Plot solution of the diffusion equation

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Reference no: EM132455169

Problem Statement 1 : Plot solution of the diffusion equation in 1D for several points in time using MATLAB, overlaying the plots on the same figure and making reasonable assumptions for the required parameters. Make sure to label the axes. (HINT: You may find the material in Lec 17 'Diffusion-Advection-Reaction solution" particularly useful.)

Problem Statement 2 : Plot solution of the advection-diffusion equation in 1D for several points in time using MATLAB, overlaying the plots on the same figure and making reasonable assumptions for the required parameters. Make sure to label the axes. (HINT: You may find the material in Lec 17 "Diffusion-Advection-Reaction solution" particularly useful.)

Problem Statement 3: For the solution of the diffusion equation in 1 D, find an expression for the maximum concentration, Cm„. Using MATLAB, plot the dependence of C„,„ on time, while making reasonable assumptions for the required parameters. Make sure to label the axes.

Problem Statement 4 : A Petri dish contains some cell culture medium (an aqueous solution of various nutrients and growth factors needed by the cells). The profile of oxygen concentration in the laminar sub-layer at the surface of the medium is:

C(z) = Csat - (C„t - C„,)er f (,,Tdsz

where C„t is the concentration of oxygen in water at saturation, Cm is the concentration of oxygen in the medium away from the liquid / air interface, d is the thickness of the concentration boundary layer (a stirrer in the medium keeps 6 = const). Find an expression for the total rate of mass flux of oxygen in the medium. (Hints: use the Fick's law; er f is the Gauss error function; you may need to define some additional parameters for the geometry of this system).

Reference no: EM132455169

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