Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN: 9781305387102
Author: Kreith, Frank; Manglik, Raj M.
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Related questions
Question
Transcribed Image Text:=
Consider 1D transient conduction in a bar with c² = 1. Let the left end be subjected to a temperature
To 10, and the right end be held at temperature T 0. The bar is initially at a constant
temperature T(x, 0) = T.
=
Compute the solution u(x, t) using the Fourier series solution for finite bars found earlier in the semester
(see HW 5, Problem 4 for an example). Compare the solution with the semi-infinite solution. Use 100
terms in the partial sums of the Fourier series. Compare the solutions for various lengths of the rod:
(a) L = 10
(b) L= 100
(c) L = 500
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps with 3 images
Knowledge Booster
Similar questions
- Use FEM to calculate the temperature at nodes 2 and 3, and the heat at nodes 1 and 4. Assume A is one unit area.arrow_forward34 Need A, B, Carrow_forwardThe oven shown in the figure has a heating element with appreciable capacitance C. The other capacitance is that of the oven air C. The corresponding temperatures are T and T, and the outside temperature is To The thermal resistance of the heater-air interface is R; that of the oven wall is R. Identify a model for T1 and T2, with input q;, the heat flow rate delivered to the heater mass. Oven air T2 C2 T. R| T C 19i R2 Heating element a. Develop the dynamic equations for this system. (submit in Connect) b. Develop the state variable Matrix form of the model in terms of the system parameter variables (not numerical values). c. Using the numerical values for the system parameters provided, use MATLAB to calculate the transfer functions 1 and 2 T and describe the expected behavior based on both of these transfer functions. d. Plot the dynamic behavior of the actual temperature of the oven chamber if the heating element is turned on with a constant heat rate of qj. Assume that the entire…arrow_forward
- What's the answerarrow_forwardYou have a 1-D steady-state conduction problem, constant thermal properties, with energy generation q_dot. The material is 4.0 cm thick and has a constant thermal conductivity of k = 65.0 (W/m-k). The temperature distribution within the object is: T(x) = a + bx^2 a = 100 Celcius b = -1000 Celcius/m^2 Starting with the Heat Diffusion Equation and using the data given above, determine the following: • Determine the heat generation rate q_dot within the wall. • Determine the heat flux q" at x=0 and at x=L.arrow_forwardK:38)arrow_forward
- Needs Complete typed solution with 100 % accuracy. Otherwise skip if you can't give complete solution don't use chat gpt or ai i definitely upvote you.arrow_forward(3) For the given boundary value problem, the exact solution is given as = 3x - 7y. (a) Based on the exact solution, find the values on all sides, (b) discretize the domain into 16 elements and 15 evenly spaced nodes. Run poisson.m and check if the finite element approximation and exact solution matches, (c) plot the D values from step (b) using topo.m. y Side 3 Side 1 8.0 (4) The temperature distribution in a flat slab needs to be studied under the conditions shown i the table. The ? in table indicates insulated boundary and Q is the distributed heat source. I all cases assume the upper and lower boundaries are insulated. Assume that the units of length energy, and temperature for the values shown are consistent with a unit value for the coefficier of thermal conductivity. Boundary Temperatures 6 Case A C D. D. 00 LEGION Side 4 z episarrow_forwardA square domain is modeled using either one bilinear rectangular element or two linear triangular elements as shown below. a) Determine the system element matrix for the Laplace equation for each discretization. b) Determine the displacement at the center of the domain (0.5,0.5) in terms of the nodal displacement. Hint: You need to assemble the stiffness matrix for the system on the right to form a 4*4 matrix from the two 3*3 element matrices. 1.0 4. 1.0 3. X- 1.0 1.0 2. 2.arrow_forward
- (NUMBER 4.) solve for Lm, Pm, and Wm. I’ve attached a reference image with the solution method, I just need clarification.arrow_forwardAn unmanned submarine is equipped with temperature and depth measuring instruments and has radio equipment that can transmit the output readings of these instruments back to the surface. The submarine is initially floating on the surface of the sea with the instrument output readings in steady state. The depth measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 50 seconds. The water temperature on the sea surface, , is 20 °C and the temperature at a depth of x meters is given by the relation: If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5 meters / second, draw a table showing the temperature and depth measurements reported at intervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error in each temperature reading.What temperature does the submarine report at a depth of 1000 meters?arrow_forwardMA Figure (2) 3- The time response of a liner spring-mass-damper system with the mass of (m), the stiffness coefficient of (k), and a dampirg constant of (c) is given below in figure (2) with a set of coordinates marked by fillec circles. x(t) is in meters, it is in seconds. Indicate the units of all quantities involved in your solutions when calculate 0 -1- (0.53, 1.78) (0,0.8) 2 (2.1,-1.3) (3.7,0.9) L 4 (5.3,-0.7) - The damping ratio of the system. Its natural frequency w., damping corstart c, and stiffness coefficient k; for (m-1.25 kg). III- The amplitude of the motion if the phase angle is given as (0.4 rad). IV. Its initial conditions. (6.86, 0.5) 10 t[sec]arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning