Task A: Using the data in Table 1 find, X the average yearly temperature in Bristol. Plot the data shown in Table 1.
|
Tmax |
Tmin |
| January |
9 |
-1 |
| February |
9 |
-2 |
| March |
11 |
0 |
| April |
14 |
1 |
| May |
17 |
3 |
| June |
20 |
6 |
| July |
21 |
9 |
| August |
21 |
10 |
| September |
19 |
6 |
| October |
15 |
2 |
| November |
11 |
-1 |
| December |
8 |
-1 |
Task B: Constant outside temperature (6 = 0).
(a) For this Task, take Ta = X and δ = 0. Write down the resulting differential equations for y1 and y2, together with the appropriate initial conditions. Find the appropriate solution of y(t) for 0 ≤ t ≤ td by hand or using Maple and present it in a clear and concise way. Illustrate the temperature of the building over five days. Note that you may wish to use the piecewise command here.
(b) With explanation, calculate the values of T1, T2, T3, T4, tb, tc and td and indicate each value on your plot produced in (a).
(c) With explanation, calculate te.
Task C Sinusoidal outside temperature (δ ≠0).
(a) For this Task, consider one particular month, and use the data in Table 1, where, for the month chosen take Ta = 1(Tmax+Tmin) and 6 = 1(Tmax-Tmin). Write down the resulting differential equations for y1 and y2, together with the appropriate initial conditions. Solve the equation for y1 by hand and verify your solution using MAPLE.
(b) Use MAPLE to find the solution to y2. Produce a single plot illustrating the temperature in the building over five days, starting from 2pm on the Thursday. Note that you may wish to use the piecewise command here.
(c) Compute the values of T1, T2, T3, T4, tb, tc, tc, and te.