1. A plane wall of thickness 0.1 m and thermal conductivity 25 W/m-K having uniform volumetric heat generation of 0.3 MW/m³ is insulated on one side, while the other side is exposed to a fluid at 92°C. The convection heat transfer coefficient between the wall and the fluid is 500 W/m²K. Determine the maximum temperature in the wall. Answer: 212°C
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- 3.16 A large, 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on one side is and on the other side is . If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it takes for the copper plate to reach a temperature of 82°C.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.Show that the rate of heat conduction per unit length through a long, hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with temperature, is given by qkL=TiTo(rori)/kmA where Ti = temperature at the inner surface To = temperature at the outer surface A=2(rori)/ln(ro/ri)km=ko[1+k(Ti+To)/2]L=lenthofcyclinder
- A cooling system is to be designed for a food storage warehouse for keeping perishable foods cool prior to transportation to grocery stores. The warehouse has an effective surface area of 1860 m2 exposed to an ambient air temperature of 32C. The warehouse wall insulation (k=0.17W/(mK)) is 7.5 cm thick. Determine the rate at which heat must be removed (W) from the warehouse to maintain the food at 4C.1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a well-insulated 40-L tank of water that is initially at 300 K. If each heater dissipates 500 W, what is the time required for bringing the water temperature in the tank to 340 K? State your assumption for your analysis.Heat is transferred at a rate of 0.1 kW through glass wool insulation (density=100kg/m3) with a 5-cm thickness and 2-m2 area. If the hot surface is at 70C, determine the temperature of the cooler surface.
- 1.19 A cryogenic fluid is stored in a 0.3-m-diameter spherical container is still air. If the convection heat transfer coefficient between the outer surface of the container and the air is 6.8 , the temperature of the air is 27°C, and the temperature of the surface of the sphere is –183°C, determine the rate of heat transfer by convection.1.39 On a cold winter day, the outside wall of a home is exposed to an air temperature of when the inside temperature of the room is at . As a result of this temperature gradient, there is heat loss through the wall to the outside. Consider the convective heat transfer coefficients for the air inside the room and at the outside wall surface to be, respectively, 12.0 and . If the composite room wall is modeled as a plane wall with a thermal resistance per unit area of , determine the temperature at the outer surface of the wall as well as the rate of heat flow through the wall per unit area. If the homeowner were to consider using a fiberglass insulation layer on the inside wall surface for reducing this heat loss by 50%, what is the required thickness of this layer and the outside wall temperature for this case?Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k=2.3 W/m °C,and surface area A= 20 m2. The left side of the wall at x= 0 is subjected of T1 = 80 C. while the right side losses heated by convection to the surrounding air at Too=15 C with a heat transfer coefficient of h=24 W/m2 .C. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall, (b) obtain a relation for the variation of temperature in the wall by solving the differential equation, and (c) evaluate the rate of heat transfer through the wall
- determine the rate of heat transfer through the wall in Watts and the temperature at the inner and outer surfaces and at the interfaces. k = 0.20 W/m-°C for the 2.5 cm thick plaster wall on the inside k = 0.038 W/m-ºC for the 9.0 cm thick fiberglass insulation layer k = 0.12 W/m-°C for the 1.25 cm plywood layer on the outside. Assume: -the inside room air is 20 °C with convection coefficient of 10 W/m²- ºC, and - the outside air at -20 °C with convection coefficient of 20 W/m²-°C. Plaster Wall Insulation 12 2.5 cm 9 cm Plywood outside 34 k -1.25 cmA large concrete wall is 300 mm thick and has a thermal conductivity of 1.2 W/m C. The heat flux through the wall is 100 W/m2. The higher-temperature surface of the wall is at 42 C. What is the temperature of the other surface of the wall?A flat wall is exposed to an environmental temperature of 38 oC. The wall is covered with a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4 W/m oC, and the temperature of the wall on the inside of the insulation is 315 oC. The wall loses heat to the environment by convection. Compute the value of the convection heat-transfer coefficient that must be maintained on the outer surface of the insulation to ensure that the outer-surface temperature does not exceed 41oC.