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. E =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.

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. E =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.

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.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.3P: 1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of...

See similar textbooks

Similar questions

1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
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.)
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.
A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6
Using Table 1.4 as a guide, prepare a similar table showing the orders of magnitude of the thermal resistances of a unit area for convection between a surface and various fluids.
1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.
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.
2.45 Heat is transferred from water to air through a brass wall . The addition of rectangular brass fins, 0.08 cm thick and 2.5 cm long, spaced 1.25 cm apart, is contemplated. Assuming a water-side heat transfer coefficient of and an airside heat transfer coefficient of , compare the gain in heat transfer rate achieved by adding fins to (a) the water side, (b) the air side, and (c) both sides. (Neglect temperature drop through the wall.)
A steam pipe carrying steam at 380 kPa pressure for a distance of 120 m in a chemical plant is not insulated. Estimate the Amount of heat saved if 16 cm steam line were covered with 85% magnesia pipe covering 5 cm thick. Take room temperature to be 36 ℃. Thermal conductivity of 85% magnesia is 0.0745 W/m−K , unit convective coefficient of room air, ho = 12 W m2−K .Take the steam temperature as 142℃. Use atleast 4 decimal places in every computation