Fundamentals of Heat and Mass Transfer
Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 8, Problem 8.105P

The mold used in an injection molding process consists of a top half and a bottom half. Each half is 60 mm × 60 × mm × 20 mm and is constructed of metal ( ρ = 7800 kg/m 3 , c = 450 J/kg K ). The cold mold ( l 00 ° C ) s to be heated w 2 00 ° C with pressurized water (available at 275 ° C and a total flow rate of 0.0 2 kg / s ) prior to injecting the thermoplastic material. The injection takes only a fraction of a second, and the hot mold ( 2 00 ° C ) is subsequently cooled with cold water (available at 25 ° C and a total flow rate of 0.0 2 kg / s ) prior to ejecting the molded part. After part ejection, which also takes a fraction of a second, the process is repeated.

(a) In conventional mold design, straight cooling (healing) passages are bored through the mold in a location where the passages will not interfere with the molded part. Determine the initial heating rate and the initial cooling rate of the mold when five 5 mm -diameter, 6 0 mm -1ong passages are bored in each half of the mold (10 passages total). The velocity distribution of the water is fully developed at the entrance of each passage in the hot (or cold) mold

(b) New additive manufacturing processes, known as selective freeform fabrication, or SFF, are used to construct molds that are configured with conformal cooling passages. Consider the same mold as before, but now a 5 mm -diameter, coiled, conformal cooling passage is designed within each half of the SFF-manufactured mold. Each of the two coiled passages has N = 2 turns. The coiled passage does not interfere with the molded part. The conformal channels have a coil diameter C = 5 0  mm . The total water flow remains the same as in part (a) ( 0.0 1 kg / s per coil). Determine the initial heating rate and the initial cooling rate of the mold.

(c) Compare the surface areas of the conventional and conformal cooling passages. Compare the rate at which the mold temperature changes for molds configured with the conventional and conformal healing and cooling passages. Which cooling passage, conventional or conformal, will enable production of more parts per day? Neglect the presence of the thermoplastic material.

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Chapter 8 Solutions

Fundamentals of Heat and Mass Transfer

Ch. 8 - Consider a circular tube of diameter D and length...Ch. 8 - Consider flow in a circular tube. Within the test...Ch. 8 - Consider a cylindrical nuclear fuel rod of length...Ch. 8 - Consider the laminar thermal boundary layer...Ch. 8 - In a particular application involving fluid flow...Ch. 8 - A flat-plate solar collector is used w heat...Ch. 8 - Atmospheric air enters the heated section of a...Ch. 8 - Fluid enters a tube with a flow rate of 0.015kg/s...Ch. 8 - Water at 300 K and a flow rate of 5kg/s enters a...Ch. 8 - Slug flow is an idealized tube flow condition for...Ch. 8 - Superimposing a control volume that is...Ch. 8 - An experimental nuclear core simulation apparatus...Ch. 8 - Water at 20°C and a flow rate of 0.1kg/s enters a...Ch. 8 - Engine oil is heated by flowing through a circular...Ch. 8 - Engine oil flows through a 25mm -diameter tube at...Ch. 8 - In the final stages of production, a...Ch. 8 - An oil preheater consists of a single tube of 10mm...Ch. 8 - Engine oil flows at a rate of 1kg/s through a 5mm...Ch. 8 - Air at p=1atm enters a thin-walled ( D=5-mm...Ch. 8 - To cool a summer home without using a vapor...Ch. 8 - Batch processes are often used in chemical and...Ch. 8 - The evaporator section of a heat pump is installed...Ch. 8 - Water flowing at 2kg/s through a 40mm diameter...Ch. 8 - Consider the conditions associated with the hot...Ch. 8 - A thick-walled, stainless steel (AISI 316) pipe of...Ch. 8 - An air heater for an industrial application...Ch. 8 - Consider fully developed conditions in a circular...Ch. 8 - Consider the encased pipe of Problem 4.29, but now...Ch. 8 - Water flows through a thick-wailed tube with an...Ch. 8 - Atmospheric air enters a 10m -long. 150mm...Ch. 8 - NaK (45%/55). which is an alloy of sodium and...Ch. 8 - The products of combustion from a burner are...Ch. 8 - Liquid mercury at 0.5kg/s is lo be heated from 300...Ch. 8 - The surface of a 50-mm-diameter. thin-walled tube...Ch. 8 - Consider a horizontal, thin-walled circular tube...Ch. 8 - Consider pressurized liquid water flowing at...Ch. 8 - Cooling water flows through the 25.4-mm -diameter...Ch. 8 - The air passage for cooling a gas turbine vane can...Ch. 8 - The core of a high-temperature, gas-cooled nuclear...Ch. 8 - Air at 200kPa enters a 2-m -long, thin-walled tube...Ch. 8 - Heated air required for a food-drying process is...Ch. 8 - Consider laminar flow of a fluid with Pr=4 that...Ch. 8 - A common procedure for cooling a high-performance...Ch. 8 - One way to cool chips mounted on the circuit...Ch. 8 - Refrigerant- 134a is being transported a 0.1 kg/s...Ch. 8 - Oil at 150°C flows slowly through a long,...Ch. 8 - Exhaust gases from a wire processing oven are...Ch. 8 - A hot fluid passes through a thin-walled tube of...Ch. 8 - Consider a thin-walled tube of 10mm diameter and...Ch. 8 - Water at a flow rate of m =0.215kg/s is cooled...Ch. 8 - To maintain pump power requirements per unit flow...Ch. 8 - Consider a thin-walled, metallic tube of length...Ch. 8 - A circular tube of diameter D=0.2mm and length...Ch. 8 - Repeat Problem 8.66 for a circular tube of...Ch. 8 - Heat is to be removed from a reaction vessel...Ch. 8 - A healing contractor must heat 0.2kg/s of water...Ch. 8 - A thin-walled tube with a diameter of 6 mm and...Ch. 8 - A 50mm -diameter, thin—walled metal pipe covered...Ch. 8 - A thin-walled, uninsulated 0.3m -diameter duct is...Ch. 8 - Pressurized water at Tm,i=200C is pumped at...Ch. 8 - Water at 290K and 0.2kg/s flows through a Teflon...Ch. 8 - The temperature of flue gases flowing through the...Ch. 8 - In a biomedical supplies manufacturing process, a...Ch. 8 - Consider the ground source heat pump of Problem...Ch. 8 - For a sharp-edged inlet and a combined entry...Ch. 8 - Fluid enters a thin-walled rube of 5-mni diameter...Ch. 8 - Air at 3104kg/s and 27C enters a rectangular duct...Ch. 8 - Air at 25C flows at 30106kg/s within 100mm -long...Ch. 8 - A cold plate is an active cooling device that is...Ch. 8 - The cold plate design of Problem 8.82 has not been...Ch. 8 - A device that recovers heat from high-temperature...Ch. 8 - Air at 1 atm and 285K enters a 2-m -long...Ch. 8 - A double-wall heat exchanger is used to transfer...Ch. 8 - Consider laminar, fully developed flow in a...Ch. 8 - You have been asked to perform a feasibility study...Ch. 8 - A coolant flows through a rectangular channel...Ch. 8 - An electronic circuit board dissipating 50W is...Ch. 8 - To slow down large prime movers like locomotives,...Ch. 8 - A printed circuit board (PCB) is cooled by...Ch. 8 - Water at m=0.02kg/s and Tm,i=20C enters an annular...Ch. 8 - tFor the conditions of Problem 8.93, how tong must...Ch. 8 - Referring 10 Figure 8.11, consider conditions in...Ch. 8 - Consider the air healer of Problem 8.38, but now...Ch. 8 - Consider a concentric tube annulus for which the...Ch. 8 - It is common practice (o recover waste heat from...Ch. 8 - A concentric lube arrangement, for which the inner...Ch. 8 - Consider sterilization of the pharmaceutical...Ch. 8 - An engineer proposes to insert a solid rod of...Ch. 8 - An electrical power transformer of diameter 230mm...Ch. 8 - A bayonet cooler is used to reduce the temperature...Ch. 8 - The mold used in an injection molding process...Ch. 8 - Prob. 8.107PCh. 8 - Prob. 8.108PCh. 8 - Consider the microchannel cooling arrangement...Ch. 8 - The onset of turbulence in a gas flowing within a...Ch. 8 - Due to its comparatively large thermal...Ch. 8 - A novel scheme for dissipating heat from the chips...Ch. 8 - An experiment is designed to study microscale...Ch. 8 - Determine the tube diameter that corresponds to a...Ch. 8 - An experiment is devised to measure liquid flow...Ch. 8 - In the processing of very long plastic tubes of...Ch. 8 - Air at 300K and a flow rate of 3kg/h passes upward...Ch. 8 - What is the convection mass transfer coefficient...Ch. 8 - Air flowing through a tube of 75mm diameter passes...Ch. 8 - Consider gas flow of mass density and rate m...Ch. 8 - Atmospheric air at 25C and 3104kg/s flows through...Ch. 8 - Air at 25C and 1atm is in fully developed flow at...Ch. 8 - A humidifier consists of a bundle of vertical...Ch. 8 - The final step of a manufacturing process in which...Ch. 8 - Dry air is inhaled at a rate of lo liter/win...Ch. 8 - A mass transfer Operation is preceded by laminar...

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