convection coefficient, h c = 18.1 W m K and the surrounding temperature to be 20 C.) (20 marks) Question 3 [35 marks]

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1 COP 311 June Examination 18 June 005 Duration: 3 hours Starting time: 08:30 Internal examiners: Prof. T. Majozi Mnr. D.J. de Kock Mnr. A.T. Tolmay External examiner: Mnr. B. du Plessis Metallurgists: Questions 1,, 4, 5 and 6 Chemical Engineering: Questions 3, 4, 5 and 6 Question 1 Two small blackened spheres of identical size are suspended by thin wires inside a large cavity of ice water where ice and liquid water is present. The one sphere is made of aluminium while the other is made of an unknown alloy of high thermal conductivity. It is found that it takes 4.8 minutes for the temperature of the aluminium sphere to drop from 3 C to 1 C, and 9.6 minutes for the alloy sphere to undergo the same change. What is the specific heat of the alloy if its density is measured at 5400 kg/m 3? (15 marks) Question [0 marks] The tip of a soldering iron consists of a 0.6 cm diameter copper rod, 7.6 cm long. If the tip temperature must be higher than 10 C, what are the required minimum temperature of the base and the heat flow into the base? (Assume that average convection coefficient, h c = 18.1 W m K and the surrounding temperature to be 0 C.) (0 marks) Question 3 [35 marks] State the necessary conditions for the applicability of the Hagen-Poiseuille equation in fluid flow. [5 marks] Figure 1 shows a section of a circular conduit through which a fluid flows VERTICALLY downwards. Assuming the conditions mentioned in hold, choose a differential control volume and derive the appropriate form of the Hagen-Poiseuille equation. In the course of your derivation, Equation (1) might prove relevant. Demonstrate the derivation of Eq. (1) under conditions applicable in this situation. υmax = υ average (1) 1

2 y x g v Figure 1 Vertical circular conduit A common type of viscometer for liquids consists of a relatively large reservoir with a very slender outlet tube, the rate of outflow being determined by timing the fall in the surface level (Fig. ). If oil of constant density flows out of the viscometer shown at the rate of 0.3 cm 3 /s, calculate the dynamic viscosity of the fluid using the expression derived in. The tube diameter is 0. cm and ρ oil is 890 kg/m 3. Oil 8 cm 55 cm Figure Viscometer

3 Question 4 (5 marks) Shown in Fig. 3 are two concentric spheres with a hollow space in between. If the surface of the inner sphere is at 100 o C and that of the outer sphere at 3 o C, (i) (ii) determine the temperature 33 cm from the centre of the inner sphere. Assume constant conductivity of air (k =. W/m /K) between the spheres and steadystate conditions. [10 marks] Demonstrate that in general, the temperature varies hyperbolically with the radius r. r T R 1 =30 cm R =40 cm T 1 T Figure 3 Two concentric spheres Question 5 (d) State the conditions under which Fick rate equation is applicable. [ marks] In situations where these conditions do not hold, what other similar correlation(s) could you propose and why? [ marks] Under what conditions is N A equal or nearly equal to J A? Kindly demonstrate this using the Fick rate equation as the basis. [7 marks] A mixture of He and N gas is contained in a pipe at 98 K and 1 atm total pressure which is constant throughout. At one end of the pipe at point 1 the partial pressure p A1 of He is 0.60 atm and at the other end 0. m away from point 1 at point the partial pressure p A of He is 0.0 atm. Calculate the flux of He at steady state if D AB of the He-N mixture is x 10-4 m /s. Use SI units. (1 atm = kpa; R = J/mol/K). [4 marks] Question 6 [35 marks] Figure 4 shows the Arnold cell arrangement that is usually used in experimental determination of the diffusion coefficient. In this experiment, gas B is insoluble in liquid A. Under peudo-steady-state conditions, the level of pure liquid inside the tube decreases at a negligible rate due to evaporation and subsequently diffusion. Taking this observation into account, kindly 3

4 demonstrate that the diffusion of component A along the diffusion path can be expressed by Equation (). N A, z ρ A = M, L A dz dt (), where ρ A,L is the density of pure liquid A and M A the molar mass. [5 marks] Assuming perfect steady-state conditions and insolubility of gas B in A, show that Equation (3) also holds. N A, z cdab z z1 ( y y ) A,1 A, yb, lm = (3), where y B,lm is the logarithmic-mean average concentration of component B and defined as y B, lm = yb, yb,1 y B, ln yb,1 In an experiment conducted in one of the laboratories it was observed that the liquid level dropped by m over hours for a pure liquid A with the following properties. M A = 5 g/mol ρ A,L = 800 kg/m 3 The length of the diffusion path before the experiment was measured to be 55 cm. The temperature and pressure along the diffusion path were maintained at 5 0 C and 105 kpa, respectively, throughout the experiment. At pseudosteady-state conditions, the partial pressure of component A was measured to be 100 kpa on the liquid surface and about 5 kpa at the top of the tube, i.e. end of the diffusion path. Using Equations () and (3) above, determine the diffusivity of gas A into gas B (D AB ) for this experimental observation. 4

5 Flow of gas B N Az z+ z z z z 1 (t 1 ) N Az z z 1 (t 0 ) Pure liquid A Figure 4 Arnold cell arrangement for determination of diffusivity 5

Introduction to Mass Transfer

Introduction to Mass Transfer Introduction Three fundamental transfer processes: i) Momentum transfer ii) iii) Heat transfer Mass transfer Mass transfer may occur in a gas mixture, a liquid solution or