) 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...
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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.
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.
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