F is called as usual the complex potential of the

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Unformatted text preview: the distance from the center. Note on Insulation: By definition, heat cannot pass through (ideal) insulation, therefore the heat flow lines can have no component along insulation., In other words, heat flow must be parallel to insulation. Or, put another way, the heat flow lines § = constant are the same as the insulation lines. (C) Mixed Boundary value Problem Solve for temperature in the following situation: insulation 20º 50º 1 This is a classical situation with T independent of r. Referring again to Topic 9, we find F(z) = -iALn(z) + B Looking at the real part, T(z) = A Arg(z) + B and we get B = 50 and A = -60/π, giving 60 T(z) = 50 ø π Notice that the heat flow lines are ln|r| = constant which is consistent with the above drawing (insulation = semicircles) (D) Using Conformal Mappings Find the temperature distribution in the following situation: 37 0º –1 Insulation 1 20º It looks best to map this thing onto something like this: 0º 20º –π/2 Insulation π/2 which we can do with the inverse sine function (see the discussion of what the sine function does muuuch earlier). On the target strip, the temperature is given by 10...
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This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.

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