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 - 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(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u5 (2, 0.1). Put uz (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 is k = 0.4. The bar's initial temperature is given by the function f(x) = 100 - 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(x, t) be the temperature in the bar at x at time t, with t measured in seconds. Find u(x, t) and then u5 (2, 0.1). Put uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

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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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 - 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(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 uz (2, 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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