Answer:
Explanation:
Generally, thermal resistance for conduction heat transfer in a sphere.
Where is the thermal resistance for conduction, K is the thermal conductivity of the material,
is the inner radius of the sphere, and
is the outer radius of the sphere.
The surface area of sphere, is given by
For aluminum sphere, the thermal resistance for conductive heat transfer is given by
Calculate the thermal resistance for conductive heat transfer through the aluminum sphere.
Where is aluminum’s thermal conductivity at
}
Thermal resistance for conductive heat transfer through the insulation.
Thermal resistance for convection is given by
Where h is convective heat transfer coefficient, is thermal resistance for convection and A is the cross-sectional area normal to the direction of flow of heat energy
Thermal resistance for convective heat transfer in-between the outer surface of the insulation and the ambient air.
Where h represents convective heat transfer coefficient at the outer surface of the insulation. Since is already defined, substituting it into the above formula yields
To obtain radial distance of the outer surface of the insulation from the center of the sphere.
where t is thickness of insulation
r=0.21+0.15=0.36m
Total thermal resistance
Where is total thermal resistance
Consider the thermal conductivity of aluminum at temperature as 234W/m.K
Rate of heat transfer for the given process
Where } is the steady state heat transfer rate in-between the inner surface of the sphere and the ambient air.
Substituting for
we obtain