CBE 3322: Heat Transfer Operations
Section 1 - Introduction
Dominic Pjontek, Ph.D., P.Eng.
University of Western Ontario
Fundamentals of heat transfer
◼ How can we define heat transfer…?
❑ Thermal energy in transit due to a temperature difference
◼ Heating or cooling of materials/streams is an indispensable part of
processing, production, or fabrication jobs in engineering practice.
◼ Anytime a temperature difference is present in a medium or
between media, heat transfer will occur.
◼ Our main objective is to find the most economic method to heat
or cool a stream, thus minimizing the respective heat loss or gain.
Introduction 2
Modes of heat transfer
Conduction Convection Radiation
◼ Conduction: heat transfer across a medium
◼ Convection: heat transfer between a solid surface and a moving fluid
◼ Radiation: heat transfer between two surfaces at different
temperatures
Introduction 3
Examples of heat transfer applications
space shuttle thermal tiles
home insulation
car radiator
Introduction 4
Applications in Chemical Engineering
◼ One of the most widely used heat exchangers in chemical processes:
❑ Shell and tube heat exchanger
◼ Can you identify the various modes of heat transfer within the unit?
Introduction 5
Heat transfer definition
◼ It is important to distinguish thermodynamics and heat transfer.
❑ Thermodynamics is concerned with equilibrium states of
matter. Hence, it can determine the amount of energy required
to pass from one equilibrium state to another.
❑ Heat transfer requires a temperature gradient, which
represents thermodynamic non-equilibrium.
◼ For example:
❑ If we cool a 1 kg bar of iron from 1000°C to 100°C in an oil
bath, what is the loss of internal energy (Q) for the iron bar?
❑ Assume CP = 450 J/kg·K
Introduction 6
Heat transfer definition
◼ However, thermodynamics cannot tell us how long we have to wait
for the temperature to reach 100°C in the previous example.
❑ This depends on the physical properties of the oil and the fluid
dynamics (i.e., mixing) in the bath.
◼ Heat transfer thus studies what thermodynamics is inherently
unable to do:
❑ Quantify the rate (q) at which heat transfer occurs in terms of
the degree of thermal non-equilibrium.
◼ How are the first and second law of thermodynamics applied to heat
transfer?
Introduction 7
Conservation of energy
◼ Since we are trying to study the rate at which heat is transferred
(q), this can be considered an extension of thermodynamics.
◼ The first law of thermodynamics (conservation of energy) is
thus valid and quite useful to solve heat transfer problems.
◼ Conservation of energy can be applied for a specific time basis,
leading to two cases for our application:
1. At a given instant (t)
2. Over a specified time interval (Δt)
Introduction 8
Conservation of energy
◼ A general form of the conservation of energy can be expressed as:
dE
Ein − Eout + Egenerated =
dt
Control Volume
Ein dE Eout
Egenerated
dt
Introduction 9
Surface energy balance
◼ One special case for energy conservation is when it is applied to the
surface of a medium. This removes the generation and
accumulation terms from the balance, resulting in the following:
E in = E out
q"rad For the simplified example on
the left, we know based on the
q"cond conservation of energy that:
q"conv q"cond = q"rad + q"conv
Introduction 10
Conduction
◼ Thermal conduction is the transfer of internal energy by
microscopic diffusion and collisions of molecules/particles within a
body. It occurs in the presence of a temperature difference and is
not accompanied by any macroscopic or bulk motion in the medium.
◼ The rate equation for conduction is known as Fourier’s Law:
" dT
q = −k
x
dx
temperature gradient [K/m]
heat flux [W/m2]
thermal conductivity [W/m·K]
Introduction 11
Conduction (Example 1)
◼ The heat flux through a wood slab 50 mm thick, whose inner and
outer surface temperatures are 40 and 20°C, respectively, has been
determined to be 40 W/m2. What is the thermal conductivity of the
wood?
Introduction 12
Conduction (Example 2)
◼ A square silicon chip (k = 150 W/m·K) with a width of 5 mm and a
thickness of 1 mm is mounted such that its side and bottom
surfaces are insulated, while the top is exposed to a coolant.
◼ If 4 W of heat are being dissipated in the circuits mounted to the
bottom surface of the chip, what is the steady-state temperature
difference between the bottom and top surfaces?
Introduction 13
Convection
◼ Convection refers to heat transfer that occurs between a surface
and a moving fluid at different temperatures. More specifically,
convection consists of two mechanisms:
❑ random molecular motion (diffusion)
❑ bulk or macroscopic motion of a fluid (advection)
◼ The rate equation for convection is Newton’s law of cooling:
heat flux [W/m2]
q" = h (TS − T ) fluid temperature [K]
surface temperature [K]
convective heat transfer coefficient [W/m2·K]
Introduction 14
Convection
◼ Different forms of convection can be classified based on the nature
of the flow:
Natural
Forced
Sensible heat
Latent heat
Boiling Condensation
Introduction 15
Convection (Example)
◼ Let’s compare the heat loss experienced when placing your hand
out of the window of a moving car to one place into flowing water.
Assume the surface of your hand is at 30°C.
❑ The car is moving at 35 km/h in air at -5°C with a convection
coefficient of 40 W/m2·K.
❑ Flowing water with a velocity of 0.2 m/s and a temperature of
10°C, where the convection coefficient is 900 W/m2·K.
❑ Compare this with a heat loss of approximately 30 W/m2 under
ambient room conditions.
Introduction 16
Radiation
◼ Thermal radiation is energy continuously emitted by matter which is
at a finite temperature.
❑ Radiation energy is transmitted by electromagnetic waves
❑ Energy transferred by radiation does not require a material
medium, in fact, it is most efficient in a vacuum.
◼ The upper limit for energy emitted by a surface (referred as an ideal
radiator or blackbody) is described by the Stefan-Boltzmann law:
E = TS4
emissive power [W/m2] surface temperature [K]
Stefan-Boltzmann constant [σ = 5.67 x 10-8 W/m2·K4]
Introduction 17
Radiation
◼ In reality, the efficiency of a surface’s energy emission is quantified
by its emissivity (0 ≤ ε ≤ 1): E out = TS4
◼ We have only considered energy emitted. We must also account for
the irradiation of a surface from its surrounding (G). Similar to the
emissivity, a surface’s ability to absorb is quantified by its
absorptivity (0 ≤ α ≤ 1): Ein = G
❑ If α < 1, the irradiation is either reflected or transmitted
Introduction 18
Radiation
◼ A special case often occurs for engineering purposes:
❑ small surface at Ts that is surrounded by much larger
isothermal surface at Tsurr
❑ the irradiation can be approximated as the emission from a
blackbody at Tsurr: Ein = G = Tsurr
4
❑ if we assume that α ≈ ε for the surface (gray surface)
◼ The net rate of radiation heat transfer from the surface is then:
q" = E out − Ein = Ts4 − Tsurr
4
(
q" = Ts4 − Tsurr
4
)
Introduction 19
Radiation (Example 1)
◼ Why does it “feel” colder in your house during the winter even if the
room temperature is the same as during the summer?
❑ Let’s assume the air temperature is maintained at 20°C
throughout the year.
❑ The wall temperature during the summer may be estimated at
27°C during the summer and 14°C during the winter.
❑ We will assume the average temperature of the exposed
surface of a person to be 32°C and that they have an
emissivity of 0.90.
❑ The natural convective heat transfer coefficient for a person
and ambient air is approximately 2 W/m2·K.
Introduction 20
Energy balance (Online Example)
◼ Hot combustion gases in a furnace are separated from the ambient
air and its surroundings, which are at 25°C, by a brick wall 0.15 m
thick. The brick has a thermal conductivity of 1.2 W/m·K and a
surface emissivity of 0.8. Under steady-state conditions, and outer
surface temperature of 100°C is measured. Free convection heat
transfer to the air adjoining the surface is characterized by a
convection coefficient of h = 20 W/m2·K.
◼ What is the brick inner surface temperature?
Introduction 21
