化工传递过程基础

1、Transport PhenomenaDepartment of Chemical EngineeringTianjin University Jingtao Wang, Ph.D Content in the Previous Class Preface: Introduction of Transport Phenomena1: Transport phenomena in life, art, research and industry2:Transport phenomena in macroscopic , microscopic and molecular level Transp

2、ort PhenomenaThe content of transport phenomena:(1) Including three closely related topics:Fluid dynamics involving the transport of momentumHeat transfer dealing with the transport of energyMass transfer concerning with the transport of mass of various chemical species(2) Reasons that the three tra

3、nsports must be studied together:They occur simultaneously.Basic equations are closely related.Mathematical tools are very similar. Outline The materials covered in todays class: Chapter 0: Introduction of Three Basic Laws of Transport PhenomenaSection 0.1: Newtons law of Viscosity (momentum transpo

4、rt)Section 0.2: Fouriers law of heat conduction (energy transport)Section 0.3: Ficks law of binary diffusion (mass transport)Section 0.4: The similarity of these three laws Transport PhenomenaSection 0.1:Newtons law of Viscosity (Momentum transport) Transport PhenomenaNewtons law of Viscosity (Momen

5、tum transport): Yt0Fluid initiallyat restLower plateset in motionVelocity buildupin unsteady flow Final velocitydistribution insteady flowt=0Vyxsmall tlarge tVVvx(y,t)vx(y)A pair of large parallel plates:area = A; distance = YThe space is filled with fluids.Lower plate is set in motion atvelocity V

6、in positive x direction.Before the steady-state, fluids gainmomentum and the velocity is a functionof position y and time t.Finally, the system reaches at steadystate. The velocity is just a linear function of position y. Transport PhenomenaNewtons law of Viscosity (Momentum transport): To maintain

7、the motion of the lower plate, a constant force F is required. where is the viscosity, a property to characterize the resistance to flow. Replacing F/A by yx and V/Y by dvx/dy: where yx is the force in the x direction on a unit area perpendicular to the ydirection. yxyx Transport PhenomenaNewtons la

8、w of Viscosity (Momentum transport): Newtons law of viscosity: This law states that the shearing force per unit area is proportional to negative of the velocity gradient. Newtonian fluids: all gases and all liquids with molecular weight of less than about 5000Non-Newtonian fluids: complex fluids suc

9、h as polymeric liquids, suspensions and slurries. Transport PhenomenaMomentum transport:Newtons law of Viscosity (Momentum transport): yx may also be interpreted as the flux（通量） of x-momentum in the positive y direction, where the term “flux” means “flow per unit area”. Transfer direction: from high

10、 velocity to low velocity Driving force: velocity gradient Transport PhenomenaNewtons law of Viscosity (Momentum transport): Units: = (Pa)(m)(m/s)-1 = Pa s yxvxyPam/smPasm2/s Transport PhenomenaNewtons law of Viscosity (Momentum transport): Kinematic viscosity (运动粘度):Units: = Pa s/(kg/m3) = (N/m2) s

11、 /(kg/m3) = (kg m/s)/m2 /(kg/m3) =m2/syxvxyPam/smPasm2/smv = ft Transport PhenomenaNewtons law of Viscosity (Momentum transport): TemperatureT (C)0204060Viscosity (mPas)Water (liquid)1.7871.00190.65300.4665Air0.017160.018130.019080.01999Note: For gases at low density, the viscosity increases with in

12、creasing temperature. For liquids the viscosity usually decreases with increasing temperature. The viscosities of fluids vary over many orders of magnitude. For example,at 20 oC, the viscosity of air is 1.8*10-5 Pas; that of glycerol (丙三醇) is 1 Pas. Transport Phenomena Example 1. There is a fluid fl

13、owing between two plates. The lower plate is fixed, while the upper plate moves with a velocity of 0.3 m s-1. The width between the two plates is 0.3 mm, and the viscosity of the fluid is 0.710-3 Pa s. Calculate the shearing force.Solution： The flow can be assumed to be steady-state. Thus, the veloc

14、ity profile of the flow between the two plates is linear. The velocity gradient of the flow isAccording to Newtons law of Viscosity, ,the shearing force should be Transport PhenomenaSection 0.2:Fouriers law of heat conduction (energy transport) Transport PhenomenaFouriers law of heat conduction (ene

15、rgy transport): Yt0Solid initially atTemperature T0 Lower surfacesuddenly raisedto temperature T1t=0yxsmall tlarge tT(y,t)T(y)T0T1T0T1A slab of solid material :area = A; thickness = YLower surface is brought to T1 and maintains at that temperatureBefore the steady-state, the temperatureprofile chang

16、es and is a function of position y and time t.Finally, the system reaches at steadystate. The temperature is just a linear function of position y. Transport PhenomenaFouriers law of heat conduction (energy transport): To maintain the linear temperature profile, a constant rate of heat flow Q through

17、 the slab is required. where k is the thermal conductivity of the slab, a property to describe the rate at which heat is conducted. Replacing Q/A by qy and T/Y by dT/dy: where qy is the local rate of heat flow per unit area (heat flux) in the positive ydirection. Transport PhenomenaFouriers law of h

18、eat conduction (energy transport): Fouriers law of heat conduction: This law states that the heat flux by conduction is proportional to negative of the temperature gradient. Transfer direction: from high temperature to low temperature Driving force: temperature gradient Transport PhenomenaConduction

19、: It is the transfer of heat energy from atom to atom within a substance. Convection: It is the transfer of heat energy in a gas or liquid by movement of currents. Radiation: It is the transfer of heat energy that does not require a material medium. Sunlight is a form of radiation that heats up our

20、planet without the aid of fluids or solids. Fouriers law of heat conduction (energy transport): Energy transport: Transport PhenomenaFouriers law of heat conduction (energy transport): Thermal diffusivity:Here Cp is the heat capacity at constant pressure. has the same unit as (m2/s). Prandtl number:

21、 This ratio indicates the relative importance of momentum and energy transport in flow systems. Thermal diffusivity and kinematic viscosity : Transport PhenomenaFouriers law of heat conduction (energy transport): qyTykCpW/ m2KmW/mKJ/K kgm2/sPa sThe values of thermal conductivity can vary from about

22、0.01 W/mK for gases to about 1000 W/mK for pure metals. Metals conduct heat readily; wood act as thermal insulators. Transport Phenomena Example 2. There is a plastic slab with a surface area of 1 m2 and a thickness of 6 mm. The temperature difference between two surfaces of the slab is 2 K. When th

23、e system reaches steady-state, the measured heat flux is 30W. Calculating the thermal conductivity of the plastic slab.Solution：The heat flux isWith regard to the slab, when it reaches the steady-state, the temperature profile is linear. So the temperature gradient should be According to Fouriers la

24、w， , the thermal conductivityis Transport PhenomenaSection 0.3:Ficks law of binary diffusion (mass transport) Transport PhenomenaFicks law of binary diffusion (mass transport): Yt0Initially both surfacein contact with air t=0yxsmall tlarge tA(y,t)A(y)A=0A= A0A=0A= A0A thin, horizontal, fused-silica

25、plate:area = A; thickness = YAir is completely insoluble in silica.Helium is soluble in silica.Before the steady-state, the concentrationprofile changes and is a function of position y and time t.Finally, the system reaches at steadystate. The concentration is just a linear function of position y.Pu

26、re helium replacesthe air below the plate. The helium slowlypenetrates into the plate.The air above the plate is replaced rapidly. So there is no accumulation of Helium. Transport PhenomenaYt0t=0yxsmall tlarge tA(y,t)A(y)A=0A= A0A=0A= A0Definition: helium “species A”, silica “species B”.mass fractio

27、ns: A= mA/(mA+mB) B= mB/(mA+mB) A = f(y) 0 y 0; A = A0 y = 0 A = 0 y = Y; A = A0 y = 0; A = 0 y = Y; A = A0 y = 0; A = f(y,t) 0 y cBl , solute B will diffuse from the cB0 side to the cBl side. Due to the extremely large volume of the solution and the stirring, the concentrations remain constant. Thu

28、s, the diffusion can be assumed to be steady. Assuming the known diffusion coefficient is D. Calculating the mass flux and the concentration profile inside the slab. Solution：When the diffusion is in steady state, the concentration anywhere in the system will not change with time. There is no mass a

29、ccumulation occurring inside the slab. Thus, the mass flux dose not vary at different sites in the slab, and the concentration gradient is constant.The concentration gradient of is From Ficks law, the mass flux of B is Transport Phenomena In order to get the concentration distribution inside the sla

30、b, the following differential equation is established：Under the steady state, the mass flux dose not vary at different sitesBy substituting Ficks law into equation above, we getAfter integration, we haveThe boundary conditions areWe can getTherefore, the concentration distribution inside the slab is

31、 Transport PhenomenaSection 0.4:The similarity of these three laws Transport PhenomenaSimilarities of these three laws: Fick (1829-1901)Fourier (1768-1830)Newton (1642-1727)Homework: Summarizing the similarities among these three laws.Examples:(1) They are all named by the famous scientists name. :

32、)(2) The transfer directions are all from a high quantity to a low quantity.(3) The fluxes are always proportional to the gradient of the quantities. Transport PhenomenaThe importance of the skills to find the similarity: Laminar flow: The velocity increases from zero at the wall to the maximum at t

33、he center of pipe. The transportation on a street: Parking cars or small businesses0People walking on footQuite low speedPeople riding bicycleLow speedCar in the right lanefasterCar in the left lanefastest Transport PhenomenaHomework: 1. Summarizing the similarities among these three laws.2. Search

34、on the webs or journals to find the recent advances of transport phenomena in nano-, micro- and macro- scales. Writing a report of 2000 words about one of these three fields. Transport PhenomenaSummary: Newtons law of Viscosity (momentum transport) Fouriers law of heat conduction (energy transport)

35、Ficks law of binary diffusion (mass transport) The similarity of these three lawsThank You ! 相似论，最初钱学森、高士其等科学家给它的定位都是思维科学理论。自然，相似论的价值在于它或许能提供我们一种科学的、正确的思维方法。从这个意义上说，相似论，那应该是认识论、方法论。只是，相似性原理最核心的认识论、方法论是哪些东西呢？相似性原理告诉我们：不论自然界还是人类的思维，由简单到复杂，由低级到高级的运动都是在相似的同与变异中进行的；一切事物都是以相似性为中介而联系的；一切创造，无论是自然界的创造还是人类的创造

36、，都是基于某种相似性而进行的。 The similarity theory was initially considered to be a kind of thinking science theories by scientists such as Xuesen Qian, Shiqi Gao, etc. Absolutely, the value of similarity theory may lies in that it can provide us a scientific and correct thinking method. In this sense, the simil

37、arity theory should be epistemology and methodology. However, whats the core epistemology and methodology of the similarity theory?The similarity theory tells us:Whether the nature or human beings, different motions from simple to complex, from low-level to high-level are all performed in the proced

38、ures of ing the same or getting variant of similarity theory;All things in nature are connected using similarity as an agency;All creations, whether made by nature or by human beings, are conducted basing on some similarity. 认识事物的科学途径就是寻找相似性、研究相似性；总结、归纳和发现科学规律的突破口也是主动寻找相似性、研究相似性；搞创造、搞发明，更是主动寻找相似性、研究相似性。找相似的过程，其实是一个化繁为简的过程，是一个寻找规律、逼近规律的过程。因为，科学规律寓于相似性之中！因为，通过相似性分析，既可以发现表面上互不相关的事物之间有多方面内在联系，又可以