A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature is given by the function f(x) = 100 - 5x degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1).
A thin bar of length L = 3 meters is situated along the x axis so that one end is at x = 0 and the other end is at x = 3. The thermal diffusivity of the bar is k = 0.4. The bar's initial temperature is given by the function f(x) = 100 - 5x degrees Celsius. The ends of the bar (x = 0 and x = 3) are then put in an icy bath and kept at a constant 0 degrees C. Let u(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u4 (2, 0.1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A thin bar of length L = 3 meters is situated along the x axis
so that one end is at x = 0 and the other end is at x = 3.
The thermal diffusivity of the bar is k = 0.4. The bar's initial
temperature is given by the function f(x) = 100 - 5x degrees
Celsius. The ends of the bar (x = 0 and x = 3) are then put
in an icy bath and kept at a constant 0 degrees C. Let
u(x, t) be the temperature in the bar at x at time t, with t
measured in seconds. Find u(x, t) and then u4(2, 0.1).
Put u4 (2, 0.1) calculated accurately to the nearest
thousandth (3 decimal places) in the answer box.
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