HeatDiffusion

Maps 1D and 2D heat diffusion across a wire or a plate.

Motivation

Apply knowledge of arrays to gain an understanding of a heat transfer model over one and two dimensional objects. An explicit method of solving finite difference approximations was used to determine heat transfer for new time instances.

Background

The one dimensional heat equation is given by . Likewise, the two dimensional heat equation is given by . To solve these equations exactly would require solving differential equations by hand. Therefore, the values for heat diffusion are approximated using the following functions:

1D:

2D:

Note that Δ represents the change in a variable, k is thermal conductivity, ρ (rho) is material density, c is the specific heat capacity of material, u is the object, and x is the location on u.

Class

CS 161: Introduction to Computer Science