Part two: One-dimensional convection diffusion problem Assignment (please read the problem description before doing the assignment) e Develop a finite difference method (FDM) formula for solving the equation. The procedure of deriving the FDM formula must be included in the report. Develop a MATLAB program and use this program to do the simulation and answer the following questions. Divide the soil depth into 200 cells when solving the problem numerically. You must attach the MATLAB program in your report. e If a=0.0002 m'/s, find out when the temperature at the depth of 1.5 m reaches 25C. o If the temperature at the depth of 1.5 m reaches 25C 1s defined as Ti.5, do the simulations for a in the range of 0.0002 m/s to 0.001 m*/s with an interval of 0.0001 m*/s and discuss how on T1s and why. Problem description Note: In the paragraph below, the number j stands for the last digit of vour student ID. For example, if vour student 1D is 2345673, 10+j = 13. The water on the ground flows into the soil through the pore space of the soil (the space between soil particles). The flow velocity is very small of 0.002x(1+}) m/s and it does not change along the vertical direction. Initially, the temperature 1s (10+)) C in the whole soil volume (including soil and the water in the soil). The temperature of the water on top of the ground level is 30C and remains constant. The warm water moves into the soil and increases the temperature in the soil. Ground level =1 =1 X A coordinate x is defined and its origin is on the ground level and pointing downwards. The governing equation is the convection diffusion equation or or o&'T =ta where T is the temperature in the soil t 1s the time u is the water flow velocity a is the heat diffusion coefficient (the influence of the soil has been considered). : Boundary condition is 7=30C at the top boundary and % =0 at the bottom boundary (at x=2 m)