ChE 149: TRANSPORT PHENOMENA Engr. Denise Ester O. Santiago Engr. Michael Vincent O. Laurio 2nd Semester A.Y. 2011 – 2012

TRANSFER with INTERNAL GENERATION

Objective Transferent property generation Mass Heat Momentum

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

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

Balance Equation:

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

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

For flat slab geometry

For cylindrical geometry

For cylindrical geometry

For cylindrical geometry

For cylindrical geometry

For cylindrical geometry

For cylindrical geometry

Example An electrical resistance wire has a melting point at 2500 oF. The electrical input to a wire 10 ftlong ¼ in in diameter gives a uniform volumetric heat generation totalling 1400000Btu/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

Answer

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.

Answer

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

Momentum Transfer with Internal Generation

For Incompressible Fluids

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

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

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

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.

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

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

Solution Step 3

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

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 2HNO3 Absorption & reaction occurs simultaneously NO2 diffuses short distance in the liquid water before it reacts. NO2 H2O

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

Mass Transfer with Internal Generation

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.

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 1.013 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 0.8654 mmHg.