A straight solid rod of circular cross section with radius=3/16 in. and length L-4 in. is...

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A straight solid rod of circular cross section with radius=3/16 in. and length L-4 in. is attached at one end to a surface at temperature Ts=200°F. The remaining rod surface is exposed to ambient air at temperature Ta=70°F with heat transfer coefficient h= 1.5 Btu / hr ft°F. The fin is made of aluminum with thermal conductivity k-132 Btu/ hr ft °F. a. Carry out a shell balance on energy and use appropriate scaling of the variables to derive a second order differential equation involving a dimensionless group N. Evaluate N with the properties given. b. Write the boundary conditions neglecting the heat flow through just the tip of the fin exposed to air. c. Estimate the temperature at the tip or other end of the fin and the total heat flow in Btu/hr from the rod to the air. Calculate the effectiveness of the fin surface. A straight solid rod of circular cross section with radius=3/16 in. and length L-4 in. is attached at one end to a surface at temperature Ts=200°F. The remaining rod surface is exposed to ambient air at temperature Ta=70°F with heat transfer coefficient h= 1.5 Btu / hr ft°F. The fin is made of aluminum with thermal conductivity k-132 Btu/ hr ft °F. a. Carry out a shell balance on energy and use appropriate scaling of the variables to derive a second order differential equation involving a dimensionless group N. Evaluate N with the properties given. b. Write the boundary conditions neglecting the heat flow through just the tip of the fin exposed to air. c. Estimate the temperature at the tip or other end of the fin and the total heat flow in Btu/hr from the rod to the air. Calculate the effectiveness of the fin surface.

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