Previous in Forum: Writing Gearbox Specifications   Next in Forum: Skidding Automobiles
Close
Close
Close
6 comments
Rate Comments: Nested
Anonymous Poster

Simple Heat Transfer Question

12/04/2006 2:18 AM

My name is Wm. Scott Smith. I am trying to tentatively work out the feisibility of a rather simple idea involving heat transfer for a project of mine.

I am looking at a table that gives a value of 205 W/m K for the thermal conductivity of Aluminum. I am trying to make sure I am understanding the proposition correctly.

Given:

  • a solid aluminum cylinder
  • perfectly insulated sides one meter long,
  • each end is one meter squared
  • one-degree K difference between the two ends

Does this imply that the cylinder will conduct heat at a rate of 205 Watts every second (once the thermal gradient is fully developed?)

If the cylinder were only 0.5 meters long, would it transfer 410 Watts every second?If not, what would be the correct solutions for these two cylinders, and how did you arrive at them? Thank you for your time!!!

scott712@hotmail.com

Reply
Interested in this topic? By joining CR4 you can "subscribe" to
this discussion and receive notification when new comments are added.
Guru
United Kingdom - Member - Olde Member!! Engineering Fields - Instrumentation Engineering - New Member

Join Date: Jul 2006
Location: Dunstable, England
Posts: 2821
Good Answers: 45
#1

Re: Simple Heat Transfer Question

12/04/2006 3:44 PM

Hmmm doesn't the table you are referring to give a dimension of the sample?

It seems odd it gives a value of 205 Watts per Kelvin without stating the volume or shape of the sample...

usually it will say for a 1" cube or 1 cm cube and assumes both sides of the cube are making good thermal connection - although if the temperature measurements are made on the cube surface it doesn't matter about any temperature gradients at the interfaces.

As you say if the table is for a 1 cm cube then if the cube dimensions are changed the thermal characteristics are changed.

John.

__________________
A little knowledge is a dangerous thing - Googling is far worse!
Reply
Active Contributor

Join Date: Apr 2005
Posts: 21
#5
In reply to #1

Re: Simple Heat Transfer Question

12/04/2006 11:21 PM

The conduction coefficient is a material property, and is given in Watts per meter per degree Kelvin.

__________________
C
Reply
Anonymous Poster
#2

Re: Simple Heat Transfer Question

12/04/2006 10:57 PM

The formula is Q = k*A*T/L

where

Q is in watts (a watt is one Joule per second)

k is in watt/metre/Kelvin, and is a property of the material

T is temperature difference between ends in Kelvins

A is cross sectional area of cylinder in metre squared

L is the length in metres


Greg

Reply
Guru
Hobbies - HAM Radio - New Member United Kingdom - Big Ben - New Member Fans of Old Computers - Altair 8800 - New Member Canada - Member - New Member

Join Date: Jun 2006
Location: Toronto
Posts: 3968
Good Answers: 120
#3

Re: Simple Heat Transfer Question

12/04/2006 10:58 PM

Yes, if the impediment to heat travel is 50% less, then the heat transfer rate will double.

http://en.wikipedia.org/wiki/Thermal_conductivity

__________________
Per Ardua Ad Astra
Reply
Active Contributor

Join Date: Apr 2005
Posts: 21
#4

Re: Simple Heat Transfer Question

12/04/2006 11:17 PM

You are correct with the exception of the fact that the heat transfer rate is measured in Watts = Joules per second, not Watts per second.

__________________
C
Reply
Active Contributor

Join Date: Nov 2006
Location: Ibadan, South Western Nigeria
Posts: 13
#6

Re: Simple Heat Transfer Question

12/10/2006 7:51 AM

Hi Scott! Thermal conductivity, k, is mathematically expressed thus:

k = Q/A gradΘ, where Q is in Watts (Joules/second)

A, in m2 is heat transfer area perpendicular to the heat flux

gradΘ in K (kelvin) is the temperature gradient or differential between the hot and cold surfaces.

From thence, it implies that thermal conductivity is a thermodynamic property of a material and it is defined as the quantity of heat in Watts (Joules/second) passing through a unit isothermal surface (in m2) when the temperature gradient is 1 degree (in this case 1 K) along every metre in the direction of normal to the surface.

k = ƒ( t °C, structure, density of the material, Pressure - for gases and liquids, humidity etc)

Therefore, the driving force in heat transfer process is temperature gradient. Using Aluminium as the heat conductor, in 1 second and at a temperature gradient/differential of 1 degree, 205 Joules of energy will be transferred through 1 metre along the normal.

olusojioyewole.msn@hotmail.com

__________________
"Be cautious of a naked man who is offering to give you a shirt" olusojihercules53
Reply
Reply to Forum Thread 6 comments
Copy to Clipboard

Users who posted comments:

Anonymous Poster (1); aurizon (1); cmac (2); Electroman (1); Hrecules53 (1)

Previous in Forum: Writing Gearbox Specifications   Next in Forum: Skidding Automobiles

Advertisement