A thin bar of length L = 3 meters is situated along thex axis so that one end is at x = 0 and the other end isat x = 3. The thermal diffusivity of the bar is k = 0.4.The bar's initial temperature f(x) = 50 degrees Celsius.The ends of the bar (x = 0 and x = 3) are then put in%3Dan icy bath and kept at a constant 0 degrees C. Letu(x, t) be the temperature in the bar at x at time t,with t measured in seconds. Find u(x, t) and thenU7 (2, 0.1).Put u (2, 0.1) calculated accurately to the nearestthousandth (3 decimal places) in the answer box.

Consider the provided question,

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) = 50 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.

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) = 50 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: The pressure of a fluid flowing through a closed system, P, after t seconds can be modeled by the…

Q: Find two antiderivatives of f (x) = cos x. Then determine the general antiderivative.

Q: o ook at the picture below. As a windmill's blade rotates, the height of its tip above ground is…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Find dy/dx for each implicit function. 27. sec (x + y) = 7 26. xy + y cot x = 0 =

Q: 5. Solve the equation (D² + 1)y = sec x tan x

Q: a²f ô²f Ôy 1. If f(x,y)= e¯* sin y then find .2

A: Using differentiation ,

Q: 50) Use Antiderivatives to write equation for P,(t). Remember to solve for all your Cs. an

A: Given: The curve showing the velocity where the data about first two hours is not given, and…

Q: On a particular summer day the temperature function in Celsius is given by (7) T(t+7) T(t) = 20 + 8…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. If the…

Q: 258. A spherical balloon is filled with air at the rate of 2 cu cm/min. Compute the time rate of…

Q: Let f(x)= 2/x and g(x)= 3/ x-1. Find the following: a. (f°g) b. (g°f

A: Given that: fx=2xgx=3x−1 To find: fogx and gofx

Q: H.W. using the relation r= Vn = show that J(x) - COs X %3D

Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

Q: 1: For each of the functions below, decide whether it solves the equation: (y)² = 1 - y². A) y(t) =…

A: Given that the differential equation is .The objective is to verify the given solutions.

Q: Given sinh(r) = then tanh(r) = Select one: a. b. + C. + d. OS Shot by Hisense H12

Q: The displacement from equilibrium of a weight oscillating on the end of a spring is given by y =…

A: For the equation: y=1.62e-0.22tcos4.9t, we need to determine the value of t such that the value of y…

Q: Find the solution of the equation cos y dy? which tends to zero as i → 0o and has the value cos y…

Q: Find an appropriate guess for y,p. You do not need to find the values of the coefficients. y" + 3y'…

Q: The function y = 17.14 sin(0.52x - 1.75) + 7.11, where x represents the number of the month, models…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2) Find the minimum value of 6 cos x 8 sin x 3) The phase shift o̟ in a certain electric circuit…

Q: SSX = 172.5, SSY = 80.6, and Σ[(X – MX) (Y – MY)] = 95.33, r = :

A: Given information, SSX = 172.5, SSY = 80.6, and Σ[(X – MX) (Y – MY)] = 95.33 SSXY= Σ[(X – MX) (Y –…

Q: Qs: The ends for an insulated rod PQ are maintained at 0°C. At time t=0 the temperature within the…

Q: Let a + 0 be a constant. Give an example of a function y = f(x) for which ay – y' = 0 and g?y – y" =…

Q: An isolated bar is kept at zero temperature at its ends. If it's given initially temperature, f(x) =…

A: First of all the question has a small error in place of (dt) (dx) was printed. Which I had corrected…

Q: 3. A thermally conducting solid bounded by two concentric spheres of radii a and b, a<b, is such…

A: Given that the temperature of the inner surface is T1 The temperature of the outer surface is…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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) = 50 degrees Celsius.
The ends of the bar (x = 0 and x = 3) are then put in
%3D
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
U7 (2, 0.1).
Put u (2, 0.1) calculated accurately to the nearest
thousandth (3 decimal places) in the answer box.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Pls help me these numbers!
3. Find for each of the following functions: 1-x (a) y = 1-tanx (b) y = u°+In(2u), where u = e 3x
If f(x)=cosx and f(x)=0, calculate x for 0°
- If V) = AT sin (2 nf t)/(2 nfT), find the energy contained in v (t).
(Zero temparature ends ) Suppose that a copper rod of lenght 50 cm was placed into a reservoir with hot water at 50° C so that half of it is in the air at 20°C.At t=Q, the rod is taken out and its ends are kept at constant ambient temparature of 20° c. Let us denote the difference between the rod's temparature and the ambient temparature by U(x,t), where x is the distance from the left end of the rod , x=0. The U(x,t) is a solution of the initial boundary value problem: U; = « Uxx x = 1.14 With boundary conditions as U(0, t) = U(50, t) = 0 30, 0