Question

1. A vertical glass plate covers a fireplace. The plate is at a temperature of 232 C and is located in a room at 23 °C. Use an average film temperature of 400 K when finding air properties. a) Find the Raleigh number for natural (free) convection from the plate. b) Find an average convection coefficient for the plate. Use the Churchill and Chu relation. e) Find the heat loss rate to the room. W Bricks Haight L=0.71 • Plate Width W=7.62m Room Conto pape) Fire

Answer 1

Properties of air caṇ change slightly from source to source. Please see your textbook for that. If any chaṇges are there, replace in the formula. Method will remain same.

Ts Height, 2-0.71 m : W=1.02 m TS=232°c = 505k - 23°c = 296 K To ܬܢ Properties of air at 400k will be -3 Ccebbicient of thermal expansion, B = 24x10 k" kinematic viscosity, 7=25.89 x106 m2 Prandth number, Pr = 0.7 Thermal conductivity: K = 0.03345 Work .. Charactenstic length of plate will be height, 420.71 m Now, Grashoft numbers. Gore gB [Ts-Te] L 3 92 9.81X9.4X10'x[505 -296]X 0.783 (25.89x106)? 9 so, Gos, -2.6875 X10 Now, A) Rayleigh number = Gr. x Pr = 2.6275x100 x 0.7 - 1.8393 8109 9 Rai = 1.8393x10 2. As, It is a vertical plate (plane). from Churchill and chu relation for Ra < 10² we have Nu = 0.387 (RqL 2 0.825 + +/0.492 9/167/27

Putting values. 2 1/6 Nu = 10.825+ 0.387 x(1.8393 x180) 9/16 8/27 0.492 0.7 so On solving, Ma 80%D7 Nu = 148.077 Now, Ny=hLc ha 148.077 X 0.03345 Nu xk Lc 0.7 (ط) soi ha h = 6.976 W/m²K Heat loss from the room - hx A x {Ts-Too = 6.976 X 0.71X1,02[505 - 296) (C) Heat loss 8 = 1055.872 W -1.056 kW