and k =43 W/m-K, respectively. The time required for the rod to reach 300 °C is seconds.
Q: A 0.6-cm-diameter mild steel rod at 38°C is suddenly immersed in a liquid at 93°C with h=110 W/m2
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Q: How do we get the uncertainty for this problem?
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- 2.30 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 plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.3.17 A 1.4-kg aluminum household iron has a 500-W heating element. The surface area is . The ambient temperature is 21°C, and the surface heat transfer coefficient is . How long after the iron is plugged in does its temperature reach 104°C?
- 3.14 A thin-wall cylindrical vessel (1 m in diameter) is filled to a depth of 1.2 m with water at an initial temperature of 15°C. The water is well stirred by a mechanical agitator. Estimate the time required to heat the water to 50°C if the tank is suddenly immersed in oil at 105°C. The overall heat transfer coefficient between the oil and the water is , and the effective heat transfer surface is .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 11.1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.
- 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 thin-wall jacketed tank heated by condensing steam at one atmosphere contains 91 kg of agitated water. The heat transfer area of the jacket is 0.9m2 and the overall heat transfer coefficient U=227W/m2K based on that area. Determine the heating time required for an increase in temperature from 16C to 60C.2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.
- An electronic device that internally generates 600 mW of heat has a maximum permissible operating temperature of 70C. It is to be cooled in 25C air by attaching aluminum fins with a total surface area of 12cm2. The convection heat transfer coefficient between the fins and the air is 20W/m2K. Estimate the operating temperature when the fins are attached in such a way that (a) there is a contact resistance of approximately 50 K/W between the surface of the device and the fin array and (b) there is no contact resistance (in this case, the construction of the device is more expensive). Comment on the design options.The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9cm1.25cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the handle of tubing 0.15 cm thick to the same rectangular shape. If the average heat transfer coefficient over the handle surface is 14 W/m K, estimate the reduction of the temperature at the grip in air at 21C.2.44 To determine the thermal conductivity of a long, solid 2.5-cm-diameter rod, one half of the rod was inserted into a furnace while the other half was projecting into air at . After steady state had been reached, the temperatures at two points 7.6 cm apart were measured and found to be and , respectively. The heat transfer coefficient over the surface of the rod exposed to the air was estimated to be 22.7 . What is thermal conductivity of the rod?