Heat_Equation
The 2-d heat equation is solved using partial differential equations generated using the Modular Program Constructor (MPC). Heat_Equation_ODE solves the problem using ordinary differential equations.
Model number: 0363
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Description
Heat equation in two dimensions is solved using partial differential equations.
Contour plots of the solution of heat equation using the prescribed Dirichlet boundary conditions at Time = 0.01, 0.02, 0.04 and 1.00 seconds.
Equations
Partial Differential Equation
Boundary Conditions
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
Download JSim model project file
References
Related Models
- Diffusion Tutorial,
- 1-D Diffusion modeled as a partial differential equation,
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- Random Walk of single particle in 2 dimensions
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- Safford 1977 Dead end pore model for Calcium diffusion in muscle
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- Suenson 1974 Diffusion in heart tissue, sucrose and water
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Key Terms
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Model History
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Acknowledgements
Please cite www.physiome.org in any publication for which this software is used and send an email
with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
[This page was last modified 14Mar18, 3:17 pm.]
Model development and archiving support at physiome.org provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.
