Forsberg Heat Transfer
Chapter 10
Multimode Heat Transfer
Procedure for Multimode Problems
At the beginning, decide
• What modes of heat transfer (conduction, convection, radiation)
are significant
• If convection is significant, is it natural or forced convection
• Is the problem steady-state or transient
• Does the problem statement contain all necessary information
If not, where will the missing info be obtained
• Should the problem be solved analytically or should it be
solved numerically
• Does the problem involve differential equations
• Does the problem involve simultaneous equations
• What software, if any, is needed for the solution
1
, Example 10.1 Cylindrical Heater
A horizontal electric cylindrical heater has an output of 50 W.
The heaterhas a diameter of 4 cm and a length of 30 cm.
The ends of the cylinder are insulated so all of the heat
output leaves through the cylindrical side of the heater.
The heater is in a large room whose walls are at 30 C,
and the room air is at 20 C. The surface of the heater has
an emissivity of 0.5.
(a) What is the temperature of the surface of the heater?
(b) What are the respective heat flows by convection and
radiation from the surface of the heater?
2
, Example 10.1
• Convection and radiation at surface of cylinder
• Convection is natural convection
• Steady-state
• All necessary info is given
• Heater output equals the convection plus radiation
from the surface
• Radiation involved. Temperatures must be
in absolute units.
• Software is needed since air properties are
temperature dependent and we have a
non-linear algebraic equation to solve.
Example 10.2 Liquid Nitrogen Container
A spherical liquid nitrogen container has a diameter of
1.5 m. The container is thin-walled and is surrounded by
another thin-walled hollow sphere of diameter 1.6 m.
The spheres are of stainless steel and have an emissivity of 0.2.
The space between the spheres is evacuated. The container
is in a room where the room air and the room enclosure
are at 22 C. The temperature of the liquid nitrogen is 77 K
and the heat of vaporization of nitrogen is 200 kJ / kg.
(a) What is the rate of heat transfer to the liquid nitrogen?
3
Chapter 10
Multimode Heat Transfer
Procedure for Multimode Problems
At the beginning, decide
• What modes of heat transfer (conduction, convection, radiation)
are significant
• If convection is significant, is it natural or forced convection
• Is the problem steady-state or transient
• Does the problem statement contain all necessary information
If not, where will the missing info be obtained
• Should the problem be solved analytically or should it be
solved numerically
• Does the problem involve differential equations
• Does the problem involve simultaneous equations
• What software, if any, is needed for the solution
1
, Example 10.1 Cylindrical Heater
A horizontal electric cylindrical heater has an output of 50 W.
The heaterhas a diameter of 4 cm and a length of 30 cm.
The ends of the cylinder are insulated so all of the heat
output leaves through the cylindrical side of the heater.
The heater is in a large room whose walls are at 30 C,
and the room air is at 20 C. The surface of the heater has
an emissivity of 0.5.
(a) What is the temperature of the surface of the heater?
(b) What are the respective heat flows by convection and
radiation from the surface of the heater?
2
, Example 10.1
• Convection and radiation at surface of cylinder
• Convection is natural convection
• Steady-state
• All necessary info is given
• Heater output equals the convection plus radiation
from the surface
• Radiation involved. Temperatures must be
in absolute units.
• Software is needed since air properties are
temperature dependent and we have a
non-linear algebraic equation to solve.
Example 10.2 Liquid Nitrogen Container
A spherical liquid nitrogen container has a diameter of
1.5 m. The container is thin-walled and is surrounded by
another thin-walled hollow sphere of diameter 1.6 m.
The spheres are of stainless steel and have an emissivity of 0.2.
The space between the spheres is evacuated. The container
is in a room where the room air and the room enclosure
are at 22 C. The temperature of the liquid nitrogen is 77 K
and the heat of vaporization of nitrogen is 200 kJ / kg.
(a) What is the rate of heat transfer to the liquid nitrogen?
3
