JNTU
JNTU B.Tech II INTRODUCTION TO TRANSPORT PHENOMENON Previous Question Paper (March 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Define and derive the Newton’s law of viscosity.
Answer
Newton's law of viscosity states that for a fluid in laminar flow between two parallel plates, the shear stress (τ) is directly proportional to the velocity gradient (dv/dy) perpendicular to the direction of flow. Mathematically, τ = μ(dv/dy), where μ is the dynamic viscosity.
To derive this, consider two parallel plates separated by a distance Y, with the bottom plate stationary and the top plate moving at velocity V. The fluid layers move at velocities proportional to their distance y from the bottom plate. The force F required to maintain the motion is proportional to the area A and the velocity gradient: F ∝ A(V/Y). Since shear stress τ = F/A, it follows that τ = μ(dv/dy).
Derive Fourier’s law of conduction.
Answer
Fourier's law of conduction states that the rate of heat transfer (Q) through a material is proportional to the negative gradient of temperature (dT/dx) and the area (A) perpendicular to the heat flow. The expression is Q = -kA(dT/dx), where k is the thermal conductivity.
Consider a slab of thickness Δx with temperatures T1 and T2 at its faces. The heat flux (q = Q/A) is driven by the temperature difference. As Δx approaches zero, the temperature gradient becomes dT/dx. The negative sign indicates that heat flows from a region of higher temperature to lower temperature, in the direction of decreasing temperature.
Derive Fick’s law of diffusion and discuss the similarities between these three transport processes.
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What is thermal conductivity and how it varies with temperature and pressure for solids and fluids.
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What is kinematic viscosity and mass diffusivity; discuss their dependency on temperature and pressure.
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Write the similarities between thermal conductivity, viscosity and mass diffusivity.
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What do you mean by coordinate systems? Distinguish between rectangular, cylindrical and spherical coordinate systems.
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What is Navier Stokes equation? Derive the equation and write its significance.
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A common channel for fluid is annulus, the space between the two concentric circular pipes. The inside of the annulus has a radius ‘r1’ and the outside ‘r2’.
Derive an expression for the velocity of flow at any radius ‘r’ in the annulus.
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Derive an expression for the radius at which the maximum velocity occurs, in terms of r1 and r2.
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Obtain the radial temperature distribution within an electrical wire with the rate of heat production given by
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Derive the relevant equations for heat conduction through composite wall.
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Write the comparison between forced and free convection in an isothermal and non-isothermal systems.
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Discuss briefly about Reynolds analogy, Chilton J-factor, Colburn J-factor.
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What do you mean by coupled phenomena in transport? Discuss briefly.
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What is diffusion? What are the different factors that may cause diffusion to occur?
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Explain in detail about the principle of molecular mass transport.
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