) A metal component is subjected to heat-treatment called normalisation. The component is eated to a temperature T, (which is above the critical phase transformation temperatures) nd cooled in air. The elementary change dT(t) of temperature T(t) of a heated component s determined from the heath energy balance equation cmdT(t)=-hA(T(1)– Tuir)dt vhere cmdT(t) is the energy which is lost due to cooling; hA(T(t)– Tuir )dt is the total heat lux from the component to the air during an infinitesimally small time interval dt. The onstant c [J/(kg K)] is the specific heath capacity, m is the mass of the component in kg, h W/(m² K)] is the heat transfer coefficient and A is the surface area in m?. Derive an eguation which gives the temperature T7) as a function of the cooling time t.
) A metal component is subjected to heat-treatment called normalisation. The component is eated to a temperature T, (which is above the critical phase transformation temperatures) nd cooled in air. The elementary change dT(t) of temperature T(t) of a heated component s determined from the heath energy balance equation cmdT(t)=-hA(T(1)– Tuir)dt vhere cmdT(t) is the energy which is lost due to cooling; hA(T(t)– Tuir )dt is the total heat lux from the component to the air during an infinitesimally small time interval dt. The onstant c [J/(kg K)] is the specific heath capacity, m is the mass of the component in kg, h W/(m² K)] is the heat transfer coefficient and A is the surface area in m?. Derive an eguation which gives the temperature T7) as a function of the cooling time t.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![b) A metal component is subjected to heat-treatment called normalisation. The component is
heated to a temperature T, (which is above the critical phase transformation temperatures)
and cooled in air. The elementary change dT(t) of temperature T(t) of a heated component
is determined from the heath energy balance equation
cmdT(t) =-hA(T(t)– Tuir)dt
where cmdT(t) is the energy which is lost due to cooling; hA(T(t)– Tuir )dt is the total heat
flux from the component to the air during an infinitesimally small time interval dt. The
constant c [J/(kg K)] is the specific heath capacity, m is the mass of the component in kg, h
[W/(m? K)] is the heat transfer coefficient and A is the surface area in m?.
Derive an equation which gives the temperature T(t) as a function of the cooling time t.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefc4cde9-56dc-4afa-9c45-879ca2c9f347%2Fc70d748b-6c29-4a48-83be-e72ed621bcfe%2Fdsr84e6_processed.png&w=3840&q=75)
Transcribed Image Text:b) A metal component is subjected to heat-treatment called normalisation. The component is
heated to a temperature T, (which is above the critical phase transformation temperatures)
and cooled in air. The elementary change dT(t) of temperature T(t) of a heated component
is determined from the heath energy balance equation
cmdT(t) =-hA(T(t)– Tuir)dt
where cmdT(t) is the energy which is lost due to cooling; hA(T(t)– Tuir )dt is the total heat
flux from the component to the air during an infinitesimally small time interval dt. The
constant c [J/(kg K)] is the specific heath capacity, m is the mass of the component in kg, h
[W/(m? K)] is the heat transfer coefficient and A is the surface area in m?.
Derive an equation which gives the temperature T(t) as a function of the cooling time t.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning