PPT: Heat Transfer | Heat Transfer - Mechanical Engineering PDF Download

 Page 1


1
Heat Transfer
Page 2


1
Heat Transfer
2
Introduction
 Typical design problems involve the determination of:
– Overall heat transfer coefficient, e.g. for a car radiator.
– Highest (or lowest) temperature in a system, e.g. in a gas turbine,
chemical reaction vessels, food ovens.
– Temperature distribution (related to thermal stress), e.g. in the walls
of a spacecraft.
– Temperature response in time dependent heating/cooling problems,
e.g. engine cooling, or how fast does a car heat up in the sun and
how is it affected by the shape of the windshield?
Page 3


1
Heat Transfer
2
Introduction
 Typical design problems involve the determination of:
– Overall heat transfer coefficient, e.g. for a car radiator.
– Highest (or lowest) temperature in a system, e.g. in a gas turbine,
chemical reaction vessels, food ovens.
– Temperature distribution (related to thermal stress), e.g. in the walls
of a spacecraft.
– Temperature response in time dependent heating/cooling problems,
e.g. engine cooling, or how fast does a car heat up in the sun and
how is it affected by the shape of the windshield?
3
Modes of heat transfer
 Conduction: diffusion of heat due to temperature gradients. A
measure of the amount of conduction for a given gradient is the
heat conductivity.
 Convection: when heat is carried away by moving fluid. The flow
can either be caused by external influences, forced convection; or
by buoyancy forces, natural convection. Convective heat transfer
is tightly coupled to the fluid flow solution.
 Radiation: transfer of energy by electromagnetic waves between
surfaces with different temperatures, separated by a medium that
is at least partially transparent to the (infrared) radiation.
Radiation is especially important at high temperatures, e.g. during
combustion processes, but can also have a measurable effect at
room temperatures.
Page 4


1
Heat Transfer
2
Introduction
 Typical design problems involve the determination of:
– Overall heat transfer coefficient, e.g. for a car radiator.
– Highest (or lowest) temperature in a system, e.g. in a gas turbine,
chemical reaction vessels, food ovens.
– Temperature distribution (related to thermal stress), e.g. in the walls
of a spacecraft.
– Temperature response in time dependent heating/cooling problems,
e.g. engine cooling, or how fast does a car heat up in the sun and
how is it affected by the shape of the windshield?
3
Modes of heat transfer
 Conduction: diffusion of heat due to temperature gradients. A
measure of the amount of conduction for a given gradient is the
heat conductivity.
 Convection: when heat is carried away by moving fluid. The flow
can either be caused by external influences, forced convection; or
by buoyancy forces, natural convection. Convective heat transfer
is tightly coupled to the fluid flow solution.
 Radiation: transfer of energy by electromagnetic waves between
surfaces with different temperatures, separated by a medium that
is at least partially transparent to the (infrared) radiation.
Radiation is especially important at high temperatures, e.g. during
combustion processes, but can also have a measurable effect at
room temperatures.
4
Overview dimensionless numbers
 Nusselt number: Ratio between total heat transfer in
a convection dominated system and the estimated conductive
heat transfer.
 Grashof number: Ratio between buoyancy
forces and viscous forces.
 Prandtl number: Ratio between momentum
diffusivity and thermal diffusivity. Typical values are Pr = 0.01 for
liquid metals; Pr = 0.7 for most gases; Pr = 6 for water at room
temperature.
 Rayleigh number:
The Rayleigh number governs natural convection phenomena.
 Reynolds number: Ratio between inertial and
viscous forces.
. /
f
k hL Nu =
. /
2 3
w
g L Gr r n r D =
a m b r m b r / /
3 2 3
T g L k T c g L Pr Gr Ra
p
D = D = =
. / k c Pr
p
m =
. / m rUL Re =
Page 5


1
Heat Transfer
2
Introduction
 Typical design problems involve the determination of:
– Overall heat transfer coefficient, e.g. for a car radiator.
– Highest (or lowest) temperature in a system, e.g. in a gas turbine,
chemical reaction vessels, food ovens.
– Temperature distribution (related to thermal stress), e.g. in the walls
of a spacecraft.
– Temperature response in time dependent heating/cooling problems,
e.g. engine cooling, or how fast does a car heat up in the sun and
how is it affected by the shape of the windshield?
3
Modes of heat transfer
 Conduction: diffusion of heat due to temperature gradients. A
measure of the amount of conduction for a given gradient is the
heat conductivity.
 Convection: when heat is carried away by moving fluid. The flow
can either be caused by external influences, forced convection; or
by buoyancy forces, natural convection. Convective heat transfer
is tightly coupled to the fluid flow solution.
 Radiation: transfer of energy by electromagnetic waves between
surfaces with different temperatures, separated by a medium that
is at least partially transparent to the (infrared) radiation.
Radiation is especially important at high temperatures, e.g. during
combustion processes, but can also have a measurable effect at
room temperatures.
4
Overview dimensionless numbers
 Nusselt number: Ratio between total heat transfer in
a convection dominated system and the estimated conductive
heat transfer.
 Grashof number: Ratio between buoyancy
forces and viscous forces.
 Prandtl number: Ratio between momentum
diffusivity and thermal diffusivity. Typical values are Pr = 0.01 for
liquid metals; Pr = 0.7 for most gases; Pr = 6 for water at room
temperature.
 Rayleigh number:
The Rayleigh number governs natural convection phenomena.
 Reynolds number: Ratio between inertial and
viscous forces.
. /
f
k hL Nu =
. /
2 3
w
g L Gr r n r D =
a m b r m b r / /
3 2 3
T g L k T c g L Pr Gr Ra
p
D = D = =
. / k c Pr
p
m =
. / m rUL Re =
5
Enthalpy equation
 In CFD it is common to solve the enthalpy equation, subject to a
wide range of thermal boundary conditions.
– Energy sources due to chemical reaction are included for reacting
flows.
– Energy sources due to species diffusion are included for multiple
species flows.
– The energy source due to viscous heating describes thermal energy
created by viscous shear in the flow.This is important when the shear
stress in the fluid is large (e.g. lubrication) and/or in high-velocity,
compressible flows. Often, however, it is negligible.
– In solid regions, a simple conduction equation is usually solved,
although convective terms can also be included for moving solids.