Fouriers Law of Heat Conduction

  • Understand and are able to recognize conduction, convection and radiation as modes of heat transfer.

  • Fourier’s law of conduction.

  • Able to solve one-dimensional heat conduction problems using the energy equation and Fourier’s law.

Conduction expressed by Fourier’s law of heat conduction as written below:

\[\dot{Q}_{\mathrm{conduction}} = - k A \frac{dT}{dx}\]

Where, \(\displaystyle \dfrac{dT}{dx}\) is the temperature gradient. k is the thermal conductivity A is the area which is normal to the direction of heat transfer.

Conduction expressed by Fourier’s law of heat conduction as written below:

Where, \(\displaystyle \dfrac{dT}{dx}\) is the temperature gradient. k is the thermal conductivity A is the area which is normal to the direction of heat transfer.

Solved Examples

Solved Example:

80-1-01

Fourier's law of heat conduction is valid for:

Solution:
Among the assumptions for Fourier's law of heat conduction, the main ones are: Steady state heat conduction, one directional heat flow and no internal heat generation. For two dimensional steady state heat conduction, Laplace equation is used.

Correct Answer: A

Solved Example:

80-1-02

Unit of thermal conductivity in S.I. units is: (ISRO URSC Tech Asst Mech Nov 2016)

Solution:
In the International System of Units (SI), thermal conductivity is measured in Watts per meter-Kelvin (W/(m$\cdot$K)). Note that Watt is Joule/second.
In Imperial units, thermal conductivity is measured in BTU/(h $\cdot$ ft $\cdot$ $^\circ$F).

Correct Answer: D

Solved Example:

80-1-03

Thermal conductivity of non-metallic amorphous solids with decrease in temperature:

Correct Answer: B

Solved Example:

80-1-04

The insulation ability of an insulator with the presence of moisture would: (BPSC AE ME 2012-Part V)

Correct Answer: B

Solved Example:

80-1-05

Heat is closely related with:

Correct Answer: C

Solved Example:

80-1-06

Pick up the wrong case. Heat flowing from one side to other depends directly on:

Correct Answer: C

Solved Example:

80-1-07

Metals are good conductors of heat because: (RSMSSB JE Mech Dec 2020)

Correct Answer: A

Solved Example:

80-1-08

Which of the following is a case of steady state heat transfer: (SSC JE ME Paper 6- Mar 2017)

Correct Answer: D

Solved Example:

80-1-09

Heat flows from one body to other when they have: (ISRO VSSC Tech Asst Mech Feb 2015)

Solution:
Heat flow takes places when the temperatures of two bodies are different. This is true even when the body with lower temperature has higher heat content. Heat flow is analogous to fluid flow, where fluid flows from higher level to lower level, even though the lower level reservoir has more fluid content. The 'level' in fluid flow is similar to 'temperature' in heat flow.

Correct Answer: D

Solved Example:

80-1-10

In heat transfer, conductance equals conductivity (kcal/hr/sqm/$^\circ$C/cm) divided by:

Correct Answer: D

Solved Example:

80-1-11

The amount of heat flow through a body by conduction is:

Correct Answer: D

Solved Example:

80-1-12

Which of the following has least value of conductivity? (UPPSC AE Mech 2013- Paper II)

Solution:
The thermal conductivity of a material is a measure of its ability to conduct heat. A material with high resistance to thermal conduction will have least value of conductivity. Water has thermal conductivity = 0.6089 W/m K compared to that of air = 0.026 W/m K, fiber reinforced plastic has 0.23 W/m K, whereas CR rubber has 0.16 W/m K. (Values referred from Wikipedia.)

Correct Answer: D

Solved Example:

80-1-13

Which of the following is expected to have highest thermal conductivity? (SSC JE ME Mar 2017- Paper 6)

Correct Answer: B

Solved Example:

80-1-14

Thermal conductivity of a material may be defined as the:

Correct Answer: D

Solved Example:

80-1-15

Which of the following has maximum value of thermal conductivity?

Correct Answer: A

Solved Example:

80-1-16

Moisture would find its way into insulation by vapour pressure unless it is prevented by:

Correct Answer: D

Solved Example:

80-1-17

Thermal diffusivity is: (TANGEDCO AE ME 2015)

Correct Answer: D

Solved Example:

80-1-18

Thermal diffusivity of a substance is:

Correct Answer: A

Solved Example:

80-1-19

Unit of thermal diffusivity is:

Correct Answer: A

Solved Example:

80-1-20

Thermal conductivity of wood depends on:

Correct Answer: D

Solved Example:

80-1-21

Heat conducted through unit area and unit thick face per unit time when temperature difference between opposite faces is unity,is called:

Correct Answer: D

Solved Example:

80-1-22

Which of the following property of air does not increase with rise in temperature:

Correct Answer: C

Solved Example:

80-1-23

The thermal diffusivities for gases are generally:

Correct Answer: A

Solved Example:

80-1-24

The thermal diffusivities for solids are generally:

Correct Answer: C

Solved Example:

80-1-25

Thermal diffusivity of a substance is:

Correct Answer: D

Solved Example:

80-1-26

Which one of the following states the fundamental modes of heat transfer?

Correct Answer: B