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Solve quickly and carry units please

rroblem I) A perfect sphere (Diameter-1 cm) of a gold alloy is placed in a special type o microwave oven. The sphere has a uniform initial temperature of 300 K. The microwave then turned on, which pr oduces u niform generation u-3,000,000 W/m2 within the sphere, and a fan produces convection heat transfer evenly over the surface of the sphere with convection coefficient h-6 W/m2 K and with air temperature Too- 300 K. Radiation heat transfer may be neglected. properties of the alloy are: Density 19,000 kg/m2, Specific Heat 170 J/kg K, Thermal Conductivity- 290 W/m K: Thermal Diffusivity- 8.978E-5 m/s (a) How long until the gold alloy reaches a temperature of 800 K? (b) Justify your analysis for part (a) using the appropriate dimensionless parameter(s) (20 points)
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