The free convection heat transfer coefficient on a thin hot

The free convection heat transfer coefficient on a thin hot vertical plate suspended in air can be determined from careful observations of the change of the plate temperature as it cools. Assuming the plate is isothermal and radiation exchange with its surroundings is negligible, evaluate the convection coefficient at the instant of time when the plate temperature is 225C and the change in plate temperature (dT/dt) = -0.22 K/s, with an ambient temperature of 25C. The plate measures 0.3 Times 0.3m with a mass of .375kg and a specific heat of 2770 J/kgK ?

Solution

Data Given

Dimension of the plate = 0.3m x 0.3m(Square)

Mass of the plate = 0.375Kg

Plate temperature(Tp) = 225 degree celsius = 498 Kelvin

Change in temperature with respect to time(dT/dt) = -0.22 Kelvin/Sec

Ambient temperature(Ta) = 25 degree celsius = 298 Kelvin

Specific heat of plate material = 2770 J/(KgK)

Solution

Heat energy emitted by the plate(Q) = m * Cp * (dT/dt)

= 0.375 * 2770 *- 0.22

= -228.53 Kcal/Hr

Heat lost by convection Q = ha * A ( Tp - Ta)

Area of the plate A = 0.3 x 0.3 = 0.09m^2

Heat transfer coefficient (ha) = Q/[A*(Tp-Ta)]

= 228.53/[0.09*200]

= 12.7 Kcal/m^2 - hr degree Kelvin