Page 1 Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_1.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis The Lecture Contains: Theoretical Analysis Theoretical Analysis (Contd.) Page 2 Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_1.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis The Lecture Contains: Theoretical Analysis Theoretical Analysis (Contd.) Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_2.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis Consider a 2D diffusion flame, (Figure 29.1) Assumptions: i. 2D steady laminar inviscid flow. ii. Velocity above the channel is constant everywhere iii. Fuel and oxidizer react in stoichiometric proportion at the flame surface with infinite reaction rate (Thin flame approximation). iv. Binary diffusion between participating species. v. Mass diffusion is along x-direction only. vi. Unity Lewis number. vii. Single step irreversible reaction. viii. Radiation heat transfer is negligibly small. ix. Constant thermophysical properties. x. Mass diffusivity of both fuel and oxidizer are the same. xi. Buoyancy force is neglected. Page 3 Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_1.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis The Lecture Contains: Theoretical Analysis Theoretical Analysis (Contd.) Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_2.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis Consider a 2D diffusion flame, (Figure 29.1) Assumptions: i. 2D steady laminar inviscid flow. ii. Velocity above the channel is constant everywhere iii. Fuel and oxidizer react in stoichiometric proportion at the flame surface with infinite reaction rate (Thin flame approximation). iv. Binary diffusion between participating species. v. Mass diffusion is along x-direction only. vi. Unity Lewis number. vii. Single step irreversible reaction. viii. Radiation heat transfer is negligibly small. ix. Constant thermophysical properties. x. Mass diffusivity of both fuel and oxidizer are the same. xi. Buoyancy force is neglected. Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_3.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis (Contd.) Conservation equations: Mass conservation: Using assumption (ii), we can have, Axial momentum conservation: Species conservation equation: Mass fraction of the product can be found from Page 4 Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_1.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis The Lecture Contains: Theoretical Analysis Theoretical Analysis (Contd.) Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_2.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis Consider a 2D diffusion flame, (Figure 29.1) Assumptions: i. 2D steady laminar inviscid flow. ii. Velocity above the channel is constant everywhere iii. Fuel and oxidizer react in stoichiometric proportion at the flame surface with infinite reaction rate (Thin flame approximation). iv. Binary diffusion between participating species. v. Mass diffusion is along x-direction only. vi. Unity Lewis number. vii. Single step irreversible reaction. viii. Radiation heat transfer is negligibly small. ix. Constant thermophysical properties. x. Mass diffusivity of both fuel and oxidizer are the same. xi. Buoyancy force is neglected. Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_3.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis (Contd.) Conservation equations: Mass conservation: Using assumption (ii), we can have, Axial momentum conservation: Species conservation equation: Mass fraction of the product can be found from Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_4.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis (Contd.) By thin flame approximation, Single step irreversible reaction, Universal concentration variables, Rate of fuel transport from the centre to the flame surface is equal to stoichiometric rate of oxidizer transport. Let be the mass fraction of the reactant, Instead of solving two equations (For fuel and oxidizer), we can solve a single equation as given below, This analysis is known as the Burke-Schumann's analysis Page 5 Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_1.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis The Lecture Contains: Theoretical Analysis Theoretical Analysis (Contd.) Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_2.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis Consider a 2D diffusion flame, (Figure 29.1) Assumptions: i. 2D steady laminar inviscid flow. ii. Velocity above the channel is constant everywhere iii. Fuel and oxidizer react in stoichiometric proportion at the flame surface with infinite reaction rate (Thin flame approximation). iv. Binary diffusion between participating species. v. Mass diffusion is along x-direction only. vi. Unity Lewis number. vii. Single step irreversible reaction. viii. Radiation heat transfer is negligibly small. ix. Constant thermophysical properties. x. Mass diffusivity of both fuel and oxidizer are the same. xi. Buoyancy force is neglected. Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_3.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis (Contd.) Conservation equations: Mass conservation: Using assumption (ii), we can have, Axial momentum conservation: Species conservation equation: Mass fraction of the product can be found from Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_4.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis (Contd.) By thin flame approximation, Single step irreversible reaction, Universal concentration variables, Rate of fuel transport from the centre to the flame surface is equal to stoichiometric rate of oxidizer transport. Let be the mass fraction of the reactant, Instead of solving two equations (For fuel and oxidizer), we can solve a single equation as given below, This analysis is known as the Burke-Schumann's analysis Objectives_template file:///D|/Web%20Course/Dr.%20D.P.%20Mishra/Local%20Server/FOC/lecture29/29_5.htm[10/5/2012 4:14:07 PM] Module 6: Diffusion Flame Lecture 29: Theoretical Analysis Theoretical Analysis (Contd.) Above equation can be converted into a diffusion equation by substituting Inner wall exists at and outer wall at The initial and boundary conditions are as follows. Applying boundary conditions, we obtain a closed form series solution where, is the non-dimensional mass fraction of the reactant. The infinite series must have a constant value at the flame surface as given belowRead More

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