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
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Please use radian measure
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.
cs Scanned with CamScanner
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. cs Scanned with CamScanner
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