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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 isk = 0.4. The bar's initial temperature f(x) = 400 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 u, (2, 0.1). Put u (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

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 isk = 0.4. The bar's initial temperature f(x) = 400 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 u, (2, 0.1). Put u (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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[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 isk = 0.4. The bar's initial temperature f(x) = 400 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 uz(2, 0.1). Put u7 (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 isk = 0.4. The bar's initial temperature f(x) = 400 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 uz(2, 0.1). Put u7 (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
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