Steady State Heat Conduction

Question 1

Draw the system for steady state heat conduction through a finite rod.

Answer 1

See footnote 17.

Question 2

Draw the control volume and fluxes for steady state heat transfer through a finite rod.

Answer 2

See footnote 18.

Question 3

Construct the energy balance for steady state heat transfer through a finite rod.

Answer 3

See footnote 19.

Question 4

Simplify the energy balance for steady state heat transfer through a finite rod using non-dimensional variables and state the new boundary conditions.

Answer 4

See footnote 20.

Question 5

Solve the non-dimensionalised differential equation for steady state heat transfer through a finite rod.

Answer 5

See footnote 21.

Question 6

Apply the boundary conditions to the nondimensionalised equation for steady state heat transfer through a finite rod.

Answer 6

See footnote 22.

Question 7

Simplify the final nondimensionalised eqution for steady state heat transfer through a finite rod back into the original variables.

Answer 7

See footnote 23.

Question 8

Derive the equation for overall heat transfer coefficient.

Answer 8

See footnote 24.

Question 9

State the three assumptions made when constructing the heat balance analysis for a cooling fin.

Answer 9

1) the fin is thin
2) temperature differences in the transverse direction are small
3) temperature is uniform across the fin thickness

Question 10

Give three situations in which cooling fins are used.

Answer 10

motorbike engines, electronic circuits, refrigeration systems

Question 11

Draw the system for heat transfer through a cooling fin.

Answer 11

See footnote 25.

Question 12

Draw the control volume and list the fluxes for heat transfer through a cooling fin.

Answer 12

See footnote 26.

Question 13

Construct the energy balance for heat transfer through a cooling fin, assuming steady state with no heat generation.

Answer 13

See footnote 27.

Question 14

Solve the equation for heat transfer through a cooling fin on the assumption it has uniform thickness and state the new boundary conditions.

Answer 14

See footnote 28.

Question 15

State the 3 situations and their boundary conditions for heat transfer through a uniform thickness cooling fin.

Answer 15

See footnote 29.

Question 16

Apply the boundary conditions for heat transfer through an infinite, uniform thickness cooling fin.

Answer 16

See footnote 30.

Question 17

Change the equation for the heat transfer through an infinite, uniform rod back to original variables.

Answer 17

See footnote 31.

Question 18

Construct the equation for total rate of heat transfer through an infinite, uniform thickness cooling fin.

Answer 18

See footnote 32.

Question 19

Give two examples of cylinders that generate heat

Answer 19

wire carrying current, nuclear fuel rod

Question 20

Draw the control volume for heat generation in a cylinder.

Answer 20

See footnote 33.

Question 21

Construct an energy balance for heat transfer for a cylinder with heat generation, assuming steady state.

Answer 21

See footnote 34.

Question 22

Solve the differential equation given for heat transfer through a heat generating cylinder.

Answer 22

See footnote 35.

Question 23

Apply the boundary conditions to the equation for temperature through a cylinder with heat generation.

Answer 23

See footnote 36.

Question 24

At which point in a cylinder that generates heat can you find the maximum temperature?

Answer 24

When r=0.

Question 25

Give the equation for maximum temperature in a cylinder that generates heat.

Answer 25

See footnote 37.