1. Chapter 2. Mathematical Expression of Conduction

2. Differential Control Volume

3. The Heat Diffusion Equation
Taylor Series Expansion

4. The thermal conductivity is constant:
The Heat Diffusion Equation
The thermal conductivity is constant:
Under steady state condition:
One dimensional/no energy generation:

5. Boundary and Initial Conditions
For transient conduction, heat equation is first order in time, requiring specification of an initial temperature distribution:
Since heat equation is second order in space, two boundary conditions must be specified.

6. Boundary and Initial Conditions
Dirichlet condition or
a B.C. of the first kind
Neumann Condition or
a B.C. of the second kind
a B.C. of the third kind