Heat flux The heat flow vector field for conducting objects is F = – k ▿ T , where T ( x , y , z ) is the temperature in the object and k > 0 is a constant that depends on the material. Compute the outward flux of F across the following surfaces S for the given temperature distributions. Assume k = 1. 62. T ( x , y , z ) = 100 e − x 2 − y 2 − z 2 ; S is the sphere x 2 + y 2 + z 2 = a 2
Heat flux The heat flow vector field for conducting objects is F = – k ▿ T , where T ( x , y , z ) is the temperature in the object and k > 0 is a constant that depends on the material. Compute the outward flux of F across the following surfaces S for the given temperature distributions. Assume k = 1. 62. T ( x , y , z ) = 100 e − x 2 − y 2 − z 2 ; S is the sphere x 2 + y 2 + z 2 = a 2
Solution Summary: The author explains how to compute the outward flux of F across the surface S.
Heat fluxThe heat flow vector field for conducting objects isF = –k▿T, where T(x, y, z) is the temperature in the object and k > 0 is a constant that depends on the material. Compute the outward flux ofFacross the following surfaces S for the given temperature distributions. Assume k = 1.
62.
T
(
x
,
y
,
z
)
=
100
e
−
x
2
−
y
2
−
z
2
; S is the sphere x2 + y2 + z2 = a2
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
University Calculus: Early Transcendentals (4th Edition)
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.
01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY