3. A 2 cm long metal wire with thermal diffusivity ² = 4cm² s¹ is used to conduct heat in a machine between a number of components. The ends of the wire are held at a constant temperature of 0°C. At time t = 0, the temperature of a point x cm from the leftmost end of the wire is given by f(x), where 50 sin 2x 0≤x≤T 10 π < x≤ 2π Find the function u(x, t) that describes the temperature in Celsius of a point x cm from the left most end of the wire after t seconds.
3. A 2 cm long metal wire with thermal diffusivity ² = 4cm² s¹ is used to conduct heat in a machine between a number of components. The ends of the wire are held at a constant temperature of 0°C. At time t = 0, the temperature of a point x cm from the leftmost end of the wire is given by f(x), where 50 sin 2x 0≤x≤T 10 π < x≤ 2π Find the function u(x, t) that describes the temperature in Celsius of a point x cm from the left most end of the wire after t seconds.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:4cms is used to conduct
3. A 2π cm long metal wire with thermal diffusivity a²
heat in a machine between a number of components. The ends of the wire are held at a
constant temperature of 0°C. At time t = 0, the temperature of a point x cm from the
leftmost end of the wire is given by f(x), where
50 sin 2x
0≤x≤T
10
π < x < 2π
Find the function u(x, t) that describes the temperature in Celsius of a point x cm from
the left most end of the wire after t seconds.
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