Suppose that the temperature in a long, thin rod placed along the x axis is initially C (2a) if x a and 0 if x a It can be shown that if the heat diffusivity of the rod is k, then the temperature of the rod at the point x at time t is To find the temperature distribution that results from an initial hot spot concentrated at the origin, we need to compute Use lHospitals Rule to find this limit T(, ) (x )2 (4k) du a 4rkt lim a 0 T(, t)

Question: Suppose that the temperature in a long, thin rod placed along the x-axis is initially C/(2a) if |x | < a and 0 if |x

Suppose that the temperature in a long, thin rod placed along the x-axis is initially C/(2a) if |x | < a and 0 if |x | > a. It can be shown that if the heat diffusivity of the rod is k, then the temperature of the rod at the point x at time t is

T(х, ) - - (x-и)2/(4k) du a /4rkt

To find the temperature distribution that results from an initial hot spot concentrated at the origin, we need to compute lim a >0 T(х, t). Use l’Hospital’s Rule to find this limit.

T(, ) - - (x-)2/(4k) du a /4rkt lim a >0 T(, t).

Step by Step Solution

★★★★★

3.45 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Both numerator and denominator approach 0 as a 0 so ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Suppose that the temperature readings for a certain gauge are uniformly distributed between 0C and 5C. Find the probability of a randomly selected temperature reading falling in the following range:...

Suppose that the temperature T at the point (x, y, z) depends only on the distance from the origin. Show that the direction of greatest increase in T is either directly toward the origin or directly...

Suppose that the temperature T on the circular plate {(x, y}: x2 + y2 ( 1} is given by T = 2x2 + y2 - y. End the hottest and coldest spots on the plate.

( 1 5 pts ) A long, thin rod lies along the x - axis. One end of the rod is located at x = 1 . 0 0 m , and the other end of the rod is located at x = 3 . 0 0 m . The linear mass density of the rod is...

Answer: 1=59.742=83.46,3=113.05, 4=150.89 Code in MATLAB Numerical Methods for Engineers Chapter 12: Problem 38 The answer that I am getting is different than the values I typed above. Could you...

Please Help!!! 7:24 webassign.net T = FV OR (1.01x105 N/m2) (495 m3) 1.7743 x 10* mol (8.314 ]/mol . K ) 338.9 0 K Finalize Since temperature in degrees Centigrade is calculated from degrees Kelvin...

1) A long thin rod is placed along the axis of a long cylindrical shell of radiuses of R. If the linear charge density of the thin rod is it > 0 and the surface charge density of the cylinder is 0' >...

Linear algebraic equations can arise in the solution of differential equations. In this problem you will develop a MATLAB code to solve the heat transfer problem in a 1-dimensional bar. The following...

MATLAB PROBLEM 1 Background Linear algebraic equations can arise when modeling distributed systems. Linear algebraic equations can arise when modeling distributed systems. Figure 1: A noninsulated...

The temperature u(x, t) of a long, thin rod of constant cross section and homogeneous conducting material is governed by the one-dimensional heat equation. If heat is generated in the material, for...

Write a paper on Organizational Behavior and Ethical Leadership And this paper also described the answer followings questions. What purpose does leadership serve, and why is it an integral part of an...

1. Determine Taylor's remainder formula (Property 2.9) for the Taylor series of cos(x) about c = and use it to determine the following: 4 (a) What is the largest a for which the formula guarantees...

Part A Graded Homework ( i ) Heidi Software Corporation provides a variety of share - based compensation plans to its employees. Under its executive stock option plan, the company granted options on...

How can social media boost the organic search engine rankings for a business?

Evaluate the definite integral. dx (1 + Jx)* 4

Verify that f (x) = sin 3 x is an odd function and use that fact to show that sin Vx dx

Use a graph to give a rough estimate of the area of the region that lies under the given curve. Then find the exact area. = 2x + 1, 0

Living Spaces sells living room sets. Sofa sells for $272 per unit and has variable costs of $155 per unit. Side Table sells for $46 per unit and has variable costs of $26 per unit. Living Spaces...

During the year, the Senbet Discount Tire Company had gross sales of $1.12 million. The firms cost of goods sold and selling expenses were $531,000 and $221,000, respectively. The firm also had notes...

Use the following Unadjusted Trial Balance for Acct 201 as of July 31, 2020 to answer Questions 11 and 12 (The information is based on Problem 3-5B, page 154): ACCT 201 Co. Unadjusted Trial Balance...