1. ChE 149: TRANSPORT PHENOMENA
Engr. Denise Ester O. Santiago
Engr. Michael Vincent O. Laurio
2nd Semester A.Y – 2012

2. TRANSFER with INTERNAL GENERATION

3. Objective
Transferent property generation
Mass
Heat
Momentum

4. Assumptions
 Transferent property is generated uniformly at all points in the system
Transferent property is continuously generated and must be continuously transferred to a boundary to achieve steady state

5. G=rate of transferent property generation units: property/ time- volume-x y x z G Δz
(ΨA)x
(ΨA)x+Δx
(ΨA)1
(ΨA)2 Δy Δx

6. Balance Equation:

8. Case 1: If G is constant for entire volume between 1&2; Case 2: A &V varies

9. Heat Transfer with Internal Generation
Ex. Nuclear reactor fuel elements Electrically heated wire From balance equation:

10. For flat slab geometry

11. For cylindrical geometry

12. For cylindrical geometry

13. For cylindrical geometry

14. For cylindrical geometry

15. For cylindrical geometry

16. For cylindrical geometry

17. Example
An electrical resistance wire has a melting point at oF. The electrical input to a wire 10 ftlong ¼ in in diameter gives a uniform volumetric heat generation totalling Btu/hr . The surface temperature of the wire is 1500oF & the thermal conductivity is 10 Btu/hr ft2(oF/ft)
Can the wire be safely used or will the center reach its melting point?
Calculate the molten core radius

18. Answer

19. Example
Heat is generated within a sphere at 2x108 Btu/hr- ft3. The sphere is 3 in in diameter. The surface temperature is 200oF. The thermal conductivity is 200 Btu/hr-ft-oF.
Calculate the temperature at the center of the sphere
Calculate the temperature at ¾ in.

20. Answer

21. SEATWORK(.^_^.)
For volumetric heat generation in a flat slab whose surfaces are at different temperatures as shown,
Derive an expression for T in terms of x as the constants of the system
Derive an expression for the value of x at which T is a maximum

22. Momentum Transfer with Internal Generation

23. For Incompressible Fluids

24. For Flow of Fluids through a circular pipe with Incompressible Newtonian Fluid

29. Example
An oil is in laminar flow in a ½ in ID tube at 6 gal/min. The oil viscosity is 300 cP and D is 60 lb/ft3. Calculate: a. ΔP/Δy (lbf/in2ft) b. τy (lbf/ft2) c. Vcenter (ft/s) d. r when point velocity =ave velocity

30. Answer a. ΔP/Δy (lbf/in2ft) =7.84 b. τy (lbf/ft2)=1.18
c. Vcenter (ft/s)=19.6
d. r =0.177 in
when point velocity =ave velocity

31. Example
Derive an expression for the laminar-flow velocity as a function of radius and average velocity for a power-law non-Newtonian fluid in a circular pipe.

32. Solution Step 1 Incompressible Non-Newtonian fluid
Laminar flow in circular duct-momentum is transferred by molecular transport
SS with GT

33. Solution
Step 2 *applicable to flow of both Newtonian and Non- Newtonian fluids

34. Solution
Step 3

35. Solution
Step 4 SEATWORK!!! You can use your notes. You can use your handouts. BUT You cannot use your seatmates.

36. Mass Transfer with Internal Generation
Ex.
Systems with chemical or nuclear reaction
Diffusion with a chemical reaction
Absorption of NO2 by water to form HNO3
2NO2+H2O HNO3
Absorption & reaction occurs simultaneously
NO2 diffuses short distance in the liquid water before it reacts.
NO2
H2O

37. Mass Transfer with Internal Generation
Consider, ECD of component a through a region in w/c the component undergoes a first order reaction For first order rxn:
plane1
Ca1
plane2
Ca2 a b
x=x1
x=x2

38. Mass Transfer with Internal Generation

46. Example
Ammonia is being cracked on a solid catalyst according to the reaction 2NH3 N2+3H2 At about 1mm from the solid catalyst surface, where pressure is 1 atm and temperature is 200oC,the analysis of the bulk gas is 33.3% NH3, 16.67% N2 and 50% H2 by volume. At this condition, mass diffusivity of NH3 to the mixture is 7.76x10- 5m2/s. The circumstances are such that NH3 diffuses from the bulk gas stream to the catalyst surface and the products of the reaction diffuse back to the bulk gas, as if by molecular diffusion through the 1mm gas film in laminar flow. Derive the expression of Ca in terms of x with the concentration at the catalyst surface equal to zero.

47. Example
Calculate the time required for the sublimation of 3g of naphthalene from a naphthalene ball of mass 4g kept suspended in a large volume of stagnant air at 45oC and bar pressure. Diffusivity of naphthalene in air under the given conditions is 6.92x10-6m2/s, its density is 1140kg/m3, and its sublimation pressure at 45oC is mmHg.