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ME 475/675 Introduction to Combustion

ME 475/675 Introduction to Combustion. Lecture 11. Announcements. Midterm 1 September 29, 2014 Review Friday, September 26 HW 5 Due Friday, September 26, 2014. Chapter 3 Introduction to Mass Transfer. x. x. x. x. x. x. o. x. o. x. x. x. x. x. x. x. o. x. x. x. o. o.

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ME 475/675 Introduction to Combustion

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  1. ME 475/675 Introduction to Combustion Lecture 11

  2. Announcements • Midterm 1 • September 29, 2014 • Review Friday, September 26 • HW 5 Due Friday, September 26, 2014

  3. Chapter 3 Introduction to Mass Transfer x x x x x x o x o x x x x x x x o x x x o o o x x x x x x o x x o o x x x x x o x o o o x x o o x o o x x o o o o x o x o x o o o o x o o • Consider two species, x and o • Concentration of “x” is larger on the left, of “o” is larger on the right • Species diffuse through each other • they move from regions of high to low concentrations • Think of perfume in a room • Mass flux is driven by concentration difference • Analogously, heat transfer is driven by temperature differences • There may also be bulk motion of the mixture (advection, like wind) • Total rate of mass flux: (sum of component mass flux) 1- Mass Fraction Y Yx Yo x 0-

  4. Chapter 3 Introduction to Mass Transfer x x x x x x o x o x x x x x x x o x x x o o o x x x x x x o x x o o x x x x x o x o o o x x o o x o o x x o o o o x o x o x o o o o x o o • Rate of mass flux of “x” in the direction Advection (Bulk Motion) Diffusion (due to concentration gradient) • Diffusion coefficient of x through o • Units • Appendix D, pp. 707-9 • For gases, book shows that Yx Yo Mass Fraction Y x

  5. Stefan Problem (no reaction) x L- • One dimensional tube (Cartesian) • Gas B is stationary: • Gas A moves upward • Want to find this • ; • but treat as constant YB YA B+A Y A

  6. Mass Flux of evaporating liquid A • For • (dimensionless) • increases slowly for small • Then very rapidly for > 0.95 • What is the shape of the versus x profile?

  7. Profile Shape =0.99 • but • Ratio: ; • For • Large profiles exhibit a boundary layer near exit (large advection near interface) =0.9 =0.5 =0.1 =0.05

  8. Liquid-Vapor Interface Boundary Condition • At interface need • So • Saturation pressure at temperature T • For water, tables in thermodynamics textbook • Or use Clausius-Slapeyron Equation (page 18 eqn. 2.19) A+B Vapor Liquid A

  9. Clausius-Clapeyron Equation (page 18) • Relates saturation pressure at a given temperature to the saturation conditions at another temperature and pressure • If given , we can use this to find • Page 701, Table B: , at P = 1 atm

  10. Problem 3.9 • Consider liquid n-hexane in a 50-mm-diameter graduated cylinder. Air blows across the top of the cylinder. The distance from the liquid-air interface to the open end of the cylinder is 20 cm. Assume the diffusivity of n-hexane is 8.8x10-6 m2/s. The liquid n-hexane is at 25C. Estimate the evaporation rate of the n-hexane. (Hint: review the Clausius-Clapeyron relation a applied in Example 3.1)

  11. Stefan Problem (no reaction) x L- • One dimensional tube (Cartesian) • Gas B is stationary • but has a concentration gradient • Diffusion of B down = advection up • ; • ; = YB YA YA,i Y

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