is that using the updated infor from this This homework set is very much based on this week's computer lab. We study the cooling of lava filled dike and derive the temperature distributions T(x,t). The lava has an initial temperature of 1150C, and surrounding host rock host rock has one of 20C. We assume the dike has a width of d=5 meters and is infinitely long in y and z directions. For rock and lava, use a heat capacity of 1.23 Joule/gramm/Kelvin, a density of 2.55 gramm/cm3, and a heat conductance of 0.042 J/cm/seconds/Kelvin. Discretize the dike into N=50 intervals. Then add a layer of host rock of width 2d on each side, which brings the total number of intervals to 5N. This determines your initial conditions. Choose Dirichlet boundary conditions, T=20, on each side