A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k = 14.9 W/m·K, r = 7900 kg/m3, cp = 477 J/kg·K, and a 5 3.95 * 10-6 m2/s) comes out of an oven at a uniform temperature of 400°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h = 60 W/m2·K. Determine the temperature at the center of the shaft 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period. Solve this problem using analytical one-term approximation method (not the Heisler charts).

A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k = 14.9 W/m·K, r = 7900 kg/m3, cp = 477 J/kg·K, and a 5 3.95 * 10-6 m2/s) comes out of an oven at a uniform temperature of 400°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h = 60 W/m2·K. Determine the temperature at the center of the shaft 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period. Solve this problem using analytical one-term approximation method (not the Heisler charts).

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 1.60P: 1.60 Two electric resistance heaters with a 20 cm length and a 2 cm diameter are inserted into a...

See similar textbooks

Related questions

Q: from the back side of the board to a medium at 37°C, with a heat transfer coefficient of 45 W/m²-K.…

Q: Hot water is flowing at an average velocity of1.5 m/s through a cast iron pipe (k = 52 W/m·K) whose…

A: In order to proceed with the problem some assumptions need to be taken into consideration. Heat…

Q: An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose properties are roughly k=0.6…

Q: Pulverized coal particles are used in oxy-fuel combustion power plants for electricity generation.…

Q: 1. In a meat processing plant, 2 cm-diameter spherical meat balls (k=0.45 W/m-K and a=0.91×10-7…

Q: A 4-mm-diameter, 10-cm-long aluminum fin (k = 237 W/m-K) is attached to a surface. If the heat…

Q: A cylindriçal fuel rod (k= 30 W/m K) of 2 cm in diameter is encased in a concentric tube and cooled…

Q: Heat is transferred at a rate of 0.1 kW through glass wool insulation (density= 100 kg/m^3) of 5cm…

A: Answer: The temperature of the cooler surface is 0.6 ℃.

Q: c) Water is to be heated from 10°C to 80°C as it flows through a 2-cm-internal-diameter, 7-m- long…

A: here 2 question are there, both are not interlinked and as per honor code and answering guidelines…

Q: If q" w = 5000 and the convection heat transfer coefficient at the pipe outlet is 1000 W/m2K,…

Q: The 4cm thick large copper plate, initially at a uniform temperature of 25 °C, is heated by passing…

A: Solution: Characteristic length of a infinitely large plate (δ)=L2=2cm Time in seconds…

Q: A 40-cm-long, 0.6-cm-diameter electric resistance wire is used to determine the convection heat…

A: Giiven A 40-cm-long, 0.6-cm-diameter the convection heat transfer coefficient = 254 surface…

Q: Q18: Heat is generated uniformly at a rate of 2.6 x10 W/m3 in a spherical ball (k = 45 W/m C) of…

Q: A10-m-long section of a 6-cm-diameter horizontal hot water pipe passes through a large room whose…

Q: A heating system is to be designed to keep the wings of an aircraft cruising at a velocity of 900…

Q: A pipe in a manufacturing plant is transporting superheated vapor at a mass flow rate of 0.3 kg/s.…

A: Convection heat transfer take place bw solid boundary and flowing fluid. It is of two types:- 1)…

Q: Consider a sphere and a cylinder of equal volume made of copper. Both the cylinder and sphere 'are…

A: The answer is in next step

Q: Consider a 2-m-high electric hot-water heater thathas a diameter of 40 cm and maintains the hot…

A: Assumptions Heat transfer is in only radial direction. Conductivity of the foam insulation is…

Q: Q16: In a nuclear reactor, heat is generated in 1-cm diameter cylindrical uranium fuel rods at a…

Q: 210: In a nuclear reactor, 1-cm-diameter cylindrical uranium rods cooled by water from outside serve…

Q: With a pressure of approximately 2 MPa, the two 6-cm-diameter, 18-cm-long aluminum bars (k = 176 W/m…

Q: Consider a stainless steel spoon (k = 15 W/m·K) partially immersed in boiling water at 95°C in a…

Q: Castor oil at 36 °C flows over a 6 m long and 1 m wide heated plate at 0.06 m/s. For a surface…

A: Given: The temperature of castor oil, To = 36 C The length of plate, L = 6 m The width of plate, b =…

Q: Required informetion A cylindrical fue! rod (k = 30 W/m K) of 2 cm in diameter is encased in a…

Q: Consider a cold aluminum canned drink that is initially at a uniform temperature of 4°C. The can is…

Q: Cold conditioned air at 12°C is flowing inside a 1.5-cm-thick square aluminum (k = 237 W/m·K) duct…

A: Given data: The given temperature of the cold conditioned air is: Ti=12 C The thickness of the…

Q: A long copper rod of diameter 2.0 cm is initially at a uniform temperature of 100°C. It is now…

A: Given: diameter = 2cm Ti = 100 deg C T = 25 deg C Tinf = 13 deg C cp = 0.385 kJ/kgK = 385 J/kgK

Q: When is heat transfer through a fluid conduction and when is it convection? For which case is the…

A: The rate of heat transfer is given

Q: A long 20 cm diameter shaft made of stainless steel 304 comes out of an oven at a uniform…

Q: Q16: In a nuclear reactor, heat is generated in 1-cm diameter cylindrical uranium fuel rods at a…

A: The value of thermal conductivity is not given so I have assumed some standard value for uranium.

Q: A cylindrical fuel rod of 2 cm in diameter is encased in a concentric tube and cooled by water. The…

A: Given data:

Q: A 6-m-long section of an 9-cm-diameter horizontal hot-water pipe passes through a large room whose…

Q: A person is found dead at 5PM in a room whose temperature is 20°C. The temperature of the body is…

A: Given, Diameter,d=30cm=0.30mradius, r=0.15mLength, L=1.70mHeat transfer coefficient,…

Q: Consider a stainless steel spoon (k = 15 W/m·K) partially immersed in boiling water at 95°C in a…

Q: The use of fins is most effective in application involving low convective heat transfer coefficient

Q: A 30-m-long section of an 8-cm-diameter horizontal hot water pipe passes through a large room whose…

Q: A pipe in a manufacturing plant is transporting superheated vapor at a mass flow rate of 0.3 kg/s.…

A: Write the differential equation for the steady state one dimension heat conduction.

Q: Water enters a thin-shelled 4-cm-diameter, 200-m-long pipe at 7°C at a rate of 0.98 kg/s and leaves…

Q: A person puts a few apples into the freezer at 215°C tocool them quickly for guests who are about to…

A: Given : The diameter of sphere, D = 9 cm The heat transfer coefficient of the surface, h = 8 W/m2-K…

Q: An average man has a body surface area of 1.8 m2 and a skin temperature of 330C. The convective…

A: Let A = Surface area of man body =1.8m2 V =1.2m/s h =Heat Transfer Coefficient =8.6XVX0.53 h…

Q: A 40-cm-long, 800-W electric resistance heating element with diameter 0.5 cm and surface temperature…

A: The length of heating element = 40 cm = 0.4 m The diameter of heating element = 0.5 cm = 0.005 m The…

Q: A 30-m-long section of an 8-cm-diameter norizontal hot water pipe passes through a arge room whose…

A: As per the calculation, the nearest option is b.

Q: sof? =120°Cand?

A: given:outer radius r2=7cminner radius r1=5cmthermal conductivity k=25W/mKT1=120CT2=50C

Question

A long 35-cm-diameter cylindrical shaft made of
stainless steel 304 (k = 14.9 W/m·K, r = 7900 kg/m3, cp =
477 J/kg·K, and a 5 3.95 * 10-6 m2/s) comes out of an oven
at a uniform temperature of 400°C. The shaft is then allowed
to cool slowly in a chamber at 150°C with an average convection
heat transfer coefficient of h = 60 W/m2·K. Determine the
temperature at the center of the shaft 20 min after the start of
the cooling process. Also, determine the heat transfer per unit
length of the shaft during this time period. Solve this problem
using analytical one-term approximation method (not the
Heisler charts).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose properties are roughly k=0.6 W/m.oC and a=0.14 x 10-6 m2/s. The egg is initially at a uniform temperature of 8 oC and is dropped into boiling water at 97 oC. Taking the convection heat transfer coefficient to be h=1400 W/m2.oC, determine how long it will take for the center of the egg to reach 70oC.
For heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the properties of water. An egg that is initially at 8°C is dropped into the boiling water at 86°C. The heat transfer coefficient at the surface of the egg is estimated to be 800 W/m2-K. If the egg is considered cooked when its center temperature reaches 60°C, determine how long the egg should be kept in the boiling/water. Solve this problem using analytical one-term approximation method (not the Heisler charts). The length of/time for the egg to be kept in boiling water is determined to be min.
A long 35 cm diameter cylinder made of stainless steel 304 (k = 14.9 W/mo C, r = 7900 kg/m3 , Cp = 477 J/kgo C and a = 3.95´10-6 m2 /s) comes out of an oven at a uniform temperature of 400o C. The cylinder is then allowed to cool slowly in a chamber at 150o C with average convection heat transfer coefficient of h = 60 W/m2oC. Determine the temperature at the center of the cylinder 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the cylinder during this time period.
water 4-26 Steel rods (p = 7832 kg/m³, c, = 434 J/kg-K, and k = 63.9 W/m-K) are heated in a furnace to 850°C and then quenched in a bath at 50°C for a period of 40 s as part of a hardening process. The convection heat transfer coefficient is 650 W/m²K. If the steel rods have diameter of 40 mm and length of 2 m, determine their average temperature when they are taken out of the water bath.
3- Stainless steel ball bearings have a diameter of 1.2 cm are to be quenched in water. The balls leave the oven at a uniform temperature of 900°C and are exposed to air at 30°C for a while before they are dropped into the water. If the temperature of the balls is not to fall below 850°C prior to quenching and the heat transfer coefficient in the air is 125 W/m² - °C, determine how long they can stand in the air before being dropped into the water. Given: Stainless steel [ k= 15.1 W/m.°C, p= 8085 kg/m3, and Cp= 0.480 kJ/kg.°C. and a=3.95 × 106 m³/s]
In an annealing process, a 50-mm-thick stainless steel plate (p = 8238 kg/m, cp = 468 J/kg-K, k= 13.4 Wim-K, and a= 3.48 106 m2/s) was reheated in a furnace from an initial uniform temperature of 230°C. The ambient temperature inside the furnace is uniform at 1000°C, and the convection heat transfer coefficient is 215 W/m2.K. If the entire stainless steel plate is to be heated to at least 61O'C, determine the time that the plate should be heated in the furnace using the analytical one-term approximation method. The time that the plate should be heated in the furnace is
18-51 A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k = 14.9 W/mK, p = 7900 kg/m³; cp = 477 J/kg - K, and a = 3.95 x 10-6 m²/s) comes out of an oven at a uniform temperature of 500°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h = 60W/m².K Determine the temperature at the center of the shaft 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period. Solve this problem using the analytical one-term approximation method. Answers: 486°C, 22,270 kJ
A slab of aluminium 10 cm thick is originally at a temperature of 500°C. It is suddenly immersed in a liquid at 100°C resulting it a heåt transfer coefficient of 1200. W/m2K. Determine the temperature at the center line and the surface 1 min after the immersion. Also the total thermal energy removal per unit area of slab during this period. The properties of aluminium for the given condition are, a = 8.4 x 10-5 m?/s, k =215 W/mK, p = 2700 kg/m3, C= 0.9.kJ/kgK.
A long 20 cm diameter shaft made of stainless steel 304 comes out of an oven at a uniform temperature of 600°C. The shaft is then allowed to cool slowly in an environment at 200°C with an average heat transfer coefficient of h = 80 W/m².K. Determine [a] the temperature at the center of the shaft and [b] the temperature of the outer surface of the shaft 45 minutes after the start of the cooling Given: Find: Schematic: Assume: Property Data: k= 14.9 W/m°C p= 7900 kg/m³ Cp = 477 J/kg:K a= 3.95 x 10-6 m²/s
Steel rods (p = 7832 kg/m2, cn= 434 J/kg.K, and k = 63.9 W/m-K) are heated in a furnace to 850°C and then quenched in a water bath at 50°C for a period of 55 seconds as part of a hardening process. The convection heat transfer coefficient is 650 W/m2.K. If the steel rods have diameter of 40 mm and length of 2 m, determine their average temperature when they are taken out of the water bath. (Round off the answer to 1 decimal point.) °C
A 0.5-ampere current is flowing through a long electrically conducting cylindrical rod. The diameter of the rod is 6 mm, the electrical resistance of the rod is R = 2000 /m, and k =0.9 W/m K for the rod. The rod is encased in a 2-mm thick Pyrex tube and a 20°C liquid is flowing over the outer surface of the Pyrex tube. The convection heat transfer coefficient for the liquid h= 800 W/m2 . K. The interfacial conductance (contact resistance) at the interface between the rod and the Pyrex tube is h = 1200 W/m² - K. a) Compute the rate of heat generation in the rod and use it compute the volumetric rate of heat generation. b) Find the temperature drop across the interface between the outer surface of the rod and the inner surface of the Pyrex tube. c) Find the temperature at the center of the rod.
A long cylindrical wood log (k-0.17 W/m-K and a=128-10-7 m²/s) is 10 cm in diameter and is initially at a uniform temperature of 26°C. It is exposed to hot gases at 455°C in a fireplace with a heat transfer coefficient of 13.6 W/m2.K on the surface. If the ignition temperature of the wood is 375°C, determine how long it will be before the log ignites. Solve this problem using the analytical one- term approximation method. The time taken is min.