chap6_introductiontoconvection传热传质

CHAPTER 6 Introduction to Convection Convection: Energy transfer between a surface and a fluid moving over the surface.Two major objectives:(1) To understand the physical mechanisms of the convection(2) To develop the means to perform convection heat transfer calculationsPhysical mechanism: diffusion, bulk motion (dominant) A unique feature of this chapter is the manner in which convection mass transfer are introduced by analogy to those of convection heat transfer. In mass transfer by convection, gross fluid motion combines with diffusion to promote the transport of a species for which there exists a concentration gradient. 5.1 The convection transfer problemHeat transferConsider the flow condition of Fig 6.1a. The surface is presumed to be at a uniform temperature,Ts,TsT. The local heat flux (6.1)where h is the local convection coefficient.l Because flow conditions vary from point to point on the surface,both and vary along the surface. The total heat transfer rate may be obtained by integrating the local flux over the entire surface.l From Equation 6.1l Defining an average convection coefficient for the entire surface, the total heat transfer rate may be expressed asFor the special case of flow over a flat plate(Fig 6.1b), h varies with the distance x from the leading edgeMass analogyl Similar results may be obtained for convection mass transfer. If a fluid of species molar concentration CA flows over a surface at which the molar concentration is maintained at some uniform value (Kmol/m3) (Fig 6.2a). The molar flux of species A , may be expressed as(6.7)where is the convection mass transfer coefficient. The total molar transfer rate for an entire surface l (6.8) l The average and local mass transfer convection coefficients are related by an equation of the forml For the special case of flow over a flat plate(Fig 6.2b)l Species transfer may be expressed as mass flux, or as a mass transfer rate, , simply by multiplying both sides of Equ. 6.7 and 6.8, respectively,by the molecular weight of species A.Sowhere is the mass density of species A.To perform a convection mass transfer calculation,it is necessary to determine the value of CA,s or A,s. Such a determination may be made by assuming thermodynamic equilibrium at the interface between the gas and the liquid or solid phase. To a good approximation,the molar concentration of the vapor at the surface may be determined from the vapor pressure through application of the equation of state for an ideal gas. 6.2 The convection boundary layers6.2.1 The velocity boundary layer Consider flow over the flat plate of Figure 6.3. The boundary layer thickness is defined as the value of y for which u=0.99 u.Figure 6.3 Velocity boundary layer development on a flat plate.The fluid flow is characterized by two distinct regions:A thin fluid layer (the boundary layer) in which velocity gradients and shear stresses are largeA region outside the boundary layer in which velocity gradients and shear stresses are negligible (the free stream). With increasing distance from the leading edge, the effects of viscosity penetrate further into the free stream and the boundary layer grows.l For external flows it provides the basis for determining the local friction coefficientl For Newtonian fluid the surface shear stress s may be evaluated from knowledge of the velocity gradient at the surface(6.15)where is a fluid property known as the dynamic viscosity.6.2.2 The thermal boundary layerl A thermal boundary layer must develop if the fluid free stream and surface temperature differ. Consider flow over an isothermal flat plate (Figure 6.4).l The temperature profile.Figure 6.4 Thermal boundary layer development on an isothermal flat plate.The region of the fluid in which temperature gradients exist is the thermal boundary layer,and its thickness t is typically defined as the value of y for which the ratio (Ts-T)/(Ts-T)=0.99. The relation between conditions in this boundary and the convection heat transfer coefficient At any distance x from the leading edge,the local heat flux may be obtained by applying the Fouriers law to the fluid at y=0. That is(6.16)This expression is appropriate because, at the surface, there is no fluid motion and energy transfer occurs only by conduction.l By combining Equation 6.16 with the Equation 6.1, we obtain(6.17)Hence conditions in the thermal boundary, which strongly influence the wall temperature gradient T/y|y=0, determine the rate of heat transfer across the boundary layer. Accordingly, the magnitude of T/y|y=0 decreases with increasing x, and it follows that qs and h decrease with increasing x.6.2.3 The concentration boundary layerl Just as the velocity and thermal boundary layers determine wall friction and convection heat transfer, the concentration boundary layer determines convection mass transfer. Figure 6.5 Species concentration boundary layer development on an isothermal flat plate.The region of fluid in which concentration gradients exist is the concentration boundary layer. Its thickness c is typically defined as the value of y for which (CA,s-CA)/(CA,s CA,)=0.99. The molar flux associated with species transfer by diffusion is determined by an expression that is analogous to Fouriers law, which is termed Ficks law, has the formwhere DAB is a property of the binary mixture known as the binary diffusion coefficient. For the condition of Fig 6.5, the species transfer is due to both bulk motion and diffusion (y0) , the species transfer is only due to diffusion (y=0). Applying Ficks law at y=0, the species flux at any distance from the leading edge is thencombining Equation 6.19 and 6.7,it follows that(6.20) l The foregoing results may also be expressed on a mass, rather than a molar,basis. Multiplying both side of Equation 6.18 by the species molecular weight,MA,the species mass flux due to diffusion is6.2.4 Significance of the boundary layersMomentumTransfer (shear stresses)Velocity boundary layerVelocity gradientShear stressesFriction coefficientHeat transferThermal boundary layerTemperature gradientHeat fluxHeat transfer convection coefficientMass transferConcentration boundary layerConcentration gradient Species fluxMass transfer convection coefficient6.3 Laminar(层流 ) and turbulent flow (湍流 ) An essential first step in the treatment of any convection problem is to determine whether the boundary layer is laminar or turbulent. As shown in Fig.6.6,there are sharp differences between laminar and turbulent flow conditions.Laminar:In the laminar boundary layer,fluid motion is highly ordered and it is possible to identify streamlines along which particles move. The velocity component v contribute significantly to the transfer of momentum, energy,or species through the boundary layer. Turbulent:Fluid motion in the turbulent boundary layer is highly irregular and is characterized by velocity fluctuation.These fluctuations enhance the transfer of momentum, energy, and species, and hence increase surface friction as well as convection transfer rates. Fluid mixing resulting from fluctuations makes turbulent boundary layer thickness is larger and boundary layer profiles flatter than in laminar flow.Velocity boundary development: laminar, transition, turbulent (Fig6.6). The boundary layer is initially laminar, but at some distance from leading edge, small disturbances are amplified and transition to turbulent flow begins to occur. In the turbulent boundary layer, three different region may be delineated. laminar sublayer: transport is dominated by diffusion and the velocity profile is linearbuffer layer: diffusion and turbulent mixing are comparableturbulent zone: transport is dominated by turbulent mixingFigure 6.7 Variation of velocity boundary layer thickness and the local heat transfer coefficient h for flow over an isothermal flat plate.It is frequently reasonable to assume that transition begins at some location xc. Reynolds numberl The critical Reynolds number is the value of Rex for which transition begins, and for flow over a flat plate, it is known to vary from approximately 105 to 3 106, depending on surface roughness and the turbulence level of the free stream.6.4 The boundary layer equationsl Steady, two-dimensional flow of a viscous, incomp