化工传递过程基础22very important

1、Transport PhenomenaDepartment of Chemical EngineeringTianjin University Jingtao Wang, Ph.D Content in the Previous ClassChapter 10: Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow Section 10.1: Shell energy balances; boundary conditions Section 10.2: Heat conduction wi

2、th an electrical heat source Section 10.6: Heat conduction through composite walls Outline The materials covered in todays class: Part II: Energy TransportChapter 9: Thermal conductivity and the mechanisms of energy transportSection 9.7: Convective transport of energySection 9.8: work associated wit

3、h molecular motion Transport PhenomenaSection 9.7:CONVECTIVE TRANSPORT OF ENERGY Transport PhenomenaEnergy may also be transported by the bulk motion of the fluid. Heat transfer by convection indoorThe boiling soup Transport PhenomenaIn Fig. 9.7-1 we show three mutually perpendicular elements of are

4、a dS at the point P, where the fluid velocity is v. Fig. 9.7-l. Three mutually perpendicular surface elements of area dS across which energy is being transported by convection of the fluid moving with the velocity v. Transport PhenomenaThe volume rate of flow across the surface element dS perpendicu

5、lar to the x-axis is vxdS. The rate at which energy is being swept across the same surface element is then in which is the kinetic energy per unit volume, and is the internal energy per unit volume. Transport PhenomenaWe can write expressions similar to for the surface elements perpendicular to the

6、y- and z-axes. If we now multiply each of the three expressions by the corresponding unit vector and add, we then get, after division by dS, and this quantity is called the convective energy flux vector. Transport PhenomenaSection 9.8:WORK ASSOCIATED WITH MOLECULAR MOTIONS Transport PhenomenaThe law

7、 of conservation of energy for an open flow system is an extension of the first law of classical thermodynamics (for a closed system at rest). In a closed system, we state that the change in internal energy is equal to the amount of heat added to the system plus the amount of work done on the system

8、. Transport PhenomenaFor flow systems we need to account for the heat added to the system (by molecular motions and by bulk fluid motion) and also for the work done on the system by the molecular motions. Therefore it is appropriate that we develop here the expression for the rate of work done by th

9、e molecular motions. Transport PhenomenaWhen a force F acts on a body and causes it to move through a distance dr, the work done is dW = (F dr). Then the rate of doing work is dW/dt = (F dr/dt) = (F v), the dot product of the force times the velocity. First we recall:We apply this formula to the thr

10、ee perpendicular planes at a point P in space shown in Fig. 9.8-1. Next: Transport Phenomena Transport PhenomenaFirst we consider the surface element perpendicular to the x-axis. The fluid on the minus side of the surface exerts a force xdS on the fluid that is on the plus side. Since the fluid is m

11、oving with a velocity v, the rate at which work is done by the minus fluid on the plus fluid is (x v)dS. Similar expressions may be written for the work done across the other two surface elements. Transport PhenomenaWhen written out in component form, these rate of work expressions, per unit area, e

12、 When these scalar components are multiplied by the unit vectors and added, we get the rate of doing work vector per unit area”. We can call this work flux: Transport PhenomenaWe now define the combined energy flux vector e as follows: The e vector is the sum of (a) the convective energy flux, (b) t

13、he rate of doing work (per unit area) by molecular mechanisms, and (c) the rate of transporting heat (per unit area) by molecular mechanisms. Transport PhenomenaThe total molecular stress tensor can now be split into two parts: The term pvcan then be combined with the internal energy term to give an

14、 enthalpy term Transport PhenomenaFor a surface element dS of orientation n, the quantity (n e) gives the convective energy flux, the heat flux, and the work flux across the surface element dS from the negative side to the positive side of dS. Transport PhenomenaIn Table 9.8-1 we summarize the notation for the various energy flux vectors introduced in thi