GATE Metallurgical Engineering Transport Phenomena and Rate Processes Syllabus

Transport Phenomena and Rate Processes syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Transport Phenomena and Rate Processes in GATE Metallurgical Engineering, not a summary of it.

1. 1

   Momentum transfer

   5 topics

   • Concept of viscosity
   • Shell balances
   • Bernoulli’s equation
   • Mechanical energy balance equation
   • Flow past plane surfaces and through pipes
2. 2

   Heat transfer

   3 topics

   • Conduction
     • Fourier’s Law
     • 1-D steady state conduction
   • Convection
     • Heat transfer coefficient relations for forced convection
   • Radiation
     • Black body radiation
     • Stefan-Boltzman Law
     • Kirchhoff’s Law
3. 3

   Mass transfer

   2 topics

   • Diffusion and Fick’s laws
   • Mass transfer coefficients
4. 4

   Dimensional analysis

   2 topics

   • Buckingham Pi theorem
   • Significance of dimensionless numbers
5. 5

   Basic laws of chemical kinetics

   5 topics

   • First order reactions
   • Reaction rate constant
   • Arrhenius relation
   • Heterogeneous reactions
   • Oxidation kinetics
6. 6

   Electrochemical kinetics

   1 topic

   • Polarization

Transport Phenomena and Rate Processes flashcards for GATE Metallurgical Engineering

21 of 50 cards from the Transport Phenomena and Rate Processes deck — real questions with worked answers.

1. Define viscosity and state its SI unit.

   Viscosity is a fluid's resistance to shear deformation (internal friction between adjacent fluid layers). Its SI unit is $\text{Pa·s}$ (equivalently $\text{kg·m}^{-1}\text{s}^{-1}$); the CGS unit is the poise, where $1\ \text{Pa·s} = 10\ \text{poise}$.

2. State Newton's law of viscosity in one dimension.

   $$\tau_{yx} = -\mu \frac{dv_x}{dy}$$ where $\tau_{yx}$ is the shear stress (momentum flux), $\mu$ is the dynamic viscosity, and $\frac{dv_x}{dy}$ is the velocity gradient. The negative sign indicates momentum flows down the velocity gradient.

3. What is kinematic viscosity and how does it relate to dynamic viscosity?

   Kinematic viscosity is the momentum diffusivity, $\nu = \frac{\mu}{\rho}$, where $\mu$ is dynamic viscosity and $\rho$ is density. Its SI unit is $\text{m}^{2}\text{s}^{-1}$ (CGS unit: stokes).

4. Distinguish Newtonian from non-Newtonian fluids.

   A Newtonian fluid has a constant viscosity independent of shear rate, so $\tau$ is linearly proportional to $\frac{dv}{dy}$ (e.g., water, air). A non-Newtonian fluid has a viscosity that varies with shear rate (e.g., shear-thinning, shear-thickening, Bingham plastics).

5. How does viscosity of liquids and gases vary with temperature?

   For liquids, viscosity decreases with increasing temperature (weaker intermolecular cohesion). For gases, viscosity increases with increasing temperature (greater molecular momentum exchange).

6. What is the shell balance method used for in transport phenomena?

   The shell balance is a technique to derive velocity, temperature, or concentration profiles by writing a conservation balance (in = out + generation − consumption) over a thin differential shell, then taking the limit as shell thickness $\to 0$ to obtain a differential equation.

7. State the general form of a shell momentum balance at steady state.

   $$(\text{rate of momentum in}) - (\text{rate of momentum out}) + (\text{sum of forces}) = 0$$ Momentum enters/leaves by both convective transport and molecular (viscous) transport; forces include pressure and gravity.

8. For steady laminar flow in a circular pipe, what is the velocity profile obtained from a shell balance?

   A parabolic profile: $$v_z(r) = v_{z,max}\left[1 - \left(\frac{r}{R}\right)^{2}\right]$$ where $R$ is the pipe radius and $v_{z,max}$ is the centerline velocity.

9. State Bernoulli's equation for steady, incompressible, frictionless flow.

   $$\frac{P}{\rho g} + \frac{v^{2}}{2g} + z = \text{constant}$$ The three terms are the pressure head, velocity head, and elevation head, respectively. It expresses conservation of mechanical energy along a streamline.

10. List the assumptions underlying Bernoulli's equation.

    Steady flow, incompressible fluid, inviscid (frictionless / no viscous losses), flow along a single streamline, and no shaft work or heat addition between the two points.

11. Write the mechanical energy balance (extended Bernoulli) equation including friction and pump work.

    $$\frac{P_1}{\rho} + \frac{v_1^{2}}{2} + g z_1 + W_s = \frac{P_2}{\rho} + \frac{v_2^{2}}{2} + g z_2 + h_f$$ where $W_s$ is shaft (pump) work per unit mass added to the fluid and $h_f$ is the friction loss per unit mass.

12. What is the Fanning friction factor and how does it give the pressure drop in a pipe?

    The Fanning friction factor $f$ relates wall shear to kinetic energy. The pressure drop is $$\Delta P = \frac{2 f L \rho v^{2}}{D}$$ where $L$ is length, $D$ is diameter, $\rho$ is density, and $v$ is the average velocity.

13. Give the Fanning friction factor for laminar pipe flow as a function of Reynolds number.

    $$f = \frac{16}{Re}$$ valid for laminar flow ($Re < 2100$). (The Darcy friction factor equals $4f = \frac{64}{Re}$.)

14. State the Hagen–Poiseuille equation for laminar flow through a pipe.

    $$Q = \frac{\pi R^{4} \Delta P}{8 \mu L}$$ where $Q$ is volumetric flow rate, $R$ the radius, $\Delta P$ the pressure drop, $\mu$ the viscosity, and $L$ the length.

15. What is the boundary layer in flow past a plane surface?

    The boundary layer is the thin region adjacent to the surface where viscous effects are significant and the velocity rises from zero at the wall (no-slip) to ~99% of the free-stream velocity. Outside it the flow is essentially inviscid.

16. Give the Blasius expression for the laminar boundary layer thickness over a flat plate.

    $$\delta = \frac{5x}{\sqrt{Re_x}}$$ where $x$ is the distance from the leading edge and $Re_x = \frac{\rho v x}{\mu}$ is the local Reynolds number.

17. What Reynolds number marks the transition from laminar to turbulent flow in a pipe, and over a flat plate?

    In a pipe, transition occurs around $Re \approx 2100$ (fully turbulent above ~4000). Over a flat plate, transition occurs near $Re_x \approx 5 \times 10^{5}$.

18. State Fourier's law of heat conduction.

    $$q_x = -k \frac{dT}{dx}$$ where $q_x$ is the heat flux ($\text{W·m}^{-2}$), $k$ is thermal conductivity ($\text{W·m}^{-1}\text{K}^{-1}$), and $\frac{dT}{dx}$ is the temperature gradient. Heat flows down the temperature gradient.

19. What is conduction as a mode of heat transfer?

    Conduction is heat transfer through a stationary medium (solid or quiescent fluid) by molecular interaction and, in metals, by free electrons, driven by a temperature gradient without bulk motion of matter.

20. Write the expression for 1-D steady-state conduction heat rate through a plane wall.

    $$Q = \frac{k A (T_1 - T_2)}{L}$$ where $A$ is the cross-sectional area, $L$ the wall thickness, and $T_1 - T_2$ the temperature difference across it.

21. Define thermal resistance for conduction through a plane wall.

    $$R_{cond} = \frac{L}{k A}$$ analogous to electrical resistance, with heat rate $Q = \frac{\Delta T}{R_{cond}}$ playing the role of current and $\Delta T$ the potential difference.

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