An insulated cylinder of solid gold (K = 310 kW/m-k) of radius ,./2 m and height 5 m is heated at one end until the temperature at each point in the cylinder is given by w(x, y, z) = (30 - z2)(2 - (x2 + y2)). 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.

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