Consider heat conduction on a slender homogeneous metal wire with constant crosssection as shown in Fig.2. L = 0.3 m. Conductivity k = 10 w/m°C. Q(x) = 100,000 W/m³. Atx=L, q=-1000 W/m², T (x = 0) = 100 °C. d'T Governing equation: -k=Q, dx² Boundary condition: T=100°C dT dx |x=L = q (0

College Physics
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Consider heat conduction on a slender
homogeneous metal wire with constant
crosssection as shown in Fig.2. L = 0.3 m.
Conductivity k = 10 w/m°C.
Q(x)= 100,000 W/m³. At x=L,
q=-1000 W/m², T (x = 0) = 100 °C.
d²T
Governing equation: -k- Q₂ (0<x<L)
dx²
Boundary condition:
T = 100°C
-k.
dx \x=L
= q
Q(x)
L
Figure 1 Heat conduction on a 1-D metal wire.
a. Following the nine-step procedure to solve for T (x) with two linear elements (X1
= 0, x₂ = 0.1m, and x3 = 0.3m).
a. Compare with analytical solutions and the maximum find numerical error.
q x
Transcribed Image Text:Consider heat conduction on a slender homogeneous metal wire with constant crosssection as shown in Fig.2. L = 0.3 m. Conductivity k = 10 w/m°C. Q(x)= 100,000 W/m³. At x=L, q=-1000 W/m², T (x = 0) = 100 °C. d²T Governing equation: -k- Q₂ (0<x<L) dx² Boundary condition: T = 100°C -k. dx \x=L = q Q(x) L Figure 1 Heat conduction on a 1-D metal wire. a. Following the nine-step procedure to solve for T (x) with two linear elements (X1 = 0, x₂ = 0.1m, and x3 = 0.3m). a. Compare with analytical solutions and the maximum find numerical error. q x
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