Solution of the 2D Heat Equation Using the Method of Lines

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Consider the unsteady-state heat conduction problem defined by



where is the temperature, is the thermal diffusivity, is the time, and and are the spatial coordinates.

This Demonstration solves this partial differential equation–a two-dimensional heat equation–using the method of lines in the domain , subject to the following Dirichlet boundary conditions (BC) and initial condition (IC):

BC 1: , where and ,

BC 2: , where and ,

BC 3: , where and ,

BC 4: , where and ,

IC: , where and .

The Demonstration gives a contour plot of the temperature for user-set values of and .


Contributed by: Housam Binous (March 2012)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.