Consider a plane wall (thermal conductivity, k = 0.8 W/m-K, and thickness, fb1 = 100 mm) of a house as shown in Fig. Q1(a). The outer surface of the wall is exposed to solar radiation and has an absorptivity of a = 0.5 for solar energy, 600 W/m². The temperature of the interior of the house is maintained at T1 = 25 °C, while the ambient air temperature outside remains at Toz = 5 °C. The sky, the ground and the surfaces of the surrounding structures at this location can be modelled as a surface at an effective temperature of Tsky = 255 K for radiation exchange on the outer surface. The radiation exchange inside the house is negligible. The convection heat transfer coefficients on the inner and the outer surfaces of the wall are h₁ = 5 W/m²-K and /₂ = 20 W/m².K, respectively. The emissivity of the outer surface is = 0.9. T₂ k T1 = 25 °C ------- 100 mm Fig. Q1(a) Assuming the heat transfer through the wall to be steady and one-dimensional: (a) Solve the steady 1D heat conduction equation for this wall, and obtain the temperature profile through the wall. à la = 600 W/m² Tay = 255 K T2 = 5°C (b) To reduce the heat loss to 10 W/m², two layers (an insulation layer, kins= 0.04 W/m-K and a brick layer, k = 0.8 W/m-K) are to be added as shown in Fig. Q1(b). The interior of the house is still maintained at a temperature of T1 = 25 °C. When the additional brick layer thickness is the = 80 mm and the outer surface temperature is T₂ = 15 °C, determine the required thickness of the insulation layer and the expected inner surface temperature (7₁) using a thermal resistance network.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Transcribed Image Text:Q1. Consider a plane wall (thermal conductivity, k = 0.8 W/mK, and thickness, fb1 = 100 mm) of a house as shown in Fig. Q1(a). The outer surface of the wall is exposed to solar radiation and has an absorptivity of a = 0.5 for solar energy, or=600 W/m². The temperature of the interior of the house is maintained at T1 = 25 °C, while the ambient air temperature outside remains at T2 = 5 °C. The sky, the ground and the surfaces of the surrounding structures at this location can be modelled as a surface at an effective temperature of Tsky = 255 K for radiation exchange on the outer surface. The radiation exchange inside the house is negligible. The convection heat transfer coefficients on the inner and the outer surfaces of the wall are h₁ = 5 W/m²-K and /1₂ = 20 W/m².K, respectively. The emissivity of the outer surface is = 0.9. T1 = 25 °C Ţ₁ Too1 = 25 °C T₁ k 100 mm Fig. Q1(a) Assuming the heat transfer through the wall to be steady and one-dimensional: (a) Solve the steady 1D heat conduction equation for this wall, and obtain the temperature profile through the wall. (b) To reduce the heat loss to 10 W/m², two layers (an insulation layer, kins = 0.04 W/m-K and a brick layer, k = 0.8 W/m-K) are to be added as shown in Fig. Q1(b). The interior of the house is still maintained at a temperature of T1 = 25 °C. When the additional brick layer thickness is the = 80 mm and the outer surface temperature is T₂ = 15 °C, determine the required thickness of the insulation layer and the expected inner surface temperature (7₁) using a thermal resistance network. k T₂ 100 mm Kins dolar = 600 W/m² Tay = 255 K sky Too2 = 5 °C x Fig. Q1(b) k T₂ = 15 °C 80 mm

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