Mass Diffusing Rate Through Hollow Cylinder With Solid Boundary Calculator

Formula Used:

\[ \text{Mass Diffusing Rate} = \frac{2\pi D_{AB} L (\rho_{A1} - \rho_{A2})}{\ln\left(\frac{r_2}{r_1}\right)} \]

Diffusion Coefficient (D_AB):

m²/s

Length of Cylinder (L):

Mass Concentration Component A in Mixture 1 (ρ_A1):

kg/m³

Mass Concentration Component A in Mixture 2 (ρ_A2):

kg/m³

Outer Radius (r₂):

Inner Radius (r₁):

Mass Diffusing Rate:

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1. What is Mass Diffusing Rate Through Hollow Cylinder?

The mass diffusing rate through a hollow cylinder with solid boundary describes the rate at which mass (component A) diffuses through the cylindrical wall from the inner surface to the outer surface, driven by a concentration gradient.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Mass Diffusing Rate} = \frac{2\pi D_{AB} L (\rho_{A1} - \rho_{A2})}{\ln\left(\frac{r_2}{r_1}\right)} \]

Where:

\( D_{AB} \) — Diffusion coefficient when A diffuses with B (m²/s)
\( L \) — Length of the cylinder (m)
\( \rho_{A1} \) — Mass concentration of component A in mixture 1 (kg/m³)
\( \rho_{A2} \) — Mass concentration of component A in mixture 2 (kg/m³)
\( r_2 \) — Outer radius of the cylinder (m)
\( r_1 \) — Inner radius of the cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: This formula calculates the steady-state mass transfer rate through a cylindrical wall, accounting for the logarithmic mean area of diffusion.

3. Importance of Mass Diffusion Calculation

Details: Accurate calculation of mass diffusing rate is crucial for designing chemical processes, membrane separation systems, and understanding transport phenomena in cylindrical geometries.

4. Using the Calculator

Tips: Enter all values in SI units. Ensure the outer radius is greater than the inner radius. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the logarithmic term?
A: The logarithmic term accounts for the varying cross-sectional area through which diffusion occurs in cylindrical coordinates.

Q2: When is this formula applicable?
A: This formula applies to steady-state diffusion through a solid cylindrical wall with constant diffusion coefficient and concentration-independent properties.

Q3: What are typical units for mass diffusing rate?
A: The mass diffusing rate is typically measured in kilograms per second (kg/s) in SI units.

Q4: What happens if inner and outer radii are equal?
A: If r₁ = r₂, the denominator becomes ln(1) = 0, resulting in division by zero, which is mathematically undefined.

Q5: Can this formula be used for gases and liquids?
A: Yes, this formula applies to both gases and liquids, provided the diffusion occurs through a solid boundary and the appropriate diffusion coefficient is used.