Chapter 2. Mathematical Expression of Conduction

Differential Control Volume

The Heat Diffusion Equation Taylor Series Expansion

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

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.

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