JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year INTRODUCTION TO TRANSPORT PHENOMENON Previous Question Paper (March - 2021 - R18)
Answer any five questions. All questions carry equal marks.
Main
Define Newton’s law of viscosity? Explain the dependence of viscosity with temperature and pressure citing at least one realistic example.
Answer
Newton's law of viscosity states that for laminar flow of a fluid, the shear stress τ is directly proportional to the velocity gradient (du/dy) perpendicular to the direction of flow. Mathematically, it is expressed as τ = -μ(du/dy), where μ is the coefficient of viscosity.
The dependence of viscosity on temperature and pressure varies by phase:
- Gases: Viscosity increases with temperature because higher kinetic energy leads to more frequent molecular collisions, increasing momentum transfer. Pressure has a negligible effect on gas viscosity at moderate ranges.
- Liquids: Viscosity decreases with temperature as intermolecular cohesive forces weaken. High pressure generally increases liquid viscosity by restricting molecular movement.
A realistic example is the lubrication of internal combustion engines: as the engine heats up, the lubricating oil's viscosity decreases, which is why multi-grade oils are used to maintain optimal flow characteristics across varying operating temperatures.
Predict the viscosity of the following gas mixture at 1 atm and 293 K from the given data on the pure components at 1 atm and 293 K.
| Species | Mole fraction, x | Molecular weight, M | Viscosity, µi(gm/cm.sec) |
|---|---|---|---|
| CO2 | 0.133 | 44 | 1462×10-7 |
| O2 | 0.039 | 32 | 2031×10-7 |
| N2 | 0.828 | 28 | 1754×10-7 |
Answer
To predict the viscosity of a gas mixture, we use the Wilke semi-empirical formula: μ_mix = Σ [x_i * μ_i / Σ (x_j * Φ_ij)], where Φ_ij = [1 + (μ_i/μ_j)^(1/2) * (M_j/M_i)^(1/4)]^2 / [8 * (1 + M_i/M_j)]^(1/2).
Given: x1=0.133 (CO2), x2=0.039 (O2), x3=0.828 (N2). M1=44, M2=32, M3=28. μ1=1462e-7, μ2=2031e-7, μ3=1754e-7.
Calculating interaction parameters Φ_ij:
- Φ_12 = 0.885, Φ_13 = 0.852, Φ_21 = 1.135, Φ_23 = 0.985, Φ_31 = 1.171, Φ_32 = 1.016
- Denominator terms: D1 = (x1*1 + x2*Φ_12 + x3*Φ_13) = 0.133 + 0.0345 + 0.705 = 0.8725
- D2 = (x1*Φ_21 + x2*1 + x3*Φ_23) = 0.1509 + 0.039 + 0.8156 = 1.0055
- D3 = (x1*Φ_31 + x2*Φ_32 + x3*1) = 0.1557 + 0.0396 + 0.828 = 1.0233
Calculating μ_mix:
μ_mix = 222.8e-7 + 78.7e-7 + 1419.5e-7 = 1721e-7 g/cm.sec.
Derive the Navier-Stokes equation in rectangular co-ordinates by making momentum balance equation and mention the assumptions made to Convert to Navier-Stokes equation.
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What is Darcy’s law? Derive the equations for flow through porous media.
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Write a step wise procedure to determine the heat flux and temperature distribution of a system by shell energy balance. Also write the boundary conditions.
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Heat flows through an annular wall of inside radius R0 and outside radius R1. The thermal conductivity of the wall varies linearly with the temperature from K0 and T0 to K1 and T1. Derive an expression for heat flow through the wall using shell energy balance.
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Derive an expression for temperature distribution in case of an incompressible Newtonian fluid between two coaxial cylinders in which the outer one is rotating and the inner one is stationary.
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Air at 27°C flows normal to a 73°C, 30mm o.d. water pipe. The air moves at 1m/s. Estimate the rate of heat transfer per unit length. Given: kinematic viscosity = 1.624 m²/s, Thermal conductivity = 0.0261 W/mk, Npr for air = 0.702.
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Chlorine is being absorbed from a gas in a small experimental wetted wall tower. The absorbing fluid is water, which is moving with an average velocity of 17.7 cm/sec. What is the absorption rate in g moles/hour if D_Cl2-H2O = 1.26 × 10^-5 cm²/sec in the liquid phase and if the saturation concentration of chlorine in water is 0.823g Cl2 per 100 g of water. Ignore chemical reaction between Cl2 and water. The tower height is 13 cm and radius 1.4 cm.
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In a catalytic reactor, a gaseous reaction nA → An takes place at the surface of the catalyst instantaneously. The product An diffuses back. It is assumed that each catalyst particle is surrounded by a stagnant gas film of thickness δ through which ‘A’ diffuses and An diffuses back. Obtain an expression for the molar flux of ‘A’ through the film. DAB is the diffusivity of ‘A’ in ‘B’. Use shell mass balance approach.
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