Concept explainers
The rate of heat transfer by natural convection.

Explanation of Solution
Given:
The temperature of top surface is
The temperature of base surface is
The emissivity of base surface
The temperature of side surface is
Calculation:
The below figure represents the cubical surface.
Figure-(1)
Consider the top surface is surface 1, the base surface is surface 2 and side surface is surface 3.
The base surface is flat; therefore the value of view factor will be zero.
Calculate the view factor from the base or top of side surface.
The value of other view factor will be as follows.
Use the energy balance for surface 3.
Use the energy balance for surface 1.
Use the energy balance for surface 2.
Calculate the heat flux at surface 2.
Solve equation (I), (II) and (III).
Calculate the rate of heat transfer between the bottom and top surface.
Calculate the rate of heat transfer between the bottom and side surface.
Thus, the emmisivity at the top surface is
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Chapter 21 Solutions
Fundamentals Of Thermal-fluid Sciences In Si Units
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