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.

Answer 1

The heat rate is

Step-by-step 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`