Question

1(30%). A thin plate black body, insulated at the bottom is placed faced up in a room with wall temperatures of 30 C. Air at 0 C is forced over the plate with a convective heat transfer coefficient of 12 W/m².C. Calculate the plate temperature under steady state condition

Answer 1

Step-by-step explanation:

The given data is as follows.

Heat transfer coefficient (h) = 12
`W/m^(2).C`

Plate temperature (
`T_(1)`) =
`30 ^(o)C` = 303 K

Steady state temperature (
`T_(2)`) = ?

Hence, formula applied for steady state is as follows.

`(h * A * \Delta T)_(air)` =
`\sigma * A * (T^(4)_(1) - T^(4)_(2))_(plate)`

Putting the given values into the above formula as follows.

`(h * A * \Delta T)_(air)` =
`\sigma * A * (T^(4)_(1) - T^(4)_(2))_(plate)`

`12 * (T_(2) - 273)` =
`5.67 * 10^(-8) * [(30 + 273)^(4) - T^(4)_(2)]`

`T_(2)` = 282.66 K

= (282.66 -273)
`^(o)C`

= 9.66
`^(o)C`

Thus, we can conclude that the steady state temperature will be 9.66
`^(o)C`.