Please solve question 4. b,c and d. Materiala² (cm²/s)Silver1.71СopperAluminum1.140.86Cast iron0.12Granite0.011Brick0.0038Water0.00144Table 1: Thermal Diffusivity Constants for Common Materials4.The solution to a heat conduction problem with homogeneous boundary conditions is:(-1)n+18u(x, t) = >-1.71n²n²t/16e(")sinn=1(a) What is the length of the rod (in centimeters)?(b) Use Table 1 to determine which material was used to make the rod.(c) Write out the first three terms of u(x, t).(d) Use your partial sum from (b) to approximate the temperature at the midpoint when t = 1, 5, 10.

Consider the given solution of the heat conduction problem.

Material a (cm?/s) Silver 1.71 Copper Aluminum 1.14 0.86 Cast iron 0.12 Granite 0.011 Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materials 4. The solution to a heat conduction problem with homogeneous boundary conditions is: u(x, t) (-1)"+l8 ,-1.71n²r²t/16 sin 4 n=1 (a) What is the length of the rod (in centimeters)? (b) Use Table 1 to determine which material was used to make the rod. (c) Write out the first three terms of u(x, t). (d) Use your partial sum from (b) to approximate the temperature at the midpoint when t = 1, 5, 10.

Material a (cm?/s) Silver 1.71 Copper Aluminum 1.14 0.86 Cast iron 0.12 Granite 0.011 Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materials 4. The solution to a heat conduction problem with homogeneous boundary conditions is: u(x, t) (-1)"+l8 ,-1.71n²r²t/16 sin 4 n=1 (a) What is the length of the rod (in centimeters)? (b) Use Table 1 to determine which material was used to make the rod. (c) Write out the first three terms of u(x, t). (d) Use your partial sum from (b) to approximate the temperature at the midpoint when t = 1, 5, 10.

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: Road Transport Department claims that the mean speed of cars on a highway is 114 km/h. An insurance…

A: Introduction: t-test The t-test is used when to test the difference between the two population…

Q: What percent of a standard Normal model is found in each region? Draw a picture first. a) z> 1.7 b)…

A: a) z>1.7 Area is the right of z=1.7 PZ>1.7=1-PZ<1.7=1-0.95543=0.04457 The percent of area…

Q: Answer parts D, E & F

A: (d) From t table at 17 degrees of freedom, the area to the right of 1.740 is 0.050.…

Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

A: We have given that. X~N( μ , ?^2 ) μ=5 , ? =1 Z-score =( x - μ )/?

Q: A hydroponic grower was trialling two different greenhouse systems for growing tomatoes. To compare…

A: (c). Explain why one of the weights in green house A was identified as an outlier: The presence of…

Q: Use triangle ABC to answer questions 1-2. 4 in. 5 in. B 3 in. 1. Which side is opposite ZA? 2. What…

A: given that

Q: In the last quarter of 2007, a group of 64 mutual funds had a mean return of 4.9% with a standard…

A: (a) Obtain the value that represents the 40th percentile of these returns. The value that represents…

Q: Sales delay is the elapsed time between the manufacture of a product and its sale. According an…

A: Dear student as per guidelines we answer the first three subparts only when multiple different…

Q: eBook A sample containing years to maturity and yield for 40 corporate bonds are contained in the…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: The checking accounts of Sun Bank are categorized by the age of account and the account balance.…

A: Given data: The total numbers of accounts are n=1000. The numbers of accounts that are less than 2…

Q: Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches…

Q: ACTIVITY Formulate a Null Hypothesis and Alternative Hypothesis for each of the following and write…

A: Since you have posted a question with multiple subparts, we will solve first three subparts for you.…

Q: Mike Jimenez is president of the teachers' union for Preston School District. In preparing for…

A: As per the given information, the President of the teacher's union of Preston school district wants…

Q: Every Normal model is defined by its parameters, the mean and the standard deviation. For each model…

A: For first part (a), it is given that the area above x=30 is 40% means 0.40. So using the standard…

Q: Consider the inhomogeneous wave equation - c?uxx = f (x,t), Utt - where 1 ifx > 0, if x 1, on which…

A: Given equation is utt-c2uxx=fx,t. Let the solution be of the form ux,t=∑n=1∞TntXnx where Xnx are…

Q: (b) x²e3 dx (d) arctan 4t dt

Q: The quarterly returns for a group of 69 mutual funds with a mean of 3.2% and a standard deviation of…

A: The cut off value for the highest 10% of the funds will be: Thus, the required cut off value is…

Q: (b) The analysis of variances F-test statistic is given by what? (This is a reading assessment…

A: Given see the handwritten solution

Q: What percent of a standard Normal model is found in each region? Draw a picture first. a) z>1.35 b)…

A: P(-1.7<Z<0.65) = P(-1.7<Z<0)+P(0<Z<0.65) We check the value of z from standard…

Q: The probability that a student at a university is a male is 0.48, that a student is a business major…

A: Define the events , A : The student is a male B : The student have a business major Given, P(A) =…

Q: Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the…

Q: 3. AN APPLICATION OF EULER PATH THEOREM. Below s the map of all the trials in a national park. A…

A: Given the map of all the trials in the national park.

Q: y=3-z.y=-1, and -2

A: As per our guidelines we can only solve one question and rest of the question will be reposted.

Q: A random sample of residents from various income brackets were asked their opinion on tax reform for…

A: a) Null Hypothesis: H0:The income brackets and tax reforms for the country of Guyana are…

Q: A simple random sample of sizen is drawn from a population that is normally distributed. The sample…

A: Solution: Given information: x= 110 Sample size s= 10 Sample standard deviation

Q: 12+x

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Let f be a continuous function. The graph of its derivative f' is shown below. "There is no such…

A: We need to determine the critical point(s) of f that is neither a local minimum nor a local maximum.…

Q: Zo) 1664 d. P(zo <Z < 0) = 0.4798 e. P(Z < zo) = 0.2090 %3D

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

Please solve question 4. b,c and d.

Material
a² (cm²/s)
Silver
1.71
Сopper
Aluminum
1.14
0.86
Cast iron
0.12
Granite
0.011
Brick
0.0038
Water
0.00144
Table 1: Thermal Diffusivity Constants for Common Materials
4.
The solution to a heat conduction problem with homogeneous boundary conditions is:
(-1)n+18
u(x, t) = >
-1.71n²n²t/16
e
(")
sin
n=1
(a) What is the length of the rod (in centimeters)?
(b) Use Table 1 to determine which material was used to make the rod.
(c) Write out the first three terms of u(x, t).
(d) Use your partial sum from (b) to approximate the temperature at the midpoint when t = 1, 5, 10.

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

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 13 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Linear Equations$

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

Q6 A 1.0 m length copper bar with a constant cross section area of 0.0001 m² have the values of density, thermal conductivity and specific heat of 8960 kg/m², 385 W/m.K and 389 J/kg.K respectively. The copper bar is perfectly insulated laterally, with ends kept at temperature 0°C. The one-dimensional heat equation, with u(x,t) as the temperature is given as: ôu ốt k a? is the thermal diffusivity of the material, where; k = thermal conductivity, o=specific op heat, and p=density of material. (i) By using the method of separation of variable, derive the expression for the heat conduction through the copper bar If the initial uniform temperature, f(x)=100sin ax, how long will it take for the (ii) maximum temperature in the bar to drop to 50°C. (Hint: maximum temperature occurs at the center of the bar)
1. JK = 17 and JN =10 %3D %3D JM = K JL% = MN = N. MK = %3D
Solve the problem y' = x²y², y(0) h = 0. 1. Select the correct answer. = 1 numerically for y(0. 2) using %3D a) 1.001 b) 1.0001 c) 1.01 O d) 1.0
5. Solve y' = x² + y, find y(0.1) by talking step size h = 0.1 given that y = 10 at x = 0 %3D initially considering terms up to the fourth degree.
Cozu.. z. [Find the value of the solution to the following initial value problem at a = 1]. (y" – 9y' = 9, 1 y(0) = 1, y'(0) = -1. %3D Lütfen birini seçin: 00 01 01 O2 O3
1. Is sin y x² dx + ydy = 0 a linear? 2. Is y' = y+x / x a homogeneous Equation?
1st Case (IBVP Summary) 1.3uxx, 0 0 u(0, t) = 70°F, u(5ft, t) = 150°F, t > 0 u(x,0) = 60°F, 0 < x < 5 ft Ut 2nd Case A 5-ft long bar (laterally insulated) has a thermal diffusivity of 1.3 ft2 /hr and initial temperature of f(x) = 60°F . After preparing the initial temperature conditions of the bar, the left and right ends of the bar are simultaneously insulated. 1. Obtain the general solution u(x, t) of each case above. 2. Substitute n = 1,x = 2 ft and t = 1 hr into each of u(x, t) of the 2 cases and compare their temperatures.
The temperature distribution 0(x, t) along an insulated metal rod of length L is described by the differential equation 0²0 1 20 əx² D Ət = (0 0), where D 7.0 is a constant. The rod is held at a fixed temperature of 0°C at one end and is insulated at the other end, which gives rise to the boundary conditions de = 0 when x = 0 for t> 0 together with 0 = 0 when x = L for st əx t> 0. The initial temperature distribution in the rod is given by tudi o (0 ≤ x ≤ L). (a) Use the method of separation of variables, with 0(x, t) = X(x)T(t), to show that the function X(r) satisfies the differential equation X" - μX = 0 for some constant . Write down the corresponding differential equation that T(t) must satisfy. 0(x,0) = 0.3 cos 7 πχ 2 L (2 JinUsore noitaupe Iaitun aliam d dos seins (*) ototul vietissiq (b) Find the two boundary conditions that X(r) must satisfy. diesb bas langs (c) Suppose that μ 0. In this case the general solution of equation (*) is X(x) = A cos(kx) + B sin(kx). Find the…
et y" +5y' +y-x"e* the particular solution of the equation can be obtained: Select one: a. By both nmethods b. By neither of these methods c. Only by method of variation of parameters. d. Only by method of undeterminant coefficients Jump to... im Return to: General
II. Integrating factors found by inspection. 1. ysin ydx+ x(sin y– ycosy)dy = 0 Ma“ – y* kdx + x{x* + y* dty = 0 2.