PPT - Conduction: One Dimensional Chemical Engineering Notes | EduRev

 Page 1


Chapter 2: Heat Conduction 
Equation
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Page 2


Chapter 2: Heat Conduction 
Equation
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Objectives
When you finish studying this chapter, you should be able to:
•
Understand multidimensionality and time dependence of heat transfer, 
and the conditions under which a heat transfer problem can be 
approximated as being one-dimensional,
•
Obtain the differential equation of heat conduction in various 
coordinate systems, and simplify it for steady one-dimensional case,
•
Identify the thermal conditions on surfaces, and express them 
mathematically as boundary and initial conditions,
•
Solve one-dimensional heat conduction problems and obtain the 
temperature distributions within a medium and the heat flux,
•
Analyze one-dimensional heat conduction in solids that involve heat 
generation, and
•
Evaluate heat conduction in solids with temperature-dependent 
thermal conductivity.
Page 3


Chapter 2: Heat Conduction 
Equation
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Objectives
When you finish studying this chapter, you should be able to:
•
Understand multidimensionality and time dependence of heat transfer, 
and the conditions under which a heat transfer problem can be 
approximated as being one-dimensional,
•
Obtain the differential equation of heat conduction in various 
coordinate systems, and simplify it for steady one-dimensional case,
•
Identify the thermal conditions on surfaces, and express them 
mathematically as boundary and initial conditions,
•
Solve one-dimensional heat conduction problems and obtain the 
temperature distributions within a medium and the heat flux,
•
Analyze one-dimensional heat conduction in solids that involve heat 
generation, and
•
Evaluate heat conduction in solids with temperature-dependent 
thermal conductivity.
Introduction
•
Although heat transfer and temperature are 
closely related, they are of a different nature.
•
Temperature has only magnitude
it is a scalar quantity.
•
Heat transfer has direction as well as magnitude 
it is a vector quantity.
•
We work with a coordinate system and indicate 
direction with plus or minus signs. 
Page 4


Chapter 2: Heat Conduction 
Equation
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Objectives
When you finish studying this chapter, you should be able to:
•
Understand multidimensionality and time dependence of heat transfer, 
and the conditions under which a heat transfer problem can be 
approximated as being one-dimensional,
•
Obtain the differential equation of heat conduction in various 
coordinate systems, and simplify it for steady one-dimensional case,
•
Identify the thermal conditions on surfaces, and express them 
mathematically as boundary and initial conditions,
•
Solve one-dimensional heat conduction problems and obtain the 
temperature distributions within a medium and the heat flux,
•
Analyze one-dimensional heat conduction in solids that involve heat 
generation, and
•
Evaluate heat conduction in solids with temperature-dependent 
thermal conductivity.
Introduction
•
Although heat transfer and temperature are 
closely related, they are of a different nature.
•
Temperature has only magnitude
it is a scalar quantity.
•
Heat transfer has direction as well as magnitude 
it is a vector quantity.
•
We work with a coordinate system and indicate 
direction with plus or minus signs. 
Introduction - Continue
•
The driving force for any form of heat transfer is the 
temperature difference.
•
The larger the temperature difference, the larger the 
rate of heat transfer.
•
Three prime coordinate systems:
–
rectangular (T(x, y, z, t)) ,
–
cylindrical (T(r, ?, z, t)),
–
spherical (T(r, ?, ?, t)).
Page 5


Chapter 2: Heat Conduction 
Equation
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Objectives
When you finish studying this chapter, you should be able to:
•
Understand multidimensionality and time dependence of heat transfer, 
and the conditions under which a heat transfer problem can be 
approximated as being one-dimensional,
•
Obtain the differential equation of heat conduction in various 
coordinate systems, and simplify it for steady one-dimensional case,
•
Identify the thermal conditions on surfaces, and express them 
mathematically as boundary and initial conditions,
•
Solve one-dimensional heat conduction problems and obtain the 
temperature distributions within a medium and the heat flux,
•
Analyze one-dimensional heat conduction in solids that involve heat 
generation, and
•
Evaluate heat conduction in solids with temperature-dependent 
thermal conductivity.
Introduction
•
Although heat transfer and temperature are 
closely related, they are of a different nature.
•
Temperature has only magnitude
it is a scalar quantity.
•
Heat transfer has direction as well as magnitude 
it is a vector quantity.
•
We work with a coordinate system and indicate 
direction with plus or minus signs. 
Introduction - Continue
•
The driving force for any form of heat transfer is the 
temperature difference.
•
The larger the temperature difference, the larger the 
rate of heat transfer.
•
Three prime coordinate systems:
–
rectangular (T(x, y, z, t)) ,
–
cylindrical (T(r, ?, z, t)),
–
spherical (T(r, ?, ?, t)).
Classification of conduction heat transfer problems:
• steady versus transient heat transfer,
• multidimensional heat transfer,
• heat generation.
Introduction - Continue