JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II INTRODUCTION TO TRANSPORT PHENOMENON Previous Question Paper (August/September -2022 - R18)

Transport phenomena refer to the study of the rates at which physical quantities, such as momentum, energy, and mass, are transferred within a system or across boundaries. These processes are driven by gradients in velocity, temperature, and concentration, respectively.

The fundamental laws governing these transport processes are:

1. Newton's Law of Viscosity (Momentum transport): τ = -μ (dv/dy), where τ is the shear stress and μ is the dynamic viscosity.
2. Fourier's Law of Heat Conduction (Energy transport): q = -k (dT/dy), where q is the heat flux and k is the thermal conductivity.
3. Fick's Law of Diffusivity (Mass transport): J = -D (dc/dy), where J is the molar flux and D is the mass diffusivity.

These laws are considered analogous because they all follow a linear flux-gradient relationship, often expressed as Flux = -(Transport Property) × (Driving Force Gradient). In each case, the transport property (viscosity, thermal conductivity, or diffusivity) acts as a proportionality constant that characterizes the resistance of the medium to the respective transport process.

The transport properties—kinematic viscosity (ν), molecular thermal diffusivity (α), and molecular mass diffusivity (D)—are sensitive to changes in temperature and pressure, primarily due to their dependence on molecular motion and mean free path.

For gases, kinetic theory predicts that these properties increase with temperature because higher thermal energy increases molecular velocity and collision frequency. Conversely, as pressure increases, the mean free path decreases, leading to a decrease in these properties. Specifically, kinematic viscosity (ν = μ/ρ) and thermal diffusivity (α = k/ρCp) are inversely proportional to pressure because the density (ρ) increases with pressure.

For liquids, the behavior is different. Kinematic viscosity decreases sharply with increasing temperature due to the weakening of intermolecular cohesive forces. Molecular diffusivity generally increases with temperature in liquids as the mobility of molecules rises. Pressure has a relatively minor effect on these properties in liquids compared to gases, as liquids are nearly incompressible; however, very high pressures can lead to a slight increase in viscosity due to increased molecular packing.