The two-dimensional heat equation \(\partial u / \partial t=abla \cdot(\chi abla u)+f\), where \(\chi\) is a function of \(u\) and \(f\) is a known function of \(\boldsymbol{x}\) and \(t\), is solved in a rectangular domain \(0 \leq x \leq L_{x}, 0 \leq y \leq L_{y}\). The boundary conditions correspond to perfect insulation on all four boundaries. Write the integral conservation equation, and approximate all integrals for an internal cell and for cells adjacent to the boundaries. Use the structured Cartesian grid with constant steps \(\Delta x\) and \(\Delta y\) (see Figure 5.5a). The resulting finite volume scheme must be of the second order of approximation.