1
Thermal and Fluids
in Architectural Engineering 3. Thermal resistances
Jun-Seok Park, Dr. Eng., Professor.
Dept. of Architectural Engineering Hanyang Univ.
Where do we learn in this chaper
Page 3/17 1. Introduction
2.The first law
3.Thermal resistances
4. Fundamentals of fluid mechanics
5. Thermodynamics 6. Application
7.Second law 8. Refrigeration,
heat pump, and power cycle
9. Internal flow 10. External flow
11. Conduction 12. Convection 14. Radiation
13. Heat Exchangers 15. Ideal Gas Mixtures
and Combustion
3.1 The First law as a Rate equation 3.2 Conduction
3.3 Radiation 3.4 Convection
3.5 Resistance Analogy for Cond. And Conv.
3-7 Resistance Analogy for Radiation 3-8 Combined Thermal Resistances
3. Thermal Resistance
3.1 The First Law as a Rate Equation
□ In previous chapter, the first law of thermodynamics was applied to the states of the beginning and the end in processes
□ To apply the first law at an instance of time, the equation can be changed as below
E Q W
W - Q )
(ΔKE ΔPE ΔU
,
dt W W
dt Q Q
W dt Q
d U dt
d PE dt
d KE
3.2 Conduction
□ From Fourier (1822)
- Heat flow rate of conduction relates with length, L, and the difference of temperature in solids
- Thermal conductivity, k, is characteristic of a substance - In a substance, temperature varies linearly between
two ends’ values
L A ΔT k
L Q A ΔT
Q
L T T
x x
T T
dx dT dx
A dT k
Q 2 1
1 2
1
2
E Q W
3.3 Radiation
□ Radiation can occur in solids, liquids, or gases
- In solids and liquids, photons are emitted and absorbed throughout the volume
- But, radiation can be considered to be a surface phenomenon, because of absorption in volume
- From Stefan-Boltzmann, radiation from the body to surrounding is given by
surface Black
in ) (Ts4 Tsur4 A
Q
E Q W
3.3 Radiation
- In real surface (gray, diffuse surfaces), the equation can be written as below
- Gray surface is that the fraction of the radiation reflected by the surface is independent of wavelength
- Diffuse surface is that the fraction of radiation reflected by the surface dose not depend on the angle of radiation
surface diffuse
gray, in
) (Ts4 Tsur4 A
Q
E Q W
3.4 Convection
□ Convection heat transfer occurs whenever a gas or liquid at the surface a solids or liquids
(Forced / Natural)
- Heat transfer by convection is expressed as
law) cooling
s (Newtion'
T A
h
Q
E Q W
3.4 Convection
□ Heat transfer coefficient, h, depends on
- geometry
- velocity of flow
- type of fluid (gas / liquid)
□ So, h, is not a fundamental physical property of a substance
( ↔ thermal conductivity, k, emissivity, ε)
E Q W
3.5 The Resistance Analogy for Cond. and Conv.
□ Heat flow can be expressed using Ohm’s law, as below
- Resistance analogy is especially useful in describing heat flow with multiple parts
A R h
R Q T
A k R L
R Q T
flow
conv conv
conv
cond cond
cond
1
flow to
resistance
potential driving
E Q W
3.5 The Resistance Analogy for Cond. and Conv.
□ Example of Figure 3-3, Heat flow can be expressed using total resistance
- U value of Walls of a building
4 3
2 1
0
Rtot
R R
R R
R Rtot Q T
E Q W
3.7 Resistance Analogy for Radiation
□ As same in the previous, heat flow by radiation can express as written,
- If a body exchange heat by both convection and radiation
W -
Q ΔU
) (
) (
1
2 2
4 4
sur s
sur s
rad
sur s
rad rad
rad
T T
T T
σ A R ε
T T
σ A Q ε
R Q T
s sur
conv rad
conv sur s
rad sur s
conv
rad T T
R R
R T T R
T Q T
Q
Q
1 1
3.8 Combined Thermal Resistance
□ The resistance analogy can be extended to rather complex system using Ohm’s law
