Question

A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x, y, z) = 15 - 4(x^2 + y^2 + z^2) °C. Use the fact that heat flow is given by the vector field F = -K?w and the rate of heat flow across a surface S within the solid is given by -K ?_S ?w dS. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K = 400 kW/(m · K)). (Use symbolic notation and fractions where needed.) -K ?_S ?w dS = kW

          A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by
w(x, y, z) = 15 - 4(x^2 + y^2 + z^2) °C. Use the fact that heat flow is given by the vector field F = -K?w and the rate of
heat flow across a surface S within the solid is given by -K ?_S ?w dS.
Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper
(K = 400 kW/(m · K)).
(Use symbolic notation and fractions where needed.)
-K ?_S ?w dS = kW

$A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x, y, z) = 15 - 4(x^2 + y^2 + z^2) °C. Use the fact that heat flow is given by the vector field F = -K?w and the rate of heat flow across a surface S within the solid is given by -K ?S ?w dS. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K = 400 kW/(m · K)). (Use symbolic notation and fractions where needed.) -K ?S ?w dS = kW$

Added by Trinidad E.

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