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ONE-DIMENSIONAL HEAT EQUATION Consider a slab with heat applied to the left and/or right side. As heat is applied, the temperature, T, at any one location in the slab will increase. Thus, T is a function of time. Additionally, there will be a temperature gradient along the slab. Thus, T is a function of space. "R" The PDE defining the temperature T(x,t) across this slab at any time and position L SXSR is given by a Ca27 at np ax20 where n a k is the specific heat, p=2.7 x 109/m3 is the material density, and C = 205 W/mK is the thermal conductivity. Assume a length of the slab is 5 m. Assume time ranges from 0 to 100 seconds. 1) Assume boundary conditions of (t) = 50+tand Tr(t) = 95 + t. Solve and surf plot the temperature throughout the slab for initial condition of T.(x) = 0 in position l of a 1x2 figure. (2 pts) 2) Re-run I) but plot in position 2 of the 1x2 figure assuming T.(x) = 20 . -2.5 - 65. (pt) 3) In general, where do you see the effect of the initial condition and what effect does it have? Verify that the initial and boundary conditions are what you expect them to be. (2 pts) 4) Assume the system changes slightly. Now, it has an initial condition of T.(x) = 100 and boundary conditions of T. (t) + 0.35 (Lt) = 0 and T (t)-0.35=(Rt) = 0. Solve and surf plot the temperature for a 10 second simulation throughout the slab in position of a 1x2 figure (Figure 2) (2 pts) 5) Re-run 4) but plot in position 2 of the 1x2 figure assuming QR = 0.15. Why does temperature rise over time, symmetrically about x in 4), but have a very different trend with QR is changed? What does this tell you about flux at boundaries with specific respect to directionality? (3 pts) ONE-DIMENSIONAL HEAT EQUATION Consider a slab with heat applied to the left and/or right side. As heat is applied, the temperature, T, at any one location in the slab will increase. Thus, T is a function of time. Additionally, there will be a temperature gradient along the slab. Thus, T is a function of space. "R" The PDE defining the temperature T(x,t) across this slab at any time and position L SXSR is given by a Ca27 at np ax20 where n a k is the specific heat, p=2.7 x 109/m3 is the material density, and C = 205 W/mK is the thermal conductivity. Assume a length of the slab is 5 m. Assume time ranges from 0 to 100 seconds. 1) Assume boundary conditions of (t) = 50+tand Tr(t) = 95 + t. Solve and surf plot the temperature throughout the slab for initial condition of T.(x) = 0 in position l of a 1x2 figure. (2 pts) 2) Re-run I) but plot in position 2 of the 1x2 figure assuming T.(x) = 20 . -2.5 - 65. (pt) 3) In general, where do you see the effect of the initial condition and what effect does it have? Verify that the initial and boundary conditions are what you expect them to be. (2 pts) 4) Assume the system changes slightly. Now, it has an initial condition of T.(x) = 100 and boundary conditions of T. (t) + 0.35 (Lt) = 0 and T (t)-0.35=(Rt) = 0. Solve and surf plot the temperature for a 10 second simulation throughout the slab in position of a 1x2 figure (Figure 2) (2 pts) 5) Re-run 4) but plot in position 2 of the 1x2 figure assuming QR = 0.15. Why does temperature rise over time, symmetrically about x in 4), but have a very different trend with QR is changed? What does this tell you about flux at boundaries with specific respect to directionality? (3 pts)