A solid material that has thermal conductivity K K in kilowatts per meter-kelvin and temperature given at

Question:

A solid material that has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x,y,z) has heat flow given by the vector field F=Kw and rate of heat flow across a surface S within the solid given by KSwdS.

An insulated cylinder of solid gold \((K=310 \mathrm{~kW} / \mathrm{m}-\mathrm{k})\) of radius \(\sqrt{2} \mathrm{~m}\) and height \(5 \mathrm{~m}\) is heated at one end until the temperature at each point in the cylinder is given by \(w(x, y, z)=\left(30-z^{2}ight)\left(2-\left(x^{2}+y^{2}ight)ight)\). Determine the rate of heat flow across each horizontal disk given by \(z=1, z=2\), and \(z=3\), identifying which has the greatest rate of heat flow across it.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

Question Posted: