MAK321 & ME321
Heat Transfer
Instructor: Erol ÇUBUKÇU
Heat Transfer mechanisms:
– Conduction
– Convection
– Radiation
1D through 3D problems
Steady state problems
Time dependent analyses
MAK321 & ME321
Heat Transfer
There are recommended books for the course.
They can be considered as references rather
than textbooks.
– Holman, J.P., (2005) Heat and Mass Transfer, 9th
Ed., John Wiley and Sons.
– Çengel, Y.A., (2004) Heat Transfer, Mc Graw Hill
– Yüncü, H., Kakaç, S., (2000) Temel Isı Transferi,
Bilim yayınları.
– Incropera, F.P., et al., (2017) Principles of Heat
and Mass Transfer 8th Ed., John Wiley and Sons.
MAK321 & ME321
Heat Transfer
Intention is for 3 written exams:
– Midterms, each with weight = 30%,
– Final, weight = 40%.
There will be no homework.
We plan to have “solution hours”.
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.
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
U or u J or J/kg
Temperature A means of indirectly assessing the
amount of thermal energy stored in matter
T K or °C
Heat Transfer Thermal energy transport due to
temperature gradients
Heat Amount of thermal energy transferred Q J
over a time interval t > 0
Heat Rate Thermal energy transfer per unit time q W
Heat Flux Thermal energy transfer per unit time and q′′ W/m 2
surface area
+
U → Thermal energy of system
u → Thermal energy per unit mass of system
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.
Heat Transfer Rates: Conduction
Heat Transfer Rates
Conduction:
General (vector) form of Fourier’s law:
q′′ =−k ∇T
Heat flux Thermal conductivity Temperature gradient
W/m 2
W/m ⋅ K °C/m or K/m
Application to one-dimensional, steady conduction across a
plane wall of constant thermal conductivity:
dT T −T
q′′x =
−k −k 2 1
=
dx L
T1 − T2
qx′′ = k (1.2)
L
Heat rate (W): q=
x qx′′ ⋅ A
Heat Transfer Rates: Convection
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:
q′′ h ( Ts − T∞ )
= (1.3a)
h : Convection heat transfer coefficient (W/m 2 ⋅ K)
Heat Transfer Rates: Radiation
Heat Transfer Rates
Radiation Involves radiation emission from the surface and
may also involve the absorption of radiation incident from
the surroundings (irradiation, G ), as well as convection
( if Ts ≠ T∞ ) .
Energy outflow due to emission:
E ε=
= Eb εσ Ts4 (1.5)
E : Emissive power ( W/m 2 )
ε : Surface emissivity ( 0 ≤ ε ≤ 1)
Eb : Emissive power of a blackbody (the perfect emitter)
σ : Stefan-Boltzmann constant ( 5.67 ×10-8 W/m 2 ⋅ K 4 )
Energy absorption due to irradiation:
Gabs = α G (1.6)
Gabs :Absorbed incident radiation (W/m 2 )
α : Surface absorptivity ( 0 ≤ α ≤ 1)
G : Irradiation ( W/m 2 )
Heat Transfer Rates: Radiation (cont.)
Heat Transfer Rates
Irradiation: Special case of surface exposed to large
surroundings of uniform temperature, Tsur
G G=
= sur σ T 4
sur
If α = ε , the net radiation heat flux from the
surface due to exchange with the surroundings is:
qrad = εσ (Ts4 − Tsur4 )
′′= ε Eb (Ts ) − α G (1.7)
