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ordinary differential equations; topic] Please solve the following problem Provide a well explained and understandable(readable) Step by step solution solution

ordinary differential equations; topic] Please solve the following problem Provide a well explained and understandable(readable) Step by step solution solution

Advanced Engineering Mathematics
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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[ordinary differential equations; topic] Please solve the following problem Provide a well explained and understandable(readable) Step by step solution solution

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) = 25 + 25x 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(r, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then us (2, 0.1). Put uz (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 is given by the function f(x) = 25 + 25x 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(r, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then us (2, 0.1). Put uz (2. 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.
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