Advanced Heat Transfer

Lecturer: Dr. Du

Chinese People’s Armed Police Force Academy

教学目的

1. 掌握传热学的基本概念、基本理论和基本计算方法

2. 了解传热学在火灾科学和消防工程中的应用

3. 接触数值模拟研究方法

4. 提高科技英语阅读和写作能力

教学计划

教学内容

1. 热传导

2. 热对流

3. 热辐射

4. 传热数值模拟初步

教学方法

1. 课堂讲授与讨论（ 30 学时）

2. 数值模拟实践（ 10 学时）

传热学在火灾科学和消防工程中的应用

主要内容：

一、传热学概述

二、传热学在火灾科学和消防工程中的应用

三、火灾科学对传热学的期待

● 热量传递的三种模式：

D

可燃混气

火焰

预混火焰在管道内的传播

Su

热传导（导热）热对流热辐射

● 研究热量传递规律的科学

一、传热学概述

1. 谢苗诺夫热自燃理论

/eCVKHQ RTEk

AnCc )( oTThSL

.

二、传热学在火灾科学和消防工程中的应用

假设物体内部温度均匀分布，表面存在对流换热

tT

KQ

zT

yT

xT

1'''

2

2

2

2

2

2

88.0cr

2cr32.3cr52.2cr立方体：

球体：无限长圆柱体：无线大平板：

2. 弗兰克—卡门涅茨基热自燃理论

边界条件： T=T0

)/exp(2

2

aA

a

n

iAAo RTEkRT

CCHEr

假设边界温度为环境温度，内部存在热传导

3. 托马斯热自燃理论

tT

KQ

zT

yT

xT

1'''

2

2

2

2

2

2

边界条件： )/()( dxdTkTTh as

假设内部热传导，边界对流换热

4. 建筑钢构件保护层厚度的计算

在规定的耐火时间内，建筑钢构件的温度不得超过其设计的临界温度。根据火灾的温度上升曲线、临界温度和耐火时间，通过传热计算，可以得到保护层厚度。

5. 建筑物之间的火焰传播

一座大楼着火，相邻的另一座大楼外表面接受的辐射热通量不得超过 1.2×104W/m2 。建筑物之间的允许间距就是以此为依据来计算的。

6. 感温报警系统的性能化设计与分析

radconvcondtotal qqqq

)( agconv TThAqq

mc

TThA

dt

dT agd)(

总传热速率：

对流传热速率：

探测元件温度变化速率：

目标：

（ 1 ）性能化设计：对要求的火灾规模或探测时间，确定探测器的间距。

（ 2 ）性能化分析：对给定的探测器间距，确定探测时间和对应的火灾规模。

三、火灾科学对传热学的期待—— 室内火灾发展过程中的传热学问题

问题 1 ：材料热分解问题 2 ：多孔介质传热问题 3 ：烟的产生

问题 5 ：烟气热辐射问题 4 ：烟的流动

受到多孔介质的结构，质量传递等因素的影响，而多孔介质的结构参数往往是未知的。

1. 多孔介质传热问题

2. 热烟气辐射传热问题 受到辐射气体

和颗粒的浓度、温度和厚度等参数的影响。除开辐射理论本身的缺陷外，在实际火灾中，这些参数又受多种因素影响，很难准确掌握。

传热学是火灾科学知识体系的重要组成部分。传热学的应用推动了火灾科学的发展，而火灾科学的发展又将不断向传热学的发展提出新的更高的要求。为了自身和学科的发展，让我们一起学习传热学的基本概念、基本理论和基本方法，以审视的眼光去发现火灾科学中的传热学问题，以期待的心情去注视传热学的最新进展，以探索的精神去尝试用传热学的知识推动火灾科学的发展。

Chapter 1 Introduction

Heat transfer is the science that seeks to predict the energy transfer that may take place between material bodies as a result of a temperature difference.

Two aspects related to heat transfer: 1. Mechanism of thermal energy transfer 2. Thermal energy transfer rate

The relationship between heat transfer and thermodynamics

WUQ

Thermodynamics: deals with systems in equilibrium.Two aspects:

1. To predict the amount of energy required to change a system from one equilibrium state to another.

First law:

2. To predict the direction of change of a system.

Second law: energy is transferred from high temperature region to lower temperature region; if the form of thermal energy does not change, the amount of thermal energy remains constant

The Difference between Heat Transfer And Thermodynamics

Thermodynamics:

tm , Q

Water ， M2

20oC

Iron Bar ， M1

300oC

Heat Transfer ：)( );,,,( fQzyxft

1-1 Conduction Heat Transfer

Definition: Thermal energy transfers between material bodies by the movement of molecules, atoms and free electrons

Conduction heat transfer can take place in solids, liquids and gases

Characteristics of heat conduction

1. Temperature difference.

2. In one material or between contacting materials.

3. By the movement of molecules, atoms and free electrons.

4. Under earth gravity, the pure heat conduction takes place only in solids.

:k C)(mW

W L

TAΦ

2m

W

L

Tk

A

Φq

： Heat flux through area A,[W]

2mW

:L

21 TTT temperature difference between two walls C

2mA： the area perpendicular to the heat flow.

q： heat transfer rate per unit area,

Thickness of the plane [m]；

Basic law of heat conduction

--Fourier’s Law

Thermal conductivity

xT

kq Degree Celsius

Governing equationsOne-dimensional heat conduction equation:

Energy conducted in left face+heat generated within element=change in internal energy+energy conducted out right face

x

TkAqx

qAdx

dxt

TcA

])([] dxx

Tk

xx

TkA

x

TkAq dxxdxx

Combining the above relations gives:

T

cqx

Tk

x)(

])([ dxx

Tk

xx

TkAdx

t

TcAqAdx

x

TkA

or

Energy in left face

Energy generated within element

Change in internal energy

Energy conducted out right face

T

cqx

Tk

x)(

For constant thermal conductivity, the above equation is written

T

k

q

x

T 12

2

c

k

is called thermal diffusivity. The larger the value of , the faster heat will diffuse through the material.

Cartesian coordinates: （正交坐标系）

t

T

k

q

z

T

y

T

x

T

1

2

2

2

2

2

2

Cylindrical coordinates: （柱坐标系）

t

T

k

qT

rr

T

rr

T

111

2

2

22

2

t

T

k

qT

r

T

rrT

rr

1

sin

1)(sin

sin

1)(

12

2

2222

2

Spherical coordinates: （球坐标系）

3-dimensional heat conduction equations

02

2

dx

Td

01

2

2

dr

dT

rdr

Td

02

2

k

q

dx

Td

02

2

2

2

dy

Td

dx

Td

Reduced forms of heat conduction equations ：Steady-state one-dimensional heat flow without heat sources

Steady-state one-dimensional heat flow in cylindrical coordinates without heat sources

Steady-state one-dimensional heat flow with heat sources

Two-dimensional steady-state heat conduction without heat sources

Thermal Conductivity

Thermal conductivity equals to the heat conduction rate

through unit area per unit time when the local temperature

gradient is unity.

It is one of material properties, indicates how fast heat will

flow in a given material, and can be determined

experimentally or theoretically.

TA

Φk

xT

kq

Conduction may be viewed as the transfer of energy from the more energetic to the less energetic particles of a substance due to interactions between the particles

The mechanism in gases: The temperature at any point can be associated with the energy of gas molecules in proximity of the point. The energy is related to the random transitional motion, as well as the rotational and vibrational motions, of the molecules.

Physical mechanism of heat-conduction

The dependence of thermal conductivities of gases on temperature

For most gases at moderate pressures the thermal conductivity is a function of temperature alone.

The faster the molecules move, the faster they will transport energy. Therefore the thermal conductivity of a gas should be dependent on temperature.The thermal conductivity of a gas varies with the square root of the absolute temperature.

The mechanism of heat conduction in liquids is similar to that in gases, but the molecules are more closely spaced and the interactions between molecules are more stronger and more frequently.

Two modes of heat conduction in solids:

Lattice vibration (晶格振动 ) : energy transfer may be attributed to atomic activities in the form of lattice vibrations.

Free electrons transport （自由电子传输） : large number of free electrons are moving about in the lattice structure, and carry thermal energy from a higher temperature region to a lower temperature region.

In a nonconductor, the energy transfer is exclusively via lattice vibration;

In a conductor, thermal energy can be transferred by both modes, but the transport by free electrons is much larger than that by lattice vibration transport.

Conclusion: good electrical conductors are almost always good heat conductors

gasliquidsolidmetalnonmetal kkkk

;)(398 CmWk copperpure

;)(6.0 CmWk water

）（ CCmWk air 20 )(026.0

The relative orders of magnitude of thermal conductivity for solids, liquids and gases.

1-2 Convection Heat Transfer Convection: when bulk movement of fluid occurs in

liquid, heat will be transferred from one part of the fluid to another.

Convection heat transfer: heat transfer between fluid and solid surface.

1-2 Convection Heat Transfer

Two mechanisms of convection heat transfer:

(1) energy transfer due to random molecular motion

(2) energy transfer by bulk, or macroscopic motion of

the fluid. Convection is accompanied by conduction in the fluid.

Characteristics of convection heat transfer

Note that Convection heat transfer is not a basic mode of heat transfer. it consists of convection and conduction

(1) It is a complex process of heat transfer

(2) The fluid must contact with the surface, and there exists relative motion and temperature difference between the fluid and the surface

(3) Due to the viscous action, the velocity will be reduced to zero at plate surface. At this point, the heat is transferred from the surface to the fluid by conduction.

Newton’s law

W )( TThAΦ w

2mW )(

fw TTh

AΦq

— heat flux [W]

q 2mW— heat flow density,

A 2m— contacting area between fluid and surface,

fw TT , C— temperatures of solid surface and the fluid,

—Convection heat transfer coefficienth

Heat transfer rate per unit surface when the temperature difference is 1 ºC

))(( TTAΦh w C)(mW 2

Affecting factors: flow velocity, fluid properties, geometry of the surface.

Convection heat transfer coefficient

Classification of convection heat transfer

Forced convection heat transfer: the flow of fluid is caused by external force.

Natural convection heat transfer: the movement of the fluid is caused as a result of density gradients near the plate.

1-3 Thermal Radiation

Thermal radiation is the energy emitted by matter which is at a finite temperature.

The higher the temperature of the matter, the more energy can be emitted. The ability of thermal radiation is dependent on the type of the material and the surface condition.

Radiation heat transfer is heat transfer between two bodies due to thermal radiation.

CHARACTERISTICS OF THERMAL RADIATION

Two materials need not contact with each other for radiation heat transfer. The energy can be transferred in vacuum.

Black body: it is an ideal material, which can absorb all radiation falling on its surface

The energy form is changed in the process of radiation heat transfer.

thermal energy

No matter what temperature is, the material is constantly emitting electro-magnetic radiation.

electro-magnetic radiation thermal energy

Stefan-Boltzmann law

Real body emissive power is less than that of black body at same surface temperature.

24 mW TE bb

— emissive power of black body, bE

T b )K(mW105.67 42-8

2mW

K

24 mW TE b— emissivity of grey body ， 0~1； Emissivity is dependent on the type of material, surface condition and the surface temperature.

— absolute temperature of surface ，— Stefan-Boltzmann constant ，

Radiant energy flux emitted by a blackbody surface is 4ATqemitted

Net radiant exchange between two surface is

)( 42

41 TT

A

q enetexchang

)( 42

41 TTAFFq G

F

GF

is an emissivity function

is a geometric “view factor”function( 几何视角因子函数 )

讨论 :

1. 举例说明传热学在消防中的应用2. 传热学要解决的主要问题是什么？3. 传热学与热力学的主要区别是什么？4. 导热、导热机理、导热基本定律5. 导热控制方程的推导6. 导热系数与导温系数（热扩散系数）的物理意义7. 气体的导热机理、导热系数与温度的关系8. 固体的饿导热机理、导体与非导体的导热机理的区别9. 热对流与对流换热、对流换热机理10.粘性对对流换热的饿影响11.对流换热的影响因素12.热辐射与辐射传热