From observations of the change in temperature with time of

From observations of the change in temperature with time of a cooling thin hot plate suspended vertically, important heat transfer parameters can be determined. At an instant of time, the plate is at 22.7 degree C and the change in plate temperature with time (dT/dt) is -0.02 K/s. Assume the plate is isothermal and that the ambient air and the surroundings are at 27 degree C. The plate measures 0.2 m times 0.2 m, has a mass of 4 kg and a specific heat of 2000 J/kg-K. Note the plate exchanges heat from both of its exposed faces Use an energy balance determine the free convection coefficient if the plate is suspended in sill air (radiation effects are negligible) Use an energy balance to determine the emissivity of the plate if it is suspended in a vacuum (no convection effects).

Solution

a) Energy balance for heat flow Q

Q= h_c2 x A₁ x dT₁ = h_c2 x A₂ x dT₂

_Where...

q = heat transferred per unit time (W, Btu/hr)

A = heat transfer area of the surface (m², ft²)

h_c = convective heat transfer coefficient of the process (W/(m²K) or W/(m^2oC), Btu/(ft² h ^oF))

dT = temperature difference between the surface and the bulk fluid (K or ^oC, F)

Then Q = h_c x (0.2 x 0.2) x (300.15-500.15)K

-0.02 = h_c x 0.04 x -200

h_{c = 400W/(m²K)...........}for free Convection - air, gases and dry vapors : 0.5 - 1000 (W/(m²K)

b) Heat emission (e)

^{Emissivity is always maximum in vaccum, as emission = absorption}

^{Emissivity value ranges from 0 to1.}

^{So in this case e= 1}