Question

If the baffle spacing in a shell and tube heat exchanger increases, then the Reynolds number of the shell side fluid:

• A. Remains unchanged
• B. Decreases
• C. Increases
• D. First increases then decreases

Hint:

Baffle spacing control parameters: - Closer Baffles (\( B \downarrow \)) \( \rightarrow \) Smaller area \( \rightarrow \) Higher velocity \( \rightarrow \) Higher Reynolds number \( \rightarrow \) Greater Heat Transfer (but accompanied by a higher pressure drop penalty). - Farther Baffles (\( B \uparrow \)) \( \rightarrow \) Larger area \( \rightarrow \) Lower velocity \( \rightarrow \) Lower Reynolds number (\( Re_s \downarrow \)).

Answer 1

The Correct Option is B

Concept: In shell and tube heat exchangers, baffles are installed internally within the main shell chamber to support the internal tube bundles, prevent structural vibration damage, and crucially force the shell-side process fluid to flow back and forth across the tube array in a cross-flow manner. This pattern enhances turbulence and increases the convective heat transfer coefficient. The definition of the Reynolds number on the shell side is given by: \[ Re_s = \frac{D_e \cdot G_s}{\mu} = \frac{D_e \cdot \dot{m}_s}{A_s \cdot \mu} \] Where:
• \( D_e \) represents the equivalent hydraulic diameter of the shell side channel.
• \( G_s \) represents the mass velocity of the fluid inside the shell (\( G_s = \dot{m}_s / A_s \)).
• \( \dot{m}_s \) represents the total mass flow rate entering the shell chamber.
• \( A_s \) represents the cross-flow area available for fluid movement near the center line.
• \( \mu \) represents the dynamic fluid viscosity parameter.

Step 1: Defining the cross-flow cross-sectional area equation.
The cross-flow area at the shell centerline, denoted as \( A_s \), is calculated using standard heat exchanger geometry equations (such as Kern's formulation method): \[ A_s = \frac{D_s \cdot C \cdot B}{P_T} \] Where:
• \( D_s \) is the internal diameter of the shell casing.
• \( C \) is the clearance distance separating adjacent parallel tubes (\( C = P_T - d_o \)).
• \( P_T \) is the center-to-center distance or tube pitch.
• \( B \) is the baffle spacing distance.

Step 2: Evaluating the mathematical effect of an increase in baffle spacing.
From the geometric definition of the flow area, we observe that the area \( A_s \) is directly proportional to the baffle spacing parameter \( B \): \[ A_s \propto B \] When the design spacing between consecutive baffles (\( B \)) is explicitly increased while holding other mechanical design aspects constant: \[ B \uparrow \quad \Rightarrow \quad A_s \uparrow \] An increase in baffle spacing provides a larger cross-flow area for the fluid inside the shell.

Step 3: Analyzing the consequence on fluid velocity and Reynolds number.
Let us substitute this area dependency back into the core formula tracking the shell-side Reynolds number: \[ Re_s = \frac{D_e \cdot \dot{m}_s}{\mu \cdot \left( \frac{D_s \cdot C \cdot B}{P_T} \right)} \] By grouping all static constants together into a single global system multiplier constant \( K \), the relationship reduces to: \[ Re_s = \frac{K}{B} \quad \Rightarrow \quad Re_s \propto \frac{1}{B} \] This expression confirms that the Reynolds number of the shell side fluid is inversely proportional to the spacing between consecutive baffles. Consequently, when the baffle spacing \( B \) is increased, the effective cross-sectional flow area \( A_s \) increases, causing the linear fluid velocity to drop. This reduction in velocity leads to a corresponding decrease in the shell-side Reynolds number (\( Re_s \)).