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Update l30.md
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fixed a few typos
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johnryantaylor authored Jan 30, 2024
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Expand Up @@ -104,13 +104,13 @@ Now, let's consider the possible steady state solutions to Eq. {eq}`eq:diffusive

```{math}
:label: eq:equilibrium_temperature_eq
A(1+\cos{\frac{2y}{R_e}})+(B-C)-DT_e + C_a \kappa \frac{d ^2 T_e}{d y^2}=0.
C(1+\cos{\frac{2y}{R_e}})+(D-A)-BT_e + C_a \kappa \frac{d ^2 T_e}{d y^2}=0.
```

Since this is a second order ODE, we need two boundary conditions. One choice is to ensure that the heat flux vanishes at the poles which requires that

```{math}
\frac{\partial T}{\partial y}= 0, \quad @ \quad y=-90^\circ, 90^\circ.
\frac{dT}{dy}= 0, \quad @ \quad y=-90^\circ, 90^\circ.
```

Based on this boundary condition and the form of Eq. {eq}`eq:equilibrium_temperature_eq`, we might guess that the solution will be of the form
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