1. Heat Transfer: Physical Origins and Rate Equations
Chapter One
Sections 1.1 and 1.2

2. Heat Transfer and Thermal Energy
What is heat transfer?
Heat transfer is thermal energy in transit due to a temperature
difference.
What is thermal energy?
Thermal energy is associated with the translation, rotation,
vibration and electronic states of the atoms and molecules
that comprise matter. It represents the cumulative effect of
microscopic activities and is directly linked to the temperature
of matter.

3. Heat Transfer and Thermal Energy (cont.)
DO NOT confuse or interchange the meanings of Thermal Energy, Temperature and Heat Transfer
Quantity
Meaning
Symbol
Units
Thermal Energy+
Energy associated with microscopic behavior of matter
Temperature
A means of indirectly assessing the amount of thermal energy stored in matter
Heat Transfer
Thermal energy transport due to temperature gradients
Heat
Amount of thermal energy transferred over a time interval  t  0
Heat Rate
Thermal energy transfer per unit time
Heat Flux
Thermal energy transfer per unit time and surface area

4. Modes of Heat Transfer
Modes of Heat Transfer
Conduction: Heat transfer in a solid or a stationary fluid (gas or liquid) due to
the random motion of its constituent atoms, molecules and /or
electrons.
Convection: Heat transfer due to the combined influence of bulk and
random motion for fluid flow over a surface.
Radiation: Energy that is emitted by matter due to changes in the electron configurations of its atoms or molecules and is transported as
electromagnetic waves (or photons).
Conduction and convection require the presence of temperature variations in a material
medium.
Although radiation originates from matter, its transport does not require a material
medium and occurs most efficiently in a vacuum.

5. Heat Transfer Rates: Conduction
General (vector) form of Fourier’s Law:
Heat flux
Thermal conductivity
Temperature gradient
Application to one-dimensional, steady conduction across a
plane wall of constant thermal conductivity:
(1.2)
Heat rate (W):

6. Heat Transfer Rates: Convection
Relation of convection to flow over a surface and development
of velocity and thermal boundary layers:
Newton’s law of cooling:
(1.3a)

7. Heat Transfer Rates: Radiation
Heat transfer at a gas/surface interface involves radiation
emission from the surface and may also involve the
absorption of radiation incident from the surroundings
(irradiation, ), as well as convection
Energy outflow due to emission:
(1.5)
Energy absorption due to irradiation:
(1.6)

8. Heat Transfer Rates: Radiation (cont.)
Irradiation: Special case of surface exposed to large
surroundings of uniform temperature,
(1.7)

9. Heat Transfer Rates: Radiation (cont.)
Alternatively,
(1.8)
(1.9)
For combined convection and radiation,
(1.10)

10. Process Identification
Problem 1.87(a): Process identification for single-and double-pane windows
Schematic:
Convection from room air to inner surface of first pane
Net radiation exchange between room walls and inner surface of first pane
Conduction through first pane
Convection across airspace between panes
Net radiation exchange between outer surface of first pane and inner surface of second pane (across airspace)
Conduction through a second pane
Convection from outer surface of single (or second) pane to ambient air
Net radiation exchange between outer surface of single (or second) pane and surroundings such as the ground
Incident solar radiation during day; fraction transmitted to room is smaller for double pane

11. Problem: Electronic Cooling
Problem 1.40: Power dissipation from chips operating at a surface temperature
of 85C and in an enclosure whose walls and air are at 25C for (a) free convection and (b) forced convection.
Schematic:
Assumptions: (1) Steady-state conditions, (2) Radiation exchange between a small surface and a large enclosure, (3)
Negligible heat transfer from sides of chip or from back of chip by conduction through the substrate.
Analysis:
(a) If heat transfer is by natural convection,
(b) If heat transfer is by forced convection,

12. Relationship to Thermodynamics
Chapter One
Section 1.3

13. Alternative Formulations
CONSERVATION OF ENERGY (FIRST LAW OF THERMODYNAMICS)
An important tool in heat transfer analysis, often
providing the basis for determining the temperature
of a system.
Alternative Formulations
Time Basis:
At an instant or
Over a time interval
Type of System:
Control volume
Control surface

14. CV at an Instant and over a Time Interval
APPLICATION TO A CONTROL VOLUME
At an Instant of Time:
Note representation of system by a
control surface (dashed line) at the boundaries.
Surface Phenomena
Volumetric Phenomena
Conservation of Energy
(1.12c)
Each term has units of J/s or W.
Over a Time Interval
Each term has units of J.
(1.12b)

15. Special Cases (Linkages to Thermodynamics)
Closed System
Special Cases (Linkages to Thermodynamics)
Transient Process for a Closed System of Mass (M) Assuming Heat Transfer
to the System (Inflow) and Work Done by the System (Outflow).
Over a time interval
(1.12a)
For negligible changes in potential or kinetic energy
Internal thermal energy
At an instant

16. Example 1.4: Application to thermal response of a conductor with Ohmic
heating (generation):
Involves change in thermal energy and for an incompressible substance.
Heat transfer is from the conductor (negative )
Generation may be viewed as electrical work done on the system (negative )

17. Example 1.6
Example 1.6: Application to isothermal solid-liquid phase change in a container:
Latent Heat
of Fusion

18. Open System
Steady State for Flow through an Open System without Phase Change or Generation:
At an Instant of Time:
(1.12d)

19. Surface Energy Balance
THE SURFACE ENERGY BALANCE
A special case for which no volume or mass is encompassed by the control surface.
Conservation of Energy (Instant in Time):
(1.13)
Applies for steady-state and transient conditions.
With no mass and volume, energy storage and generation are not pertinent to the energy
balance, even if they occur in the medium bounded by the surface.
Consider surface of wall with heat transfer by conduction, convection and radiation.

20. METHODOLOGY OF FIRST LAW ANALYSIS
On a schematic of the system, represent the control surface by
dashed line(s).
Choose the appropriate time basis.
Identify relevant energy transport, generation and/or storage terms
by labeled arrows on the schematic.
Write the governing form of the Conservation of Energy requirement.
Substitute appropriate expressions for terms of the energy equation.
Solve for the unknown quantity.

21. Problem: Silicon Wafer
Problem 1.57: Thermal processing of silicon wafers in a two-zone furnace.
Determine (a) the initial rate of change of the wafer
temperature and (b) the steady-state temperature.
SCHEMATIC:

22. Problem: Silicon Wafer (cont.)
or, per unit surface area
<

23. Problem: Silicon Wafer (cont.)
<

24. Problem: Cooling of Spherical Canister
Problem 1.64: Cooling of spherical canister used to store reacting chemicals.
Determine (a) the initial rate of change of the canister temperature,
(b) the steady-state temperature, and (c) the effect of convection
on the steady-state temperature.
535 J/kg·K

25. Problem: Cooling of Spherical Canister (cont.)
SCHEMATIC:
<

26. Problem: Cooling of Spherical Canister (cont.)
<
<

27. Problem: Cooling of Spherical Canister (cont.)

28. SECOND LAW OF THERMODYNAMICS
An important tool to determine how heat transfer affects
the efficiency of energy conversion.
For a reversible heat engine neglecting heat transfer effects between the heat engine and large reservoirs, the Carnot efficiency is
(1.15, 1.16)
where and are the absolute temperatures of large cold and hot reservoirs,
respectively.
For an internally reversible heat engine with heat transfer to and from the large reservoirs properly accounted for, the modified Carnot efficiency is
(1.17)
where and are the absolute temperatures seen by the internally reversible heat engine. Note that and are heat transfer rates (J/s or W).

29. The modified Carnot efficiency may ultimately be expressed as
Second law (cont.)
Heat transfer resistances associated with, for example, walls separating the
internally reversible heat engine from the hot and cold reservoirs relate the heat transfer rates to temperature differences:
(1.18 a,b)
In reality, heat transfer resistances (K/W) must be non-zero since according to the rate equations, for any temperature difference only a finite amount of heat may be transferred.
The modified Carnot efficiency may ultimately be expressed as
(1.21)
From Eq. 1.21,