Assignment MT1-2015-4

Section 1(Based on lecture notes)

Note: - Use the notations used in the class whenever necessary

Q.1.1) What are the ways to obtain mass transfer coefficient?

Q.1.2) Derive an expression for mass transfer coefficient using following theories.a) Film theoryb) Penetration theoryc) Surface renewal theoryd) Boundary layer theory

Q.1.3) Discuss how the flow of fluid associated with convective mass transfer is accounted for in the theories listed in Q.3

Q.1.4) Write the dimensionless numbers related to heat and mass transfer along with the physical significance of them

Q.1.5) Explain Reynolds’s analogy and Coulburn analogy.

Q.1.6) Explain different type of Mass Transfer Coefficient and develop the relationship among them.

Q.1.7) Provide the expressions for different type of Mass Transfer Coefficient for the following cases.

a) A is diffusing through non-diffusing B.b) Equimolar counter diffusion.

Section-2(Based on the worked out problems in the text book)

From book: Principle of Mass Transfer by B.K.Dutta

Ex.3.1 Page no.79

Ex.3.2 Page no.80

Ex.3.3 Page no.87

Ex.3.4 Page no.89

Ex.3.5 Page no.99

Ex.3.6 Page no.100

Ex.3.7 Page no.101

Ex.3.8 Page no.104

Ex.3.9 Page no.105

From book: Treybal

Ex. 3.4 page no.69

What is the heat-transfer analog to this Eq.

Section 3Unsolved Problems

3.1)A stream of air at 100 kPa pressure and 300 K is flowing on the top surface of a thin flat sheet of solid naphthalene of length 0.2 m with a velocity of 20 m/sec. The other data are:

Mass diffusivity of naphthalene vapor in air = 6 * 10–6 m 2/secKinematic viscosity of air = 1.5 * 10–5 m 2.sc

Concentration of naphthalene at the air-solid naphthalene interface =1 * 10–5 kmol/m3

Calculate:

(a) the overage mass transfer coefficient over the flat plate(b) the rate of loss of naphthalene from the surface per unit width

Note: For heat transfer over a flat plate, convective heat transfer coefficient for laminar flow can be calculated by the equation.

you may use analogy between mass and heat transfer

3.2) The mass flux from a 5 cm diameter naphthalene ball placed in stagnant air at 40 C and atmospheric pressure, is 1.47 * 10–3  mol/m2. sec. Assume the vapor pressure of naphthalene to be 0.15 atm at 40C and negligible bulk concentration of naphthalene in air. If air starts blowing across the surface of naphthalene ball at 3 m/s by what factor will the mass transfer rate increase, all other conditions remaining the same?

For spheres :

Sh = 2.0 + 0.6 (Re) 0.5 (Sc)0.33

Where Sh is the Sherwood number and Sc is the Schmids number. The viscosity and density of air are 1.8 * 10–5 kg/m.s and 1.123 kg/m3, respectively and the gas constant is 82.06 cm3 . atm/mol.K.

3.3) A solid disc of benzoic acid 3 cm in diameter is spin at 20 rpm and 25C. Calculate the rate of dissolution in a large volume of water. Diffusivity of benzoic acid in water is 1.0 * 10–5 cm2/sec, and solubility is 0.003 g/cc. The following mass transfer correlation is applicable:

Sh = 0.62 Re ½

Sc 1/3

Where and is the angular speed in radians/time.

3.4) Air flows over a solid slab of frozen carbon dioxide (dry ice) with an exposed cross-sectional surface area of 1*10-3 m2. The carbon dioxide sublimes into the 2 m/s flowing stream at a total release rate of 2.29 *10-4 mol/s. The air is at 293 K and 1.013* 105 Pa pressure. At that temperature, the diffusivity of carbon dioxide in air is 1.5 *10-5 m2/s and the kinematic viscosity of the air is 1.55*10-5 m2/s.

3.5) Determine the Schmidt number for methanol in air at 298 K and 1.013 *105 Pa and in liquid water at 298 K.

3.6) Dittus and Boelter proposed the following equation for correlating the heat-transfer coefficient for turbulent flow in a pipe

What should be the corresponding equation for the mass-transfer coefficient when the transfer is to a turbulent fluid flowing in a pipe?

3.7) Determine the Schmidt number for(a) oxygen in air at 300 K and 1.0 atm; and(b) oxygen in liquid water at 300 K.At 300 K, the diffusion coefficient of oxygen in liquid water is1.5*10-9 m2/s.

3.8) Silicon tetrachloride, SiCl4, is a key chemical in the silicon chemical vapor deposition. It is used in the production of silane, SiH4. The purity of SiCl4 is essential to the production of high-quality silicon films. To eliminate trichlorosilane, SiHCl3, within the high-purity silicon tetrachloride, chlorine gas is bubbled through the liquid SiCl4

at 298 K to promote the following reaction:

The HCl is then easily removed in a stripper, using nitrogen as the stripping gas.To determine the mass-transfer coefficient of chlorine in liquid SiCl4, a Schmidt number is needed. Evaluate the Schmidt number for chlorine in liquid silicon tetrachloride at 298 K. Thfollowing information is available for SiCl4 at 298 K:

The diffusivity for chlorine in silicon tetrachloride can be evaluated using the Wilke–Chang equation.

3.9) A container of acetone was accidently spilled, covering the top, smooth surface of a laboratory bench located in a semiconductor-fabrication building. The exhaust fan for thefabrication building produced a 6 m/s air flow parallel to the 1-m-wide bench surface. The air was maintained at 298 and 1.013*105 Pa. The vapor pressure of acetone at 298 K 3.066 *104 Pa and the diffusivity of acetone in air at 298 K and 1.013*105 Pa is 0.93*10-5 m2/s.(a) Determine the mass-transfer coefficient at 0.4 m downstream from the leading edge of the laboratory bench.(b) Determine the amount of acetone evaporating per 1 m2 of surface area each second.