a)[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 thermaldiffusivity of the bar is k = 0.4. The bar's initial temperature is given by the function f(x) = 20 + 10x degrees Celsius. The ends of thebar (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 attime t, with t measured in seconds. Find u(x, t) and then u; (2, 0.1).Put uz (2. 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

Answered: A thin bar of lengthL=3 meters is…

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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) = 20 + 10x 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 uz (2. 0.1) calculated accurately to the nearest thousandth (3 decimal places) in the answer box.

Expert Solution

Step 1

Consider a tin bar of length L=3 meters is situated along x- axis and the other is at x=3.

The thermal diffusivity of the bar is k=0.4. the bar’s initial temperature is:

$f (x) = 20 + 10 x$

The objective is to find $u (x, t)$ and $u_{5} (2, 0.1)$ .

Step by step

Solved in 2 steps with 11 images

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