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Heat Lecture-3

Boundary Conditions and Initial Conditions

·         Objective: To determine T = f (x, y, z, t) for given b.c.’s and i.c.

·        Homogeneous medium in 3-D

·        Heat equation in Cartesian coordinates

·       Heat equation in cylindrical coordinates (r, ?, z)

·       Heat equation in spherical coordinates (r, ?, ?)

·        Boundary and Initial Conditions for Heat Diffusion

·       Boundary conditions are the physical conditions at the boundaries of a medium or system, which can be expressed in mathematical forms. Examples are:

1.     Constant surface temperature (Ts) - Dirichlet

2.   Constant surface heat flux (qs”) - Neumann

a) Finite heat flux

b) Adiabatic or Insulated Surface 

3.    Convection surface condition - Cauchy

•        Since the heat diffusion equation is 2^nd order in spatial coordinates,  two  boundary conditions must be specified for each coordinate needed to describe a system.

•        The heat equation in also 1^st order in time, and one initial condition (usually at t = 0) must be specified in order to solve the diffusion equation.