Investigation of Fourier’s law for linear conduction of heat along simple bar
1.0 TITLE
Heat Conduction- Simple Bar
2.0 OBJECTIVES
Investigate Fourier’s law for linear conduction of heat along simple bar
3.0 THEORY
Conduction Heat Transfer
Conduction is the heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If the one end of the metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones.
Heat flows from a body of higher temperature to a body of lower temperature. For a controlled conduction, this continues until a “steady-state” where no more heat transfer occurs. A diagram below illustrates the direction of heat transfer and the variables involved in linear heat conduction through a plane wall.
Fourier’s Law of Heat Conduction
The law of heat conduction , also known as Fourier’s law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperatures and to the area, at right angles to the gradient, through which the heat is flowing. We can state this law in two equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flow rates or fluxes of energy locally.
The Fourier’s law for linear heat conduction states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat is flowing.
If a plane wall of thickness (x) and area (A) and thermal conductivity (k) supports a temperature difference (T) then the heat transfer rate by conduction is given by the equation:
Assuming a constant thermal conductivity throughout the material and a linear temperature distribution, this is:
4.0
Heat Conduction- Simple Bar
2.0 OBJECTIVES
Investigate Fourier’s law for linear conduction of heat along simple bar
3.0 THEORY
Conduction Heat Transfer
Conduction is the heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If the one end of the metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones.
Heat flows from a body of higher temperature to a body of lower temperature. For a controlled conduction, this continues until a “steady-state” where no more heat transfer occurs. A diagram below illustrates the direction of heat transfer and the variables involved in linear heat conduction through a plane wall.
Fourier’s Law of Heat Conduction
The law of heat conduction , also known as Fourier’s law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperatures and to the area, at right angles to the gradient, through which the heat is flowing. We can state this law in two equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flow rates or fluxes of energy locally.
The Fourier’s law for linear heat conduction states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat is flowing.
If a plane wall of thickness (x) and area (A) and thermal conductivity (k) supports a temperature difference (T) then the heat transfer rate by conduction is given by the equation:
Assuming a constant thermal conductivity throughout the material and a linear temperature distribution, this is:
4.0