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 f(x) = 200 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 us (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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5)

[ordinary differential equations topic]

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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 f(x) = 200 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 us (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
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 f(x) = 200 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 us (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
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