Question

. Air at 200 C blows over a 50 cm x 75 cm plain carbon steel (AISI 1010) hot plate with a constant surface temperature of 2500 C. The convection heat transfer coefficient is 25 W/m2K. Assume that 300 W is lost from the surface by radiation. Calculate the inside plate temperature. Assume that the plate is 2 cm thick. State all assumptions

Answer 1

The inside temperature,
`T_(in)` is approximately 248 °C.

Step-by-step explanation:

The parameters given are;

Temperature of the air = 20°C

Carbon steel surface temperature 250°C

Area of surface = 50 cm × 75 cm = 0.5 × 0.75 = 0.375 m²

Convection heat transfer coefficient = 25 W/(m²·K)

Heat lost by radiation = 300 W

Assumption,

Air temperature = 20 °C

Hot plate temperature = 250 °C

Thermal conductivity K = 65.2 W/(m·K)

Steady state heat transfer process

One dimensional heat conduction

We have;

Newton's law of cooling;

q = h×A×(
`T_s` -
`T_{\infty`) + Heat loss by radiation

= 25×0.325×(250 - 20) + 300

= 2456.25 W

The rate of energy transfer per second is given by the following relation;

`P = (K * A * \Delta T)/(L)`

Thermal conductivity K = 65.2 W/(m·K)

Therefore;

`2456.25 = (65.2 * 0.375 * (250 - T_(in)))/(0.02)`

`T_(in) = 250 - (2456.25 * 0.02)/(65.2 * 0.375) = 247.99 ^(\circ)C`

The inside temperature,
`T_(in)` = 247.99 °C ≈ 248 °C.