Apply ADI methods to two dimensional heat equation and find T+1 at the internal grid points in the mesh shown in figure. Also, find the length a and b, initial condition are: x Tn = 1- along y = 0 3Ax y Tn = 1- along left side 3Ay от [a²T ǝ²T] Ξα + at ax2 y2 Where: T=0 everywhere else, and the boundary conditions remain fixed at these initial value. k=240 W/m.°C, p=2700 Kg/m³, Cp= 920 J/kg.k, R=1 cm. R R y 2 cm b a Ay. 2R/3 Ax 2 cm x

(3) For the given boundary value problem, the exact solution is given as = 3x - 7y. (a) Based on the exact solution, find the values on all sides, (b) discretize the domain into 16 elements and 15 evenly spaced nodes. Run poisson.m and check if the finite element approximation and exact solution matches, (c) plot the D values from step (b) using topo.m. y Side 3 Side 1 8.0 (4) The temperature distribution in a flat slab needs to be studied under the conditions shown i the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I all cases assume the upper and lower boundaries are insulated. Assume that the units of length energy, and temperature for the values shown are consistent with a unit value for the coefficier of thermal conductivity. Boundary Temperatures 6 Case A C D. D. 00 LEGION Side 4 z epis

What's the answer

Use the Lax method to solve the inviscid Burgers' equation using a mesh with 51 points in the x direction. Solve this equation for a right propagating discontinu- ity with initial data u = 1 on the first 11 mesh points and u = 0 at all other points. Repeat your calculations for Courant numbers of 1.0, 0.6, and 0.3 and compare your numerical solutions with the analytical solution at the same time.