A flat plate of polished copper of surface emissivity 0.1 is 0.1 m long and 0.1 m wide. The plate is placed vertically, with one side heated

Question

A flat plate of polished copper of surface emissivity 0.1 is 0.1 m long and 0.1 m wide. The plate is placed vertically, with one side heated to a surface temperature of 500 K, and the other side remaining insulated. The heated side is exposed to quiescent air at 300 K and the surroundings are also at 300 K. Assume that air can be taken as an ideal gas. Estimate the heat rate from the flat plate.

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Edana Edana 3 months 2021-09-02T15:26:45+00:00 1 Answers 3 views 0

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    2021-09-02T15:28:25+00:00

    Answer:

    The heat rate is  

    Explanation:

    From the question we are told that

      The surface emissivity is  e=0.1

       The length is  L  = 0.1 \ m

        The width is  W = 0.1 \ m

         The surface temperature of one side is  T_1  = 500 \ K

         The temperature of the quiescent air T_c  = 300 \ K

          The temperature of the surrounding is  T_s  =  300 \ K

    The heat rate from the flat plate is mathematically represented as

             Q = \sigma A e (T_1^4 - T_a^4)

    Where \sigma is the quiescent air Stefan-Boltzmann constant  and it value is

           \sigma =  5.67*10^{-8} m^{-2} \cdot  K^{-4}

         A is the area which is mathematically evaluated  as

               A =  W * L

    substituting values

               A =  0.1 * 0.1

               A =  0.01 \ m^2

    substituting values

              Q = 5.67 *10^{-8} * (0.01) *(500^4 -300^4)

              Q =3.045 \ Watt

             

           

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