Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is described by the differential equation du = -a(u' – T*) (1. dt where u(t) is the absolute temperature of the body at time t, T is th absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is nuch larger than T, then solutions of equation (1) are well pproximated by solutions of the simpler equation du = -qu". -au". (2 dt Suppose that a body with initial temperature 2450 K is surrounded medium with temperature 280 K and that a = 6 × 10-1²K-³/s. ) Determine the temperature of the body at any time by solving equation (2). u(t) K p) Use a graphing utility to plot the graph of u versus t. :) Find the time r at which u(7) = 560 –that is, twice the ambient temperature. Up to this time the error in using equation (2) to approximate the solutions of equation (1) is no more than 1%.

Heat transfer from a body to its surroundings by radiation, based or he Stefan-Boltzmann law, is described by the differential equation du = -a(u' – T*) (1. dt where u(t) is the absolute temperature of the body at time t, T is th absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is nuch larger than T, then solutions of equation (1) are well pproximated by solutions of the simpler equation du = -qu". -au". (2 dt Suppose that a body with initial temperature 2450 K is surrounded medium with temperature 280 K and that a = 6 × 10-1²K-³/s. ) Determine the temperature of the body at any time by solving equation (2). u(t) K p) Use a graphing utility to plot the graph of u versus t. :) Find the time r at which u(7) = 560 –that is, twice the ambient temperature. Up to this time the error in using equation (2) to approximate the solutions of equation (1) is no more than 1%.

Advanced Engineering Mathematics
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
icon
Related questions
Topic Video
Question

Please solve & show steps...

Heat transfer from a body to its surroundings by radiation, based on the Stefan-Boltzmann law, is described by the differential equation du = -a(u' – T*) (1) dt where u(t) is the absolute temperature of the body at time t, T is the absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is much larger than T, then solutions of equation (1) are well approximated by solutions of the simpler equation du = -qut, dt (2) Suppose that a body with initial temperature 2450 K is surrounded by a medium with temperature 280 K and that a = 6 × 10-1'K-3/s. a) Determine the temperature of the body at any time by solving equation (2). u(t) K b) Use a graphing utility to plot the graph of u versus t. c) Find the time 7 at which u(T) = 560 –that is, twice the ambient temperature. Up to this time the error in using equation (2) to approximate the solutions of equation (1) is no more than 1%. T =
Transcribed Image Text:Heat transfer from a body to its surroundings by radiation, based on the Stefan-Boltzmann law, is described by the differential equation du = -a(u' – T*) (1) dt where u(t) is the absolute temperature of the body at time t, T is the absolute temperature of the surroundings, and a is a constant depending on the physical parameters of the body. However, if u is much larger than T, then solutions of equation (1) are well approximated by solutions of the simpler equation du = -qut, dt (2) Suppose that a body with initial temperature 2450 K is surrounded by a medium with temperature 280 K and that a = 6 × 10-1'K-3/s. a) Determine the temperature of the body at any time by solving equation (2). u(t) K b) Use a graphing utility to plot the graph of u versus t. c) Find the time 7 at which u(T) = 560 –that is, twice the ambient temperature. Up to this time the error in using equation (2) to approximate the solutions of equation (1) is no more than 1%. T =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Propositional Calculus
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.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS