Heat And Mass Transfer

Step 1: Understanding the function of baffles.
Baffles are used in heat exchangers to promote turbulence in the fluid, which increases the heat transfer rate. They help to direct the flow of fluid, causing it to pass through different sections of the heat exchanger, increasing the heat exchange efficiency.

Step 2: Analysis of options.
- (A) decrease heat transfer area: Baffles do not decrease heat transfer area; they help maintain the area available for heat exchange. - (B) decrease pressure drop: Baffles typically cause some increase in pressure drop as they obstruct flow, which can lead to more turbulent flow. - (C) increase rate of heat transfer: This is the correct option as baffles enhance turbulence and thus increase the heat transfer rate. - (D) decrease vibrations: Baffles are not intended to reduce vibrations in the system.

Final Answer:

Step 1: Use the Fourier's Law for heat conduction.
The heat flow through a wall is given by Fourier's law: Where: - is the heat flow, - is the thermal conductivity (1 kJ/hr.m°C), - is the surface area (2 m²), - and are the temperatures of the inner and outer surfaces (1000°C and 200°C), - is the thickness of the wall (1 m).

Step 2: Substitute the known values.
Substitute , , , , and into the equation:

Final Answer:

Step 1: Formula for overall heat transfer coefficient.
The overall heat transfer coefficient considering fouling is calculated by: Where: - is the overall heat transfer coefficient with fouling, - is the clean heat transfer coefficient, - is the fouling resistance.

Step 2: Solve for the dirty heat transfer coefficient.
Substitute the known values into the equation:

Final Answer:

Step 1: Understanding the Nusselt number in forced convection.
In forced convection, the Nusselt number (Nu) is used to quantify the enhancement of heat transfer due to convection as compared to conduction. The Nusselt number is a function of the Reynolds number (Re), which represents the flow regime (laminar or turbulent), and the Prandtl number (Pr), which characterizes the fluid's thermal properties.

Step 2: Explanation of the options.
- (A) The Nusselt number in forced convection is indeed a function of both the Reynolds number (Re) and the Prandtl number (Pr). - (B) The Grashof number (Gr) is related to natural convection, not forced convection. - (C) The Prandtl number (Pr) and Grashof number (Gr) are involved in natural convection. - (D) The Schmidt number (Sc) is related to mass transfer, not directly to heat transfer in forced convection.

Final Answer:

Step 1: Recall the energy balance equation for the tank.
The rate of change of temperature inside the tank depends on the inflow rate, outflow rate, and the heat transfer. The correct model for this situation is given by the equation in option (A).

Step 2: Conclusion.
The correct answer is (A).

Step 1: Steady-state heat conduction in a plane wall.
For steady-state heat conduction through a plane wall with constant thermal conductivity, the temperature distribution is linear. This follows from Fourier's law of heat conduction: Where: - is the heat flux (constant in steady-state), - is the thermal conductivity (constant), - is the temperature gradient. The solution to this equation, given constant properties and boundary conditions, results in a linear temperature distribution across the plane wall.

Final Answer: