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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

Diffusion in a single region with advection

Model number: 0169

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## Description

 	This is the 1-D avection-diffusion problem. Note that
the left inflow boundary condition is a Robin (row-ban')
condition.



## Equations

#### Partial Differential Equation

$\large \frac{\partial C_p}{\partial t} = (-F \cdot L/V) \cdot \frac{\partial C_p}{\partial x} + D_p \cdot \frac{\partial^2 C_p}{\partial x^2}$

#### Left Boundary Condition

$\large (-F \cdot L/V) \cdot (C_p-C_{ in}) + D_p \cdot \frac{\partial C_p}{\partial x} =0$ .

#### Right Boundary Condition

$\large {\it {\frac {\partial }{\partial x}}C_p=0$

#### Initial Condition

$\large C_p(x,t=t.min)=if(x=x.min) \ C_{ in}(t=t.min) \ else \ C_p0(x)$ .

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.

## References

 None.



## Key Terms

diffusion, Tutorial, flow, boundary conditions, PDE

## 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.