Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F= -KVT, which means that heat energy flows from hot regions to cold regions. The constant k> 0 is called Fonds=- the conductivity, which has metric units of J/(m-s-K). A temperature function T for a region D is given below. Find the net outward heat flux -KSS VT n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k=1. T(x,y,z)=85-x²-y²-2²: D is the sphere of radius a centered at the origin. The net outward heat flux across the boundary is 480xa (Type an exact answer, using a as needed.)
Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F= -KVT, which means that heat energy flows from hot regions to cold regions. The constant k> 0 is called Fonds=- the conductivity, which has metric units of J/(m-s-K). A temperature function T for a region D is given below. Find the net outward heat flux -KSS VT n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral. Assume that k=1. T(x,y,z)=85-x²-y²-2²: D is the sphere of radius a centered at the origin. The net outward heat flux across the boundary is 480xa (Type an exact answer, using a as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Fourier's Law of heat transfer (or heat conduction) states that the heat flow vector F at a point is proportional to the negative gradient of the temperature; that is, F= -KVT, which means that heat energy flows from hot regions to cold regions. The constant k> 0 is called
Fonds=-
the conductivity, which has metric units of J/(m-s-K). A temperature function T for a region D is given below. Find the net outward heat flux
-KSS VT n dS across the boundary S of D. It may be easier to use the Divergence Theorem and evaluate a triple integral.
Assume that k=1.
T(x,y,z)=85ex²-y²-2²: D is the sphere of radius a centered at the origin.
The net outward heat flux across the boundary is 480x³
(Type an exact answer, using x as needed.)
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 5 steps with 5 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
