2) (a: score 30%) Use the explicit method to solve by hand the 1D heat equation (see Lecture 27) for the temperature distribution in a laterally insulated wire with a length of 1 cm, whose ends are kept at T(0) = 0 °C and T(1) = 0 °C, for 0 < x < 1 and 0 < t < 0.5. At t= 0, the temperature of the wire is subjected to initial condition T(x) 100sin(nx). Use the following values of k= 0.15 cm/s, x = 0.25 cm, and At = 0.1 s. Calculate by hand the values of temperature at the internal mesh points only for the first time row at t = 0.1 s. (b: Score 10%) Run MATLAB's Heat1DFD.m and Heat1DCN.m M-files and calculate the distribution within the temperature space-time domain 0 < x < 1 and 0 < t s 0.5 using the parameters and steps from (a). Verify the values of temperature at t = 0.1 s calculated by hand. (c: score 10%) Use Heat1DCN.m M-file to solve the 1D heat equation within the space-time

Elements Of Electromagnetics
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Would someone explain in detail the by hand part? I do not understand. Thank you!

11:56
O ul 53%
Page Break
2) (a: score 30%) Use the explicit method
to solve by hand the 1D heat equation (see
Lecture 27) for the temperature distribution
in a laterally insulated wire with a length of
1 cm, whose ends are kept at T(0) = 0 °C
and T(1) = 0 °C, for 0 < x <1 and 0 < t s
0.5. At t = 0, the temperature of the wire is
subjected to initial condition T(x)
100sin(nx). Use the following values of k=
0.15 cm/s, Ax = 0.25 cm, and At = 0.1 s.
Calculate by
temperature at the internal mesh points
only for the first time row at t = 0.1 s.(b:
Score 10%) Run MATLABs Heat1DFD.m
and Heat1DCN.m M-files and calculate the
hand
the
values
of
distribution
within
the
temperature
space-time domain 0 < x < 1 and 0 < t <
0.5 using the parameters and steps from
(a). Verify the values of temperature at t =
0.1 s calculated by hand. (c: score 10%)
Use Heat1DCN.m M-file to solve the 1D
heat equation
domain 0 < x< 1 and 0 sts2 with Ax =
0.05 cm and At = 0.1 s. Make the plot of
within the
space-time
temperature surface.
Transcribed Image Text:11:56 O ul 53% Page Break 2) (a: score 30%) Use the explicit method to solve by hand the 1D heat equation (see Lecture 27) for the temperature distribution in a laterally insulated wire with a length of 1 cm, whose ends are kept at T(0) = 0 °C and T(1) = 0 °C, for 0 < x <1 and 0 < t s 0.5. At t = 0, the temperature of the wire is subjected to initial condition T(x) 100sin(nx). Use the following values of k= 0.15 cm/s, Ax = 0.25 cm, and At = 0.1 s. Calculate by temperature at the internal mesh points only for the first time row at t = 0.1 s.(b: Score 10%) Run MATLABs Heat1DFD.m and Heat1DCN.m M-files and calculate the hand the values of distribution within the temperature space-time domain 0 < x < 1 and 0 < t < 0.5 using the parameters and steps from (a). Verify the values of temperature at t = 0.1 s calculated by hand. (c: score 10%) Use Heat1DCN.m M-file to solve the 1D heat equation domain 0 < x< 1 and 0 sts2 with Ax = 0.05 cm and At = 0.1 s. Make the plot of within the space-time temperature surface.
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