Transcribed TextTranscribed Text

A body of conical section fabricated from stainless steel is immersed in air at a temperature Ta = 0. It has circular cross section that varies with x. The large end is located at x = 0 and is held at temperature TA = 5 as shown in the figure. The small end is located at x = L = 2 and is held at TB = 4. To TA T(x) TB Ta x x = 0 x = L Conservation of energy can be used to develop a heat balance equation at any cross section of the body. When the body is not insulated along its length and the system is at a steady state, its temperature satisfies the following ODE: d-T 2 a = where a(x), b(x), and f(x) are functions of the cross-sectional area, heat transfer coefficients, and the heat sinks inside the body. In the present example, they are given by + x+3 + and Write a function that uses finite differencing to solve the problem. Discretize the interval from X = 0 to x = L using N + 1 points (including the boundary points): The temperature at point j is denoted by Tj (i) Discretize the differential equation using the central difference formulas for the second and first derivatives. The discretized equation is valid for j = 1,2, N and therefore yields N- - 1 equations for the unknowns To T1, TN+1. (ii) Obtain two additional equations from the boundary conditions (TA = 5 and TB = 4) and write the system of equations in matrix form A T = f. Solve this system with N = 20. Plot the temperature. Challenge: Reformulate the problem to implement the insulated boundary condition at x = L. If the body is insulated at x = L, the boundary condition becomes dT/dx = 0. You need to write a difference equation for the boundary condition. Set up the new system of equations and solve the problem and plot the temperature.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution1.pdf and

    for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Python Programming Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats