Step 1: Understanding concentration polarization
In reverse osmosis (RO), water permeates through the membrane while solutes are rejected. However, solutes accumulate near the membrane surface, creating a concentrated boundary layer — this phenomenon is called concentration polarization.
Step 2: Effect on driving force (water flux)
Due to solute accumulation, the effective osmotic pressure at the membrane surface increases. Since net driving pressure is \[ \Delta P_{\text{net}} = \Delta P - \Delta \pi, \] where \(\Delta \pi\) is osmotic pressure difference, the higher osmotic pressure reduces the net driving force. Thus, water flux decreases.
Step 3: Effect on solute rejection
At higher solute concentration near the membrane surface, more solute tends to diffuse through the membrane. This reduces the overall solute rejection capability of the process.
Conclusion:
Concentration polarization leads to: \[ \text{Reduced water flux and reduced solute rejection.} \]
An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity \( k = 0.1 \) W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface __________°C (rounded off to 1 decimal place).

GIVEN:
Kinematic viscosity: \( \nu = 1.0 \times 10^{-6} \, {m}^2/{s} \)
Prandtl number: \( {Pr} = 7.01 \)
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]
The first-order irreversible liquid phase reaction \(A \to B\) occurs inside a constant volume \(V\) isothermal CSTR with the initial steady-state conditions shown in the figure. The gain, in kmol/m³·h, of the transfer function relating the reactor effluent \(A\) concentration \(c_A\) to the inlet flow rate \(F\) is:

A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. The initial temperature (at time $t = 0$) of the hot plate and cold plate are $T_h$ and $T_c$, respectively. Assume perfect contact between the plates. Which one of the following is an appropriate boundary condition at the surface $S$ for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for $t>0$?

The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:

\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is _________ MPa (rounded off to 3 decimal places).