Basic of Conduction Heat Transfer

1. Conduction refers to the transport of energy in a medium (solid, liquid or gas) due to a temperature gradient.
2. The physical mechanism is random atomic or molecular activity
3. Governed by Fourier’s law

In this chapter we will learn

• The definition of important transport properties and what governs thermal conductivity in solids, liquids and gases
• The general formulation of Fourier’s law, applicable to any geometry and multiple dimensions
• How to obtain temperature distributions by using the heat diffusion equation.
• How to apply boundary and initial conditions

Thermal Properties of Matter

Recall from Chapter 1, equation for heat conduction:

 

The proportionality constant is a transport property, known as thermal conductivity k 

•Usually assumed to be isotropic (independent of the direction of transfer): kx=ky=kz=k

Thermal Conductivity: SolidsThermal Conductivity: Solids

•Solid comprised of free electrons and atoms bound in lattice

•Thermal energy transported through

- Migration of free electrons, ke

            - Lattice vibrational waves, kl

  

Thermal Conductivity: Fluids

• Intermolecular spacing is much larger
• Molecular motion is random 
• Thermal energy transport less effective than in solids; thermal conductivity is lower

 Kinetic theory of gases:

 where n the number of particles per unit volume, the mean molecular speed and l the mean free path (average distance travelled before a collision)