(5) Consider a wall (as shown above) of thickness L=1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h=1 W/m²K and an ambient temperature T-1 K. Heat generation inside the wall is q=1W/m³. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x).
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- As a designer working for a major electric appliance manufacturer, you are required to estimate the amount of fiberglass insulation packing (k = 0.035 W/m K) that is needed for a kitchen oven shown in the figure below. The fiberglass layer is to be sandwiched between a 2-mm-thick aluminum cladding plate on the outside and a 5-mm-thick stainless steel plate on the inside that forms the core of the oven. The insulation thickness is such that the outside cladding temperature does not exceed 40C when the temperature at the inside surface of the oven is 300C. Also, the air temperature in the kitchen varies from 15Cto33C, and the average heat transfer coefficient between the outer surface of the oven and air is estimated to be 12.0W/m2K. Determine the thickness of the fiberglass insulation that is required for these conditions. What would be the outer surface temperature when the inside surface of the oven is at 475C?1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.yo lo:ll O %AV L. مرتضی نشط الآن Q5: The piston cylinder device (radius=10 cm) contains a liquid with a pressure 100 kpa and temperature of 20 ° C and has a liquid convection heat coefficient =93 WmK. Connect its fixed side to a cubic piece of aluminum (side length 15 cm) with a thermal conductivity coefficient of aluminum = 239 W mK. At the bottom of the aluminum piece there is a heat source with a temperature of 150 ° C, noting that the heat source is located in a vacuum chamber. Radiation thermal resistance = 3.17 K/W. Calculate the change in piston height during I sec. if you know that there is no change in the internal energy of the piston cylinder device. Note IK Watt 1KJ/s : Aa
- Consider a copper plate that has dimensions of 3 cm x 3 cm x 7 cm (length, width, and thickness, respectively). As shown in the following figure, the copper plate is exposed to a thermal energy source that puts out 126 J every second. The density of copper is 8,900 kg/m³. Assume there is no heat loss to the surrounding block. 126 J Copper Insulation Ⓡ What is the specific heat of copper (in J/(kg K))? J/(kg. K) What is the mass of the copper plate (in kg)? kg How much energy (in J) will be consumed during 11 seconds? J Determine the temperature rise (in K) in the plate after 11 seconds.Determine the temperature distribution (nodal temperatures) of the structure shown in the figure using two equal-length, linear finite elements with the cross-sectional area of 1 m². The thermal conductivity is 10 W/m/°C. The left side is maintained at 300 °C. The right side is subjected to heat loss by convection with h = 1 W/m²/°C and T₁ = 30 °C. All other sides are insulated. T= 300 °C Exercise T₁ Insulated 20 m T₂ T3 T₁= 30 °C 43(Q3) sk) - A 5mx7m wall consists of 3 glass windows of 1.5mx1.5m dimensions. The wall has thickness of 0.125 m and a thermal conductivity of 0.5 W/m.K. while the glass windows are 6 mm thick with a thermal conductivity of 1:24 W/mK. The values of internal and external surface conductance for the wall (including glass) are 8.1W/m2 K and 34.2 W/m² K, respectively. The internal and external temperatures are 20°C and -30°C, respectively. Calculate the total heat transfer rate through the wall. What percentage of this heat transfer is through the windows? R
- 67 l all M O 2 o 9:05 the test.pdf Q1/ The thermal contact conductance at the interface of two 1.5-cm-thick copper plates is measured to be 19,000 W/m2 °C. Determine the thickness of the copper plate whose thermal resistance is equal to the thermal resistance of the interface between the plates. The thermal conductivity of copper k = 401 W/m-°C Q2/ A 4-m-internal-diameter spherical tank made of 1.75-cm-thick stainless steel (k 15 W/m °C) is used to store iced water at 0°C. The tank is located in a room whose temperature is 35°C. The walls of the room are also at 35°C. The outer surface of the tank is black, and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are 80 W/m2 °C and 10 W/m2 °C, respectively. Determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0°C that melts during a 1-h…2-88 A 1.5-mm-diameter stainless-steel rod [k = 19 W/m.°C] protrudes from a wall maintained at 45°C. The rod is 12 mm long, and the convection coefficient is 500 W/m² . °C. The environment temperature is 20°C. Calculate the temperature of the tip of the rod. Repeat the calculation for h = 200 and 1500 W/m² . °C.Heat transfer A nuclear reactor can be modelled as the plane wall shown in figure below. The thermal conductivity of the wall is 12 W/m.K. Heat is generated in the plane wall with the rate of 106644 W/m3. Left side of the wall is insulated, and the right side is cooled by air at 90°C. The convection heat transfer coefficient is 0.5 kW/m2.K. What is the maximum temperature in the wall (oC)?
- As shown in the sketh below, a steam pipe of 0.12-m inside diameter is insulated with a layer of calcium silicate. "2. Ta2} 1. Ta,1} Steam Insulation (a) If the insulation is 10 mm thick and its inner and outer surfaces are maintained at T, = 800 K and Ta = 490 K. respectively,. what is the rate of heat loss per unit length (q) of the pipe, in W/m? (b) Determine the rate of heat loss per unit length (d), in W/m, and outer surface temperature T,2, in K, for the steam pipe with the Inner surface temperature fixed at T = 800 K, inner radius = 0.06 m, and outer radius n = 0.18 m. The outer surface is exposed to an airflow (T 25°C) that maintains a convection coefficient of h = 25 W/m2-K and to large surroundings for which Tur = T, = 25°C. The surface emissivity of calcium silicate is approximately 0.8.A Multi-layer wall of a building is shown in the following figure. The thermal conductivity of A, B, C, D, and E are: 30, 5, 1.67, 10.5, 6 W/m k, respectively. Assume one dimentional heat transfer. The area of A = D = E =4 m?, and B = C= 2 m². The thickness of each layer is 10 cm. The temperature of surface A is 25 °C, and the temperature of surface E is 38 °C. Calculate the heat transfer rate through the wall. B A D E C4x F2 # 3 E 4, F3 54 $ R F4 Ac = 1m² ▬ H DII x= 1 m (4) Consider a wall (as shown above) of thickness L-1 m and thermal conductivity k-1 W/m-K. The left (x=0) and the right (x=1 m) surfaces of the wall are subject to convection with a convectional heat transfer coefficient h= 1 W/m²K and an ambient temperature T. 1 K. There is no heat generation inside the wall. You may assume 1-D heat transfer, steady state condition, and neglect any thermal contact resistance. Find T(x). % To,1 = 1 K h₁ = 1 W/m²K 5 Q Search F5 T T₁ A 6 x=0 F6 à = 0 W/m³ k= 1W/mK L=1m Y 994 F7 & 7 T₂ U Ton2 = 1 K h₂ = 1 W/m²K1 PrtScn F8 Page of 7 ) 0 PgUp F11 P