Li Xuemei Invitation to Heat Transfer Li xuemei

Li Xuemei CH2 Steady State Conduction -- review  What is required in all modes of heat transfer?  What’s the basic equation of condunction heat transfer?  What does the numerical value of the thermal conductivity indicate?  critical insulation thickness  Define fin efficiency.  What is meant by thermal contact resistance?

Li Xuemei CH2 Steady State Conduction  what is required in all modes of heat transfer? temperature difference  What’s the basic equation of condunction heat transfer? Fouriers’law of heat conduction  What does the numerical value of the thermal conductivity indicate?thermal conductivity It indicates how fast heat will flow in a given material.  Define fin efficiency.

Li Xuemei  What is meant by thermal contact resistance?

Li Xuemei Fouriers’law of heat conduction t 0  x dx dt Q q : the heat transfer rate ( 热流率 ), W dt/dx: temperature gradient in the direction of heat flow( 热流方向上的温度梯度） λ: the thermal conductivity of the material( 导热系数 ), W/(m ·K) -: to satisfy the second principle of thermodynamics. （热流密度 与温度梯度方向相反，从高温流向低温）

Li Xuemei thermal conductivity ★ strongly temperature dependent. ★ unit: W/(m· ℃ ) ★ Indicates how fast heat will flow in a given material. ★ For most gases at moderate pressures, λis a function of temperature alone. ★ Good electrical conductors are almost always good heat conductors. ★ Superinsulation: multiple layers of highly reflective materials separated by insulating spacers. ( 超绝热体：被绝热体隔开的多层强反射材料）

Li Xuemei 4.4 reduced form of the general heat-conduction equation (2) steady-state one-dimension heat flow in cylindrical coordinates (no heat generation) (3) steady-state one-dimension heat flow with heat sources (1) steady-state one-dimension heat flow (no heat generation)

Li Xuemei 4.5 boundary condition (1) (2) (3)

Li Xuemei o  t1t1 t t2t2 reduced form of heat-conduction equation boundary condition 5.the plane wall boundary condition

Li Xuemei Fourier’law linear distribution

Li Xuemei thermal conductivity varies with temperature then,

Li Xuemei t1t1 t2t2 t3t3 t4t4 t1t1 t2t2 t3t3 t4t4 multilayer wall

Li Xuemei the thermal resistance r and the R value thermal resistance: (K/W) (m 2 · K/W) the R value

Li Xuemei 6.cylinder

Li Xuemei temperature distribution:

Li Xuemei multiple-layer cylindrical walls

Li Xuemei convection boundary conditions convection resistance:

Li Xuemei h1h1 h2h2 7.the overall heat-transfer coefficient

Li Xuemei 8.critical thickness of insulation or

Li Xuemei 9.heat-source systems Engineering application: nuclear reactors, electrical conductors, chemically reacting systems, etc. plane wall with heat sources ◇ practical situation: passing a current through an electrically conducting materials. ◇ q v : the heat generated per unit volume ◇ the differential equation: ◇ boundary conditions: t=t w at x= ±L

Li Xuemei general solution: with boundary conditions, we get: C 1 =0; t 0 = C 2 t 0 : temperature at the midplane (x=0) temperature distribution: differentiating the above equation, we obtain: parabolic distribution

Li Xuemei at stead-state conditions: the total heat generated=the heat lost at two surfaces then temperature at the midplane (x=0)

Li Xuemei 10.conduction-convection systems make an energy balance on an element of the fin of thickness dx energy in left face =energy out right face + energy lost by convection energy in left face = energy out left face = energy lost by convection= the energy balance yields:

Li Xuemei (1)The fin is very long, and the temperature at the end of the fin is essentially that of the surrounding fluid. (2) The fin is of finite length and loses heat by convection from its end. (3) The end of the fin is insulated so that dt/dx =0 at x = H

Li Xuemei 双曲余弦函数双曲正切函数 双曲正弦函数 boundary conditions:

Li Xuemei x ＝ H：x ＝ H：

11.Fins 11.1 Different types of finned surfaces

Li Xuemei

11.2 the fin effectiveness 

Li Xuemei 11.3 Conditions when fins do not help The installation of fins on a heat-transfer surface will not necessarily increase the heat-transfer rate. the conduction resistance > the convection resistance the fin may produce a reduction in heat transfer the value of h is large

Li Xuemei Conditions when fins do not help If the value of h is large, as it is with high- velocity fluids or boiling liquids, the fin may produce a reduction in heat transfer because the conduction resistance then presents a large impediment to the heat flow than the convection resistance.

Li Xuemei 12. Thermal Contact Resistance The temperature drop at the contact plane is said to be the result of a thermal contact resistance. insulated

Li Xuemei The physical mechanism of thermal contact resistance No real surface is perfectly smooth, and the actual surface roughness play a central role in determining the contact resistance. The solid-to-solid conduction at the spots of contact The conduction through entrapped gases in the void spaces created by the contact