Solutions Manual For Thermal Radiation Heat Transfer 6th
Edition By John R. Howell , M. Pinar Mengüç , Robert Siegel
9781466593268 ALL Chapters
name and define the 3 heat transfer modes (not equations) - ANSWER: 1) conduction - heat transfer
through a solid or stationary fluid (nothing is moving)
2) convection - heat transfer between a surface and a moving fluid
3) radiation - heat transfer via electromagnetic waves (no medium is required)
describe the physical phenomena that drives conduction - ANSWER: conduction is sustained by
atomic and molecular activity i.e. transfer of energy from more energetic to less energetic particles of
a substance due to interactions between the particles (phonons are collective particle vibrations)
equation for conductive heat transfer - ANSWER: fourier's law where q = -kAdT/dx [W]
where the negative sign denotes heat is transferred in direction of decreasing temperature i.e.(T_2 <
T_1), k is thermal conductivity of the substance [W/ m*K], A is the cross sectional area of substance in
same direction of flow
describe the physical phenomena that drives convection - ANSWER: convection is driven by random
molecular motion and by bulk macroscopic motion of the fluid
equation for convective heat transfer - ANSWER: newton's law of cooling where q = hA(T_s - T_inf)
where h is the convection coefficient [W/m^2*K], A is the surface area exposed to fluid, T_s is the
surface temperature, and T_inf is the fluid temperature
True or False: Forced convection typically has a larger convection coefficient compared to convection
with phase change. - ANSWER: False because typically free convection has the smallest convection
coefficient, then forced convection, then convection with phase change having the largest possible
convection coefficient
True or False: liquids can achieve higher convection coefficients compared to gases - ANSWER: True
because most liquids have a larger thermal conductivity than gases
describe the physical phenomena that drives radiation - ANSWER: thermal radiation is always emitted
from solids, liquids, and gases that are at a nonzero temperatures where regardless of the matter, the
emission is attributed to changes in electron configurations of the atoms or molecules
analogous thermal resistance equation to an electrical system (delV = I*R_e) - ANSWER: delT =
Q*R_th
True or False: resistance in a series connected circuit is the sum of the individual resistances (thermal
or electric circuit) - ANSWER: True because R = R_1 + R_2 for 2 resistors when connected in series
True or False: total resistance in a parallel connected circuit is the sum of the reciprocal of the
individual resistances (thermal or electric circuit) - ANSWER: True because R = (1/R_1 + 1/R_2)^-1 for
2 resistors when connected in parallel
define mean free path of molecules - ANSWER: the average distance any particle (atom, molecule, or
photon) travels before substantially changing its direction or energy due to collisions with other
particles
, what are the 2 conditions for which Fourier's law can become invalid/ need correction? - ANSWER: 1)
length scale is smaller than the mean mean free path of the energy carriers
2) the time scale is smaller than the relaxation time constant of the energy carriers
equation for effective mean free path - ANSWER: the effective mean free path is the inverse of the
sum of the reciprocals of the intrinsic and boundary distances; the intrinsic represents the volume of
interactions (scattering cross section x relative distance traveled) and the boundary is the separation
distance between walls
how does mean free path as a function of temperature affect thermal conductivity? - ANSWER: 1) at
low temperatures, boundary scattering is dominant (phonons hitting boundaries such as impurities,
grain boundaries); k~T^3
2) at high temperature, Umklapp scattering is dominant (phonons running into other phonons); k~T^-
1
True or False: in microstructure form, not bulk form, the grain and/or molecular orientation impacts
the thermal conductivity - ANSWER: True because diamond has a higher thermal conductivity (k_z) in
the vertical direction which is the same direction as the grain boundaries
define the Weideman Franz law - ANSWER: the relationship between electrical conductivity and
thermal conductivity and verified at all scales including atomic level
True or False: K_electron >> K_phonon in crystalline materials - ANSWER: False because phonons are
the dominant energy transport mechanism in crystalline materials, however it is true that K_electron
>> K_phonon for metallic materials
how can the bulk thermal conductivity be related to a small-scale system? - ANSWER: using the
concept of a thin nanowire where the mean free path can be approximated by the diameter of a solid
nanowire and used with the mean free path of the bulk material; use when the system size is smaller
than the bulk mean free path of the material
define an electron - ANSWER: a stable subatomic particle with a negative charge of electricity found in
all atoms and acting as the primary carrier of electricity in solids; has mass of 9.109 e^-31 kg
define a photon - ANSWER: a particle representing a quantam of light or other electromagnetic
radiation; is massless
define a phonon - ANSWER: a collective excitation in a period, elastic arrangement of atoms or
molecules in solids and some liquids such as sound or vibration of a crystal lattice; is responsible for
heat conduction in semiconductors and insulators
define a molecule - ANSWER: a group of 2 more atoms held together by attractive forces from
chemical bonds
derive the 3D heat diffusion in cartesian coordinates - ANSWER: general steps:
1) energy balance
2) define each term
3) taylor expansion of energy out terms
4) substitute expansion into energy balance
5) substitute Fourier's law in each direction into energy balance
6) simplify by writing as gradient of T
derive the 3D heat diffusion in cylindrical coordinates - ANSWER: general steps:
1) energy balance
2) define each term
3) taylor expansion of energy out terms
Edition By John R. Howell , M. Pinar Mengüç , Robert Siegel
9781466593268 ALL Chapters
name and define the 3 heat transfer modes (not equations) - ANSWER: 1) conduction - heat transfer
through a solid or stationary fluid (nothing is moving)
2) convection - heat transfer between a surface and a moving fluid
3) radiation - heat transfer via electromagnetic waves (no medium is required)
describe the physical phenomena that drives conduction - ANSWER: conduction is sustained by
atomic and molecular activity i.e. transfer of energy from more energetic to less energetic particles of
a substance due to interactions between the particles (phonons are collective particle vibrations)
equation for conductive heat transfer - ANSWER: fourier's law where q = -kAdT/dx [W]
where the negative sign denotes heat is transferred in direction of decreasing temperature i.e.(T_2 <
T_1), k is thermal conductivity of the substance [W/ m*K], A is the cross sectional area of substance in
same direction of flow
describe the physical phenomena that drives convection - ANSWER: convection is driven by random
molecular motion and by bulk macroscopic motion of the fluid
equation for convective heat transfer - ANSWER: newton's law of cooling where q = hA(T_s - T_inf)
where h is the convection coefficient [W/m^2*K], A is the surface area exposed to fluid, T_s is the
surface temperature, and T_inf is the fluid temperature
True or False: Forced convection typically has a larger convection coefficient compared to convection
with phase change. - ANSWER: False because typically free convection has the smallest convection
coefficient, then forced convection, then convection with phase change having the largest possible
convection coefficient
True or False: liquids can achieve higher convection coefficients compared to gases - ANSWER: True
because most liquids have a larger thermal conductivity than gases
describe the physical phenomena that drives radiation - ANSWER: thermal radiation is always emitted
from solids, liquids, and gases that are at a nonzero temperatures where regardless of the matter, the
emission is attributed to changes in electron configurations of the atoms or molecules
analogous thermal resistance equation to an electrical system (delV = I*R_e) - ANSWER: delT =
Q*R_th
True or False: resistance in a series connected circuit is the sum of the individual resistances (thermal
or electric circuit) - ANSWER: True because R = R_1 + R_2 for 2 resistors when connected in series
True or False: total resistance in a parallel connected circuit is the sum of the reciprocal of the
individual resistances (thermal or electric circuit) - ANSWER: True because R = (1/R_1 + 1/R_2)^-1 for
2 resistors when connected in parallel
define mean free path of molecules - ANSWER: the average distance any particle (atom, molecule, or
photon) travels before substantially changing its direction or energy due to collisions with other
particles
, what are the 2 conditions for which Fourier's law can become invalid/ need correction? - ANSWER: 1)
length scale is smaller than the mean mean free path of the energy carriers
2) the time scale is smaller than the relaxation time constant of the energy carriers
equation for effective mean free path - ANSWER: the effective mean free path is the inverse of the
sum of the reciprocals of the intrinsic and boundary distances; the intrinsic represents the volume of
interactions (scattering cross section x relative distance traveled) and the boundary is the separation
distance between walls
how does mean free path as a function of temperature affect thermal conductivity? - ANSWER: 1) at
low temperatures, boundary scattering is dominant (phonons hitting boundaries such as impurities,
grain boundaries); k~T^3
2) at high temperature, Umklapp scattering is dominant (phonons running into other phonons); k~T^-
1
True or False: in microstructure form, not bulk form, the grain and/or molecular orientation impacts
the thermal conductivity - ANSWER: True because diamond has a higher thermal conductivity (k_z) in
the vertical direction which is the same direction as the grain boundaries
define the Weideman Franz law - ANSWER: the relationship between electrical conductivity and
thermal conductivity and verified at all scales including atomic level
True or False: K_electron >> K_phonon in crystalline materials - ANSWER: False because phonons are
the dominant energy transport mechanism in crystalline materials, however it is true that K_electron
>> K_phonon for metallic materials
how can the bulk thermal conductivity be related to a small-scale system? - ANSWER: using the
concept of a thin nanowire where the mean free path can be approximated by the diameter of a solid
nanowire and used with the mean free path of the bulk material; use when the system size is smaller
than the bulk mean free path of the material
define an electron - ANSWER: a stable subatomic particle with a negative charge of electricity found in
all atoms and acting as the primary carrier of electricity in solids; has mass of 9.109 e^-31 kg
define a photon - ANSWER: a particle representing a quantam of light or other electromagnetic
radiation; is massless
define a phonon - ANSWER: a collective excitation in a period, elastic arrangement of atoms or
molecules in solids and some liquids such as sound or vibration of a crystal lattice; is responsible for
heat conduction in semiconductors and insulators
define a molecule - ANSWER: a group of 2 more atoms held together by attractive forces from
chemical bonds
derive the 3D heat diffusion in cartesian coordinates - ANSWER: general steps:
1) energy balance
2) define each term
3) taylor expansion of energy out terms
4) substitute expansion into energy balance
5) substitute Fourier's law in each direction into energy balance
6) simplify by writing as gradient of T
derive the 3D heat diffusion in cylindrical coordinates - ANSWER: general steps:
1) energy balance
2) define each term
3) taylor expansion of energy out terms
