the radiator has already reached a steady average temperature. So, the internal energy of the radiator itself is not changing. Thus the rate at which heat is transferred to the radiator from the water equals the rate at which the radiator transfers heat to the room.

Oops. I misinterpreted the question. Yes, you are of course correct.