The 0.5 m x 1.2 m wall of an industrial furnace is constructed from L = 0.15-m-thick fireclay brick having a thermal conductivity of 1.7 W/m-K. The temperature distribution, at an instant in time, is T(x) = a + bxwhere a = 1400 K and b = -1050 K/m. Determine the heat fluxes, q, and heat rates, q,, at x = 0 and x = L, in W/m2 and W respectively. Do steady-state conditions exist? W/m2 1x=0 i W/m? i W Ix=0 = Ir=L = i W Steady-state conditions exist.
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- Water at a temperature of 77C is to be evaporated slowly in a vessel. The water is in a low-pressure container surrounded by steam as shown in the sketch below. The steam is condensing at 107C. The overall heat transfer coefficient between the water and the steam is 1100W/m2K. Calculate the surface area of the container that is required to evaporate water at a rate of 0.01 kg/s. Problem 1.162.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)A cylindrical liquid oxygen (LOX) tank has a diameter of 1.22 m, a length of 6.1 m, and hemispherical ends. The boiling point of LOX is -179.4C. An insulation is sought that will reduce the boil-off rate in the steady state to no more than 11.3 kg/h. The heat of vaporization of LOX is 214 kJ/kg. If the thickness of this insulation is to be no more than 7.5 cm, what would the value of its thermal conductivity have to be?
- A 0.6-cm diameter mild steel rod at 38C is suddenly immersed in a liquid at 93C with hc=110W/m2K. Determine the time required for the rod to warm to 88C.2.2 A small dam, which is idealized by a large slab 1.2 m thick, is to be completely poured in a short Period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3. If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete can be taken as 0.84 W/m K.Determine the rate of heat transfer per meter length to a light oil flowing through a 2.5-cm-ID, 60-cm-long copper tube at a velocity of 0.03 m/s. The oil enters the tube at 16C, and the tube is heated by steam condensing on its outer surface at atmospheric pressure with a heat transfer coefficient of 11.3 kW/m K. The properties of the oil at various temperatures are listed in the following table: Temperature, T(C) 15 30 40 65 100 (kg/m3) 912 912 896 880 864 c(kJ/kgK) 1.80 1.84 1.925 2.0 2.135 k(W/mK) 0.133 0.133 0.131 0.129 0.128 (kg/ms) 0.089 0.0414 0.023 0.00786 0.0033 Pr 1204 573 338 122 55
- Sipho’s mother is making a fire in the stove inside a shack using coal. A fan is used to extract the flue gasfrom the fire via a chimney made of zinc material. The wall thickness of Chimney is L=4mm and the walltemperature of the chimney on the flue gas side is T_si=60˚C. Sipho, playing outside next to the chimneyexperiences an ambient temperature of 20˚C. The surrounding temperature is T_sur=35˚C and the emissivityis ε=0.95. Assume the convection coefficient is 20W/m2K and the chimney is grey material.Under these conditions determine the outer surface (air side) temperature T_so=? of the chimney.Conduction 1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P= 5 MW of net power production. The compressor, at an average temperature of T. = 400°C, is driven by the turbine at an average temperature of T₁ = 1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal conductivity k = 40 W/m K. Compressor min T Combustion chamber Shaft L Turbine Th out (a) Compare the steady-state conduction rate through the shaft connecting the hot turbine to the warm compressor to the net power predicted by the thermodynamics- based analysis. (b) A research team proposes to scale down the gas turbine of part (a), keeping all dimensions in the same proportions. The team assumes that the same hot and cold temperatures exist as in part (a) and that the net power output of the gas turbine is proportional to the overall volume of the device. Plot the ratio of the conduction through the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a…6. a. The heat flux applied to the walls of the biomass combustion furnace is 20 W/m2. The furnace walls have a thickness of 10 mm and a thermal conductivity of 12 W/m.K. If the wall surface temperature is measured to be 50oC on the left and 30oC on the right, prove that conduction heat transfer occurs at a steady state!b. Heating the iron cylinder on the bottom side is done by placing the iron on the hotplate. This iron has a length of 20 cm. The surface temperature of the hotplate is set at 300oC while the top side of the iron is in contact with the still outside air. To reach the desired hotplate temperature, it takes 5 minutes. Then it takes 15 minutes to measure the temperature of the upper side of the iron cylinder at 300oC. Show 3 proofs that heat transfer occurs transiently
- 8--The reactor from uniform carbide and graphite as a cylinder rod with diameter of 12 mm. The volumetric heat liberationis 3.88x108 W/m3 The thermal conductivity of the rod material is 85 W/mC.. Determine the heat losses from the rod and the surface temperature if the maximum temperature of the rod is 200C...Ans Tw=1940 C,,Heat losses=1.164 MW/m2.2. For a saturated dry steam at 1,500 KPa that passes through a 100 mm (OD) steel pipe with a thickness of 5 mm and a length of 100 meters. The steam line is insulated with a 50 mm thickness and a thermal conductivity of 0.25 W/m.C. For a mass flow rate of 600 kg of steam per hour. The surface film conductance of steam is h = 5,500 W/m?.C, surface film conductance of air is h = 12 W/m?.C , thermal conductivity of pipe material is k = 153 W/m.C and the ambient air temperature is -10°C . Determine the following: a) The quality of steam after passing through the pipe b) Explain the concepts/principles that were considered and the factors that affected the condition of the above mentioned items (a & b) @ 1,500 KPa (tsat = 198.32°C) kJ 2,792.20- kg k] 844.89 kg kJ 1,947.30- kg 1 hg 2 hf hfgA chip that is of length L = 5.5 mm on a side and thickness t = 2.0 mm is encased in a ceramic substrate, and its exposed surface is convectively cooled by a dielectric liquid for which h = 150 W/m² K and To = 20°C. . Th Chip, q, T₁, P, Cp The time is Substrate In the off-mode the chip is in thermal equilibrium with the coolant (T; = T). When the chip is energized, however, its temperature increases until a new steady state is established. For purposes of analysis, the energized chip is characterized by uniform volumetric heating with a = 9 x 106 W/m³. Assuming an infinite contact resistance between the chip and substrate and negligible conduction resistance within the chip, determine the steady-state chip temperature Tƒ. Following activation of the chip, how long does it take to come within 1°C of this temperature? The chip density and specific heat are p = 2000 kg/m³ and c = 700 J/kg-K, respectively. The steady-state chip temperature Tf is i S. °C.