Lecture 13 - Transport properties for gas mixture Notes | EduRev

Created by: Kamran Nasir

: Lecture 13 - Transport properties for gas mixture Notes | EduRev

 Page 1


Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_1.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
The Lecture Contains:
Transport properties for gas mixture
Mass conservation equation
Momentum conservation equation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 2


Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_1.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
The Lecture Contains:
Transport properties for gas mixture
Mass conservation equation
Momentum conservation equation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_2.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Transport properties for gas mixture
Viscosity of gas mixture
Wassilijewa equation
 
Mason and Saxena modification
 
 is the viscosity of the pure component
  is the mole fraction of the i
th
 component
  
Thermal Conductivity of gas mixture
Wassilijewa equation
 
 Mason and Saxena modification
 
 is the thermal conductivity of the pure component
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 3


Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_1.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
The Lecture Contains:
Transport properties for gas mixture
Mass conservation equation
Momentum conservation equation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_2.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Transport properties for gas mixture
Viscosity of gas mixture
Wassilijewa equation
 
Mason and Saxena modification
 
 is the viscosity of the pure component
  is the mole fraction of the i
th
 component
  
Thermal Conductivity of gas mixture
Wassilijewa equation
 
 Mason and Saxena modification
 
 is the thermal conductivity of the pure component
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_3.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Diffusion Coefficient of any component in a gas mixture
Wilke equation
  
  
Where, 
 
 
 is the collision diameter in 
 
 is the pressure (Bar) 
 
 is the molecular weight of the components 
 
 is the collision integral
 
 
 =Boltzman's constant
 
 =Intermolecular potential
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 4


Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_1.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
The Lecture Contains:
Transport properties for gas mixture
Mass conservation equation
Momentum conservation equation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_2.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Transport properties for gas mixture
Viscosity of gas mixture
Wassilijewa equation
 
Mason and Saxena modification
 
 is the viscosity of the pure component
  is the mole fraction of the i
th
 component
  
Thermal Conductivity of gas mixture
Wassilijewa equation
 
 Mason and Saxena modification
 
 is the thermal conductivity of the pure component
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_3.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Diffusion Coefficient of any component in a gas mixture
Wilke equation
  
  
Where, 
 
 
 is the collision diameter in 
 
 is the pressure (Bar) 
 
 is the molecular weight of the components 
 
 is the collision integral
 
 
 =Boltzman's constant
 
 =Intermolecular potential
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_4.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Mass conservation equation
Principle of mass conservation
 
------ (1)
Rate of accumulation in fluid element = ------ (2)
Rate of mass in fluid element across face A = ------ (3)
Rate of mass leaving fluid element across face B = ------ (4)
The net efflux in x-direction = ------ (5)
The net efflux in y-direction = ------ (6)
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Page 5


Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_1.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
The Lecture Contains:
Transport properties for gas mixture
Mass conservation equation
Momentum conservation equation 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_2.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Transport properties for gas mixture
Viscosity of gas mixture
Wassilijewa equation
 
Mason and Saxena modification
 
 is the viscosity of the pure component
  is the mole fraction of the i
th
 component
  
Thermal Conductivity of gas mixture
Wassilijewa equation
 
 Mason and Saxena modification
 
 is the thermal conductivity of the pure component
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_3.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Diffusion Coefficient of any component in a gas mixture
Wilke equation
  
  
Where, 
 
 
 is the collision diameter in 
 
 is the pressure (Bar) 
 
 is the molecular weight of the components 
 
 is the collision integral
 
 
 =Boltzman's constant
 
 =Intermolecular potential
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_4.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
 
Mass conservation equation
Principle of mass conservation
 
------ (1)
Rate of accumulation in fluid element = ------ (2)
Rate of mass in fluid element across face A = ------ (3)
Rate of mass leaving fluid element across face B = ------ (4)
The net efflux in x-direction = ------ (5)
The net efflux in y-direction = ------ (6)
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Objectives_template
file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture13/13_5.htm[10/5/2012 11:38:36 AM]
 Module 3: Physics of Combustion
 Lecture 13: Transport properties for gas mixture
  
Substituting (2), (5) and (6) in (1)
 
Differential form of continuity equation
In vector notation,
 
Where, is the gradient operator
  is the divergence of 
For incompressible flow,
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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