A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a?u a?u + = 0. ax2 ' ay2 Find the steady state temperature u(x, y), by assuming the solution to be of the form и(х, у) —D (АеРх + Ве рх)(С сos py + D sin pyу).
A rectangular steel sheet is bounded by the axis x = 0, y = 0,x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x, y) denote the temperature satisfying the equation a?u a?u + = 0. ax2 ' ay2 Find the steady state temperature u(x, y), by assuming the solution to be of the form и(х, у) —D (АеРх + Ве рх)(С сos py + D sin pyу).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...
Related questions
Question
Find the steady state temperature.
Laplace, two dimensional heat equation.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,