How to Draw a Differential Equation in Matlab

How do you solve these coupled differential equations in Matlab?

I have three partial differential equations (PDEs) and an analytical solution for a variable as shown. With these equations I want to solve for \ phi (x, y, t), p (x, y, t), C_ {a} (x, y, t) and C_ {b} (x, y, t). ie in terms of space and time.

I know there is a function in Matlab to solve initial boundary value problems for parabolic-elliptical PDEs in 1-D. I would like to know how this function or another can be used in Matlab to solve the problem described below which is 2-D and coupled.


The following two equations represent PDEs for two species A and B, respectively:

Where D_ {h} and q are given as:

Here R_ {a} = R_ {b} = R, where R as indicated:

Finally, the last equation is given:

Initial and boundary conditions:

The total domain size is 10 cm × 5 cm and the width of the Y-shaped subdomain is 0.5 cm. This subdomain has an initial phi of 0.50, while in the surrounding matrix it is \ phi = 0.26. Constant p of 1 Pa and 0 Pa are held at the limits (1) and (2), respectively, which corresponds to a gradient of about 10 ^ -3 m m -1. The p on limits (3) and (4) are determined by linear gradients between the limits (1) and (2). Constant C of C_ {a} = 2 molm ^ -3 and C_ {b} = 0.2302 molm ^ -3 are kept at the limit (3), while the concentrations at the limit (4) are set to C_ {a} become. = 1 mol m ^ -3 and C_ {b} = 0.4603 molm ^ -3. The concentrations at the limit (1) are determined by constant gradients between the limits (3) and (4), while an advective flow limit condition $$ (\ frac {\ partial C} {\ partial x} = 0) $$ is set at the exit at (2).


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