Mathematical modeling paper on the efficacy of double glass
1. Thermal insulation effect of single-layer glass: In this case, the factors to be considered are the temperature T 1 and T2 on both sides of the glass at this time. Here, for the convenience of calculation, we set T 1 to 20℃ and T2 to-10℃. At the same time, we also consider the thickness d of glass and the thermal conductivity K 1. Similarly, we set the glass thickness d as 1. Because the thermal conductivity of glass changes with temperature, we take the intermediate temperature of 20℃ and-10℃ as 5℃. Look-up table shows that the thermal conductivity of glass at 5℃ is 5× 10-3 j/cm. S℃, and the area s of the glass, that is, the cross-sectional area of heat passing through the glass. Let's assume that the time t is set to 100s and the heat conduction direction is from T 1 to T2 (as shown in figure 1), then the heat q passing through the glass window with an area of 5000cm2 in unit time 100s can be easily calculated. Using the formula Q = STK1= 5000 cm2×100s× 5×13 j/cm.s. ℃× = 75000 J2, when the temperature difference is 30℃ and the area is 5000 cm2, the heat of single-layer glass is 75438+. Thermal insulation effect of double glass: In this case, the heat conduction path should be considered when establishing the model. First, it is conducted to the air part through the inner glass, that is, the glass with high temperature, and then to the outer glass through the air, and finally the required heat is conducted. According to the solution of single-layer glass, we also assume that T 1 is 20℃, T2 is-10℃, the area s is 5000cm2, the time is 100s, and the thickness of both layers of glass is 1cm. In this case, we also regard the thermal conductivity of glass as the value at 5℃, which is 5× 65438. Look-up table shows that the thermal conductivity of dry and immobile air at this time is 2.55× 10-4 J/cm.s℃, and the air thickness L is 5cm. The schematic diagram of thermal conductivity is shown in Figure 2. According to the law of conservation of heat, it is concluded that the heat generated by the temperature difference between T 1 and Ta is equal to the heat generated by the temperature difference between Ta and Tb, and between Tb and T2. Expressed by the formula: q = STK 1 = STK2 = STK1(1) From the formula (1), we can get the formula t1+T2 = ta+TB (2) (1). cm . s .℃×= 5000 cm2× 100s×2.5× 10-4J/cm . s .℃×= 5000 cm2× 10-3j/cm . s .℃×Ta+TB = t 1+T2 =- 10℃+20℃= 1 0℃ synthesis (65438) When L takes different values, Ta and Tb will change, which will lead to the change of Q. Through calculation, we compare the values of Ta, Tb and Q under different L values. As shown in the following table: air thickness L (cm) 2345678 ... internal glass external temperature Ta (℃)13.519.519.713.219.5 65438 ... Kloc-0/625012501000 750170001250 500 ... According to the data in the table, it can be seen that the double-layer glass conducts electricity. The specific schematic diagram is shown in the following figure: This figure shows the law that the heat conduction of double-layer glass first decreases, then increases and then gradually decreases, that is, when the glass spacing is 2 to 4 times of the glass thickness, the heat loss gradually decreases, that is, the heat preservation effect gradually increases, but when the distance between double-layer glasses is 5 times of the glass thickness, the heat loss decreases again, indicating that the heat preservation effect increases. Considering the actual situation, if people choose double-layer glass, they will only choose that the distance between glasses is 4 to 4 times that of glass, not more than 7 times. Because the middle distance is too large, it does not conform to the thickness of the wall in reality, and the cost is too high, so the insulation effect of double-layer glass is better when the distance is still 4 to 5 times.