Average Mass Transfer Coefficient by Penetration Theory Calculator

✖The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit.ⓘ Diffusion Coefficient (DAB) [D_AB]			+10% -10%
✖Average Contact Time is the variable used to define the time for contacting between liquid and vapor phases.ⓘ Average Contact Time [t_c]			+10% -10%

✖The Average Convective Mass Transfer Coefficient is a function of geometry of the system and the velocity and properties of the fluid similar to the heat transfer coefficient.ⓘ Average Mass Transfer Coefficient by Penetration Theory [k_{L (Avg)}]

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Average Mass Transfer Coefficient by Penetration Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))
k_{L (Avg)} = 2*sqrt(D_AB/(pi*t_c))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Average Convective Mass Transfer Coefficient - (Measured in Meter per Second) - The Average Convective Mass Transfer Coefficient is a function of geometry of the system and the velocity and properties of the fluid similar to the heat transfer coefficient.
Diffusion Coefficient (DAB) - (Measured in Square Meter Per Second) - The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit.
Average Contact Time - (Measured in Second) - Average Contact Time is the variable used to define the time for contacting between liquid and vapor phases.

STEP 1: Convert Input(s) to Base Unit

Diffusion Coefficient (DAB): 0.007 Square Meter Per Second --> 0.007 Square Meter Per Second No Conversion Required
Average Contact Time: 11 Second --> 11 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_{L (Avg)} = 2*sqrt(D_AB/(pi*t_c)) --> 2*sqrt(0.007/(pi*11))

Evaluating ... ...

k_{L (Avg)} = 0.0284647737853237

STEP 3: Convert Result to Output's Unit

0.0284647737853237 Meter per Second --> No Conversion Required

FINAL ANSWER

0.0284647737853237 ≈ 0.028465 Meter per Second <-- Average Convective Mass Transfer Coefficient

(Calculation completed in 00.020 seconds)

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DJ Sanghvi College of Engineering (DJSCE), Mumbai

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Average Mass Transfer Coefficient by Penetration Theory Formula

LaTeX Go

Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))
k_{L (Avg)} = 2*sqrt(D_AB/(pi*t_c))

What is Penetration Theory?

The “Penetration Theory” or “Higbie’s model” assumes that each liquid element at the gas-liquid interface is exposed to the gas for a short time. The basic assumptions of the theory are: (1) Mass transfer from the gas into a liquid element occurs under unsteady-state conditions once they are in contact; (2) Each of the liquid elements stays in contact with the gas for same time period; and (3) Equilibrium exists at the gas-liquid interface. This theory was considered an improvement from the two-film theory since mass transfer occurs under unsteady-state conditions in many industrial processes. The Penetration Theory expresses the liquid-side mass transfer coefficient in terms of the contact time and the molecular diffusivity of the gas in the liquid.

How to Calculate Average Mass Transfer Coefficient by Penetration Theory?

Average Mass Transfer Coefficient by Penetration Theory calculator uses Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time)) to calculate the Average Convective Mass Transfer Coefficient, The Average Mass Transfer Coefficient by Penetration Theory formula is used to calculate the average mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory. Average Convective Mass Transfer Coefficient is denoted by k_{L (Avg)} symbol.

How to calculate Average Mass Transfer Coefficient by Penetration Theory using this online calculator? To use this online calculator for Average Mass Transfer Coefficient by Penetration Theory, enter Diffusion Coefficient (DAB) (D_AB) & Average Contact Time (t_c) and hit the calculate button. Here is how the Average Mass Transfer Coefficient by Penetration Theory calculation can be explained with given input values -> 0.028465 = 2*sqrt(0.007/(pi*11)).

FAQ

What is Average Mass Transfer Coefficient by Penetration Theory?

The Average Mass Transfer Coefficient by Penetration Theory formula is used to calculate the average mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory and is represented as k_{L (Avg)} = 2*sqrt(D_AB/(pi*t_c)) or Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time)). The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 second under the influence of a gradient of one unit & Average Contact Time is the variable used to define the time for contacting between liquid and vapor phases.

How to calculate Average Mass Transfer Coefficient by Penetration Theory?

The Average Mass Transfer Coefficient by Penetration Theory formula is used to calculate the average mass transfer coefficient for the liquid phase in contact with the other phase based on penetration theory is calculated using Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time)). To calculate Average Mass Transfer Coefficient by Penetration Theory, you need Diffusion Coefficient (DAB) (D_AB) & Average Contact Time (t_c). With our tool, you need to enter the respective value for Diffusion Coefficient (DAB) & Average Contact Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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