13–86 A radiation shield that has the same emissivity e3 on both sides is placed between two large parallel plates, which are maintained at uniform temperatures of T1 5 650 K and T2 5 400 K and have emissivities of e1 5 0.6 and e2 5 0.9, respectively. Determine the emissivity of the radiation shield if the radiation heat transfer between the plates is to be reduced to 15 percent of that without the radiation shield.

The emissivity of the radiation shield is    

Explanation:

From the question we are told that

   The temperature of the first parallel plate is  

    The temperature of the second  parallel plate is  

    The  emissivity of first plate is  

    The  emissivity of first plate is  

Generally the total radiation heat that is been transferred without the shield is mathematically represented as

Where   is the Stefan-Boltzmann constant which has a value  

Substituting values

From the question we are told the that using the radiation shield would reduce the radiation heat transfer by 15%

  So the new heat transfer is

 So    

Now this new radiation heat transfer can be mathematically represented as  

   Where the emissivity of the  radiation shield and n is the number of radiation shield

Substituting values

temp rises, and expansion