Calculating Heat Flow Through a Rod: Step-by-Step Guide

In summary, the conversation discusses finding the rate of heat flow through a cross-section of a rod in steady state using the formula ΔQ/Δt = [KA($2 - $1)] /x, where ΔQ/Δt is the heat current, A is the area of cross section, and x is the thickness. The person mentions using integration due to the varying cross-sectional area and asks for guidance. The correction of $2 > $2 to $2 > $1 is also mentioned. The formula H=-k*pi*r^2*(dT/dx) is derived and the challenge of integrating with 3 variables is brought up.
  • #1
Wiz
21
0
Hi,
I have to find the rate of heat flow through a cross-section of the rod in steady state as shown in the figure.Thermal conductivity of the rod is K.
I have used a $(dollar) sign for theta.
The formula i know is ΔQ/Δt = [KA($2 - $1)] /x
where ΔQ/Δt is the heat current,where A is area of cross section and x is the thickness.
since the area of cross section varies.i think integration will be used...
can ANYBODY GUIDE ME THROUGH..??
[NOTE - THE FIGURE READ THAT $2 > $2 , which is a mistake and the correction is $2 > $1.]
Thanks,
 

Attachments

  • heat conduction.gif
    heat conduction.gif
    1.1 KB · Views: 558
Physics news on Phys.org
  • #2
1. assume that the steady state
2. get a thin slice of tube
3. since steady state: heat enter=heat exit
4. this means H is constant over all x
5. our equation:
H=-kA(dT/dx)​
H=-k*pi*r^2*(dT/dx)​
7. well, pi is constant over all x
8. well, r is not constant over all x
9. good luck integrating...
 
  • #3
??

how do i relate x and r...
there are 3 variables and we need only 2 for integration.
hope u understand,
wiz

(btw - all the steps u wrote were know to me already0
 

FAQ: Calculating Heat Flow Through a Rod: Step-by-Step Guide

1. How do you calculate heat flow through a rod?

To calculate heat flow through a rod, you will need to know the thermal conductivity of the material, the cross-sectional area of the rod, the temperature difference between the ends of the rod, and the length of the rod. You can then use the formula Q = kAΔT/L, where Q is the heat flow, k is the thermal conductivity, A is the cross-sectional area, ΔT is the temperature difference, and L is the length of the rod.

2. What is the unit of measurement for heat flow?

The unit of measurement for heat flow is Watts (W), which represents the amount of energy transferred per unit of time.

3. How does the thermal conductivity of a material affect heat flow through a rod?

The thermal conductivity of a material measures its ability to conduct heat. A material with a higher thermal conductivity will allow for more efficient heat flow through a rod, whereas a material with a lower thermal conductivity will impede heat flow.

4. Can heat flow through a rod be affected by the temperature difference between the ends?

Yes, the temperature difference between the ends of a rod has a direct impact on the amount of heat flow. A larger temperature difference will result in a higher heat flow, while a smaller temperature difference will result in a lower heat flow.

5. How can I use the heat flow equation to solve real-world problems?

The heat flow equation can be used in a variety of real-world scenarios, such as calculating the efficiency of insulation in a building, determining the required size of a heat exchanger, or predicting the temperature distribution in a material. By plugging in the appropriate values, you can use the equation to solve for heat flow and better understand the transfer of thermal energy.

Similar threads

How Does Thermal Conductivity Affect Heat Transfer Between Two Water Vessels?
Replies
1
Views
1K
Two rods are connected one silver and the other gold.
Replies
3
Views
7K
Heat flow through aluminium rod
Replies
6
Views
2K
How Does Heat Transfer Through Different Metals?
Replies
2
Views
4K
Heat flow problem (copper pipe)
Replies
2
Views
2K
What is the Work Done by a Heated Metal Rod?
Replies
2
Views
3K
Heat transfer through a cylindrical shell
Replies
3
Views
3K
Behavior of heat addition in a compressible flow
Replies
9
Views
1K
How calculate the Heat flux requiered to evaporate sub cool water
Replies
1
Views
2K
Heat Flow in Three Identical Rods of Metal
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top