Question

Q3 (6 marks) The window in your room is 2 meters 3 meters. Assuming all other walls are well insulated and that heat loss only occurs through the window, the air in the room is under free convection of 35 W/m2K. The outside surface of the window is 6 °C and the thermal conductivity of window glass is 0.78 W/m K. The thickness of the window glass is 4 mm Calculate the size of the heater that you need in your room to maintain the room tomperature 25 °C i Calculate the Saudi Riyal (SAR) saving per year if you double the thickness of window glass, 8 mm. The price of electricity at Saudi is 0.18 SAR/KWhr. Assume the heater is working 18 hr per day, 120 days per year. Neglect the price of window glass

Answer 1

Please refer following image for solution:

Given, Demensions of window = 2x3 m susface area a window A=6 m² convective heat Benslez coeff: inside the soom h= 35 W/m²K outez susface temperature [=6°C Thermal conductivity of window K= 0.78 W/mie Thickness of the glass dx=4mm = 4X103 m

I Solution :- 1) In osdes to maintain inside temperature 25°c The heat loss through window QL has to be calculated. Qu= AT ax KA As to calculate heat loss we have to consider convertive sesistance q soomlands & conductive sesistance of glass Care S. AT=T-T2, where T, is inside room temperature. ..QL = 25-6 48103 0.78 x6 * 35 x6 0.78

ta -= 0.0056167 = 3382.76 w 53385 W Qu= 3.385kw

This much hear is sejected to atmosphere, so the size of heates should be (3.385kW] ii) For 8mm thickness a window, let us find the hear loss Q2 by using some formula except dx=8x 103 m AT Qurder than ax KA ha - 25-6 88 + 0.78x6 + 35x6 - 19 0.00171 +0.005762 22935. I w 22-935 kW The heates capacity sequired in this case is 2.935kw Toral saving of energy = 3.385-2.935 = 0.45 kw .. Energy saved per year 20.45 X 18x120 . = 972 kwhe saving in Riyals = .0.188972 = 174.96 SAR