8.9 One end of a 9-in long × 7-in diameter copper bar is heated to 59.4°F, the far end of the bar is held at 23°C. If the sides of the bar are covered with thermal insulation, what is the rate of heat transfer?

8.9 One end of a 9-in long × 7-in diameter copper bar is heated to 59.4°F, the far end of the bar is held at 23°C. If the sides of the bar are covered with thermal insulation, what is the rate of heat transfer?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.30P: 2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is...

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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.)
2.33 One end of a 0.3-m-long steel rod is connected to a wall at 204°C. The other end is connected to a wall that is maintained at 93°C. Air is blown across the rod so that a heat transfer coefficient of 17 W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38°C, what is the net rate of heat loss to the air? 0.3 m- Wall Wall 204°C 93°C Steel rod 5-cm diameter Air 38°C Problem 2.33
Q2/ A composite wall is formed of a 2.5 cm copper plate, a 3.2 mm layer of asbestos, and a 5 cm layer of fiberglass. The wall is subjected to an overall temperature difference of 560 C. Calculate the heat flow per unit area through the composite structure.
1. For a steam pipe with a given diameter of 10 cm covered by two (2) layers of insulation. The first insulation has a thickness of 4 cm and a coefficient of thermal conductivity of 0.08 W/m.K. and the second insulation has a thickness of 3 cm and a thermal conductivity of 0.15 W/m.K. The steam main conveys steam at a pressure of 1.70 MPa with 25°C superheat. Outside temperature is 27°C. The pipe is 30 meters in length. (tsat @ 1.70 MPa = 204°C). Determine the following: a) The heat loss in KW b) Explain the concepts/principles that were considered and the factors that affected the condition of the above mentioned items (a & b).
16. A steel pipe 1.5-m in length has an inside diameter of 7.6 cm with a wall thickness of 11.6 mm. The steel has a thermal conductivity of 46 W/m K. The pipe is covered with a 4 cm thick layer of insulation with a thermal conductivity of 0.4 W/m K. What is the total thermal resistance from the inside surface of the pipe to the outside surface of the insulation layer? Express your answer in °C/W or K/W.
For your company you need to mass produce 20-cmx10-cm heat sinks to dissipate heat quickly from an equipment. After considering several other parameters, you have short-listed two possible designs: A. 72 straight pin fins made of an alloy (thermal conductivity 240 W/m-°C) that costs $9,000 per m³. Each pin is 4 cm long and 1-cm diameter. E.=3'18; $204 B. 64 straight rectangular fins made of another alloy (thermal conductivity 180 W/m.°C) that costs $12,000 per m³. Each pin is 4 cm long and has 2-cmx1-cm cross-section. Eo =7:94%$ 6·14 The convection coefficient of the operating condition is approximated as 15 W/m2.°c. Consider that the manufacturing cost is same for both designs but the material cost differs. Calculate and compare the cost and performance (in terms of heat transfer gains by the heat sinks) of the two heat sinks so that a decision can be made to select a design.
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
2.16 A standard 4-in. steel pipe (ID = 4.026 in., OD = 4.500 in.) carries superheated steam at 1200°F in an enclosed space where a fire hazard exists, limiting the outer surface temperature to 100°F. In order to minimize the insulation cost, two materials are to be (a) Specify the thickness for each insulating mate- rial. (b) Calculate the overall heat transfer coefficient based on the pipe OD. (c) What fraction of the total resistance is due to (1) steam-side resistance, (2) steel pipe resistance, (3) insulation (the combina- tion of the two), and (4) outside resistance? (d) How much heat is transferred per hour per foot length of pipe? used: first a high-temperature (relatively expensive) insulation is to be applied to the pipe, and then magnesia (a less expensive material) will be applied on the outside. The maximum temperature of the magnesia is to be 600°F. The following constants are known: steam-side coefficient h = 100 Btu/hr ft² °F high-temperature insulation conductivity k =…
VI.2 A coolant is transported in a pipe with external wall temperature of -30 °C and with outer diameter of 10 cm. The tube is thermally isolated by two layers: 1) an internal layer of foamed polypropylene with thermal conductivity of 0.08 W.m.K and thickness of 10 cm, and 2) an external felt layer with thermal conductivity of 0.05 W.m.K and thickness of 5 cm. Temperature of the outer surface is 25 °C. Calculate the heat flow from the surroundings to the tube with length of 100 m. What is the temperature on the boundary between polypropylene and felt layers? Result: The heat flow from the surroundings is approx. 1.77 kW. Temperature between layers of isolation is 8.8 °C.
4. The section of a vertical wall is made up of fiberglass insulation slabs separated by wooden studs. The thermal conductivity of fiberglass and wood are 0.04 W/m-K and 0.18 W/m-K, respectively. The thickness of the wall is 160 mm. The temperatures of the inner and outer surfaces of the wall section are 22 °C and 4 °C, respectively. The ratio of the insulation area to the total wall area is 0.8. Calculate the total heat flow rate (in W/m2) through the wall per unit area. Wooden Stud Fiberglass Insulation Follow-up question to Question 4, calculate the rate of heat flow (in W/m2) through unit area of studs.
Question 5: A copper bar 35 cm long, with square cross-section 2 cm x 2 cm is fitted with a resistive heater at one end, and a large heat sink at the other. The bar itself is ideally thermally lagged. (i) (ii) Sketch how you think the two thermometers would behave when the heater is switched on; (ii) Calculate the thermal conductivity if in the steady-state, T1=64.7 deg C and T2=40.0 deg C. Hint: rate of flow of heat = k*A*AT/X V=6 V, I=2.5A heater T1 25 cm T2 Heat sink
Example 16.3 Determine the thickness of a glass window 120 × 120 cm² that separates a room at temperature of 25°C from outside temperature of 44°C and allows not more than 7 × 10° cal of heat to enter the room each day. Assume thermal conductivity of glass as 0.0024 cal/cm.s.K.