QUESTION 1 A new building to be located in a cold climate...

QUESTION 1 A new building to be located in a cold climate is being designed with a basement that has an L = 200-mm-thick wall. Inner and outer basement wall temperatures are Ti = 20 °C and To = 0°C, respectively. The architect can specify the wall material to be either aerated concrete block with kac = 0.15 W/m K, or stone mix concrete. To reduce the conduction heat flux through the stone mix wall to a level equivalent to that of the aerated concrete wall, what thickness of extruded polystyrene sheet must be applied onto the inner surface of the stone mix concrete wall. Note: Heat transfer through Aerated concrete wall of thickness of 200 mm is equal to heat transfer through polystyrene + stone mix concrete, thickness of stone mix concrete is 200 mm but we are looking for t=? thickness of polystyrene thickness. Stone mix concrete (300 K): ksm = 1.4 W/m·K; Rigid extruded polystyrene sheet: kps = 0.027 W/m·K. Aerated concrete: kac = 0.15 W/m·K are given. a. t = 35 mm b. t = 32 mm c. t = 40 mm d. t = 50 mm

Transcript

00:01 We are given here a new building to be located in a cold climate so that is a here we are given here new building and they are located in a cold climate cool climate so we can make cool climate and design it within the basement this length we are given here which is equal to 200 millimeter thick wall and inner and outer base amount of temperature t1 so we can write for inner temperature there's a temperature is 20 celsius and the outer temperature t's temperature t's and the outer temperature 10 to which is we can write here the zero celsius so that and we are also we are given here the archidac conservation with the material can be it can be either a rated concentrated block which we are given here k a c which is equal to value is 0 .15 watt per meter kelvin now here we in this question we want to find the time here we find the thickness not time you're going to find the thickness in the millimeter first we can write the heat flux first we can write the heat flux through a rated concentrate so we can write heat flux q double prime which is equal we can write kac x multiple liby we can write t i minus t o divided by l so we can write here q double prime which is equal we can write 0 .15 multiple by we can write 20 minus 0 divided by we can write here 20 meter you can write 0 .20 meter we can write 0 .20 meter which is equal to we can write 15 watt per meter square what per meter square this is the heat flux now let's solve the next next is the heat also heat flux but this it looks different this it works through a stone so we're using this formula and finding the time video so the way using the heat flux q double prime which is equal to 15 watt per meter square so we can write this q double prime which is equal to t minus t0 divided by we can write t divided by kps plus we can write l divided by k s m k sm so we can write here the q double prime which is equal to 20 minus 0 divided by we can write here t divided by 0 .0 27 plus we can write 0 .2 0 divided by we can write here 1 point and we just simplify this all the values and q prime which is equal we know the 0 point here 15 q prime which is equal to 15 now we just simplify this all values and we can write here t which is equal to 0 .0 3 2 meter or we can say 32 millimeter so this is the thickness also we know the area or the area we can write here area with area duly by a so we can write area which is equal to 0 .032 multiply by we have 20 meter more and 30 meter 20 plus 30 which is equal to to we just simply and multiple by two here which is equal to we can write 3 .2 meter square so this is the area also finding the cost here we are just finding the cost so the entire which is equal to the cost for per year so we can write here there is a fifty dollar meter per meter per meter square fifty dollar per meter square per month so we just multiply by this 12 multiple by 12 so and also 3 .2 meters square which is equal to answer is $1 ,920 per year...

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