and
q
""
≡
"" A s
q
or q = q
A s
3
Heat Conduction Equations
where T s is the surface temperature ( ◦ C or K), T ∞ the fluid temperature ( ◦ C
or K), h the heat transfer coefficient (W/m 2 K), k f the thermal conductivity of
fluid (W/m K), A s the surface area for convection, exposure to flow (m 2 ).
It is noted that the heat transfer coefficient depends on fluid properties
(such as air or water as coolant), flow conditions (i.e., laminar or turbulent
flows), surface configurations (such as flat surface or circular tube), and so
on. The heat transfer coefficient can be determined experimentally or analytically. This textbook focuses more on analytical solutions. From Equation 1.3,
the heat transfer coefficient can be determined by knowing the temperature
profile in the cooling fluid during convection and then taking the cooling
fluid temperature gradient near the wall. However, this requires solving 2-D
boundary-layer equations and will be the subject of the following chapters.
Before solving 2-D boundary-layer equations, one needs heat transfer coefficient as the convection boundary condition (BC) in order to solve the heat
conduction problem. Therefore, Table 1.1 provides some typical values of
heat transfer coefficient in many convection problems. As can be seen, in
general, forced convection has more heat transfer than natural convection;
water as a coolant removes much more heat than air; and boiling or condensation, involving phase change, has a much higher heat transfer coefficient
than single-phase convection.
1.1.3 Radiation
Radiation is caused by electromagnetic waves from solids, liquid surfaces, or
gases. For example, Figure 1.3 shows that heat is radiated from a solid surface
TABLE 1.1
Typical Values of Heat Transfer Coefficient
Type of convection
h, W /m 2 · K
Natural convection
Caused by ΔT : air
5
Caused by ΔT : water
25
Forced convection
Caused by fan, blower: air
25–250
Caused by pump: water
50–20,000
Boiling or condensation
Caused by phase change
Water � Steam
10,000–100,000
Freon � Vapor
2500–50,000
q
""
≡
"" A s
q
or q = q
A s
3
Heat Conduction Equations
where T s is the surface temperature ( ◦ C or K), T ∞ the fluid temperature ( ◦ C
or K), h the heat transfer coefficient (W/m 2 K), k f the thermal conductivity of
fluid (W/m K), A s the surface area for convection, exposure to flow (m 2 ).
It is noted that the heat transfer coefficient depends on fluid properties
(such as air or water as coolant), flow conditions (i.e., laminar or turbulent
flows), surface configurations (such as flat surface or circular tube), and so
on. The heat transfer coefficient can be determined experimentally or analytically. This textbook focuses more on analytical solutions. From Equation 1.3,
the heat transfer coefficient can be determined by knowing the temperature
profile in the cooling fluid during convection and then taking the cooling
fluid temperature gradient near the wall. However, this requires solving 2-D
boundary-layer equations and will be the subject of the following chapters.
Before solving 2-D boundary-layer equations, one needs heat transfer coefficient as the convection boundary condition (BC) in order to solve the heat
conduction problem. Therefore, Table 1.1 provides some typical values of
heat transfer coefficient in many convection problems. As can be seen, in
general, forced convection has more heat transfer than natural convection;
water as a coolant removes much more heat than air; and boiling or condensation, involving phase change, has a much higher heat transfer coefficient
than single-phase convection.
1.1.3 Radiation
Radiation is caused by electromagnetic waves from solids, liquid surfaces, or
gases. For example, Figure 1.3 shows that heat is radiated from a solid surface
TABLE 1.1
Typical Values of Heat Transfer Coefficient
Type of convection
h, W /m 2 · K
Natural convection
Caused by ΔT : air
5
Caused by ΔT : water
25
Forced convection
Caused by fan, blower: air
25–250
Caused by pump: water
50–20,000
Boiling or condensation
Caused by phase change
Water � Steam
10,000–100,000
Freon � Vapor
2500–50,000