which, when differentiated with respect to gives x, Replacing using Eq. and rearranging the resulting equation gives Ix Similarly, for the y-direction, Now, according to Kirchhoff’s current law, the sum of the currents entering the junction of the two TLs must equal zero, and so which simplifies to Using Equations and to replace the derivatives of the currents gives From Eq. , = and so this can be rewritten as rx y, Now, from Eq. , , and so this becomes It is clear that a transmission line network of this kind is analogous to the CRDE in two dimensions when
which, when differentiated with respect to x, gives Replacing Ix using Eq. and rearranging the resulting equation gives Similarly, for the y-direction, Now, according to Kirchhoff’s current law, the sum of the currents entering the junction of the two TLs must equal zero, and so which simplifies to Using Equations and to replace the derivatives of the currents gives From Eq. , rx = y, and so this can be rewritten as Now, from Eq. , , and so this becomes It is clear that a transmission line network of this kind is analogous to the CRDE in two dimensions when
Numerical_modelling_of_convection-reaction-diffusion_problems_using_electrical_analogues.docx