Mass Transfer Coefficient by Surface Renewal 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%
✖Surface Renewal Rate is the fractional rate or frequency of surface renewal.ⓘ Surface Renewal Rate [s]			+10% -10%

✖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.ⓘ Mass Transfer Coefficient by Surface Renewal Theory [k_L]

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Formula

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Mass Transfer Coefficient by Surface Renewal Theory

Formula

`"k"_{"L"} = sqrt("D"_{"AB"}*"s")`

Example

`"0.009165m/s"=sqrt("0.007m²/s"*"0.012/s")`

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Mass Transfer Coefficient by Surface Renewal Theory Solution

STEP 0: Pre-Calculation Summary

Formula Used

Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate)
k_L = sqrt(D_AB*s)
This formula uses 1 Functions, 3 Variables

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

Convective Mass Transfer Coefficient - (Measured in Meter per Second) - 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.
Surface Renewal Rate - (Measured in 1 Per Second) - Surface Renewal Rate is the fractional rate or frequency of surface renewal.

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
Surface Renewal Rate: 0.012 1 Per Second --> 0.012 1 Per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_L = sqrt(D_AB*s) --> sqrt(0.007*0.012)

Evaluating ... ...

k_L = 0.00916515138991168

STEP 3: Convert Result to Output's Unit

0.00916515138991168 Meter per Second --> No Conversion Required

FINAL ANSWER

0.00916515138991168 ≈ 0.009165 Meter per Second <-- Convective Mass Transfer Coefficient

(Calculation completed in 00.008 seconds)

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Created by Vaibhav Mishra

DJ Sanghvi College of Engineering (DJSCE), Mumbai

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< 20 Mass Transfer Theories Calculators

Liquid Phase Mass Transfer Coefficient by Two Film Theory

Go Overall Liquid Phase Mass Transfer Coefficient = 1/((1/(Gas Phase Mass Transfer Coefficient*Henry's Constant))+(1/Liquid Phase Mass Transfer Coefficient))

Instantaneous Mass Transfer Coefficient by Penetration Theory

Go Instantaneous Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)/(pi*Instantaneous Contact Time))

Gas Phase Mass Transfer Coefficient by Two Film Theory

Go Overall Gas Phase Mass Transfer Coefficient = 1/((1/Gas Phase Mass Transfer Coefficient)+(Henry's Constant/Liquid Phase Mass Transfer Coefficient))

Average Mass Transfer Coefficient by Penetration Theory

Go Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))

Instantaneous Contact Time by Penetration Theory

Go Instantaneous Contact Time = (Diffusion Coefficient (DAB))/((Instantaneous Convective Mass Transfer Coefficient^2)*pi)

Diffusivity by Instanataneous Contact Time in Penetration Theory

Go Diffusion Coefficient (DAB) = (Instantaneous Contact Time*(Instantaneous Convective Mass Transfer Coefficient^2)*pi)

Fractional Resistance Offered by Liquid Phase

Go Fractional Resistance Offered by Liquid Phase = (1/Liquid Phase Mass Transfer Coefficient)/(1/Overall Liquid Phase Mass Transfer Coefficient)

Average Contact Time by Penetration Theory

Go Average Contact Time = (4*Diffusion Coefficient (DAB))/((Average Convective Mass Transfer Coefficient^2)*pi)

Diffusivity by Average Contact Time in Penetration Theory

Go Diffusion Coefficient (DAB) = (Average Contact Time*(Average Convective Mass Transfer Coefficient^2)*pi)/4

Overall Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase

Go Overall Liquid Phase Mass Transfer Coefficient = Liquid Phase Mass Transfer Coefficient*Fractional Resistance Offered by Liquid Phase

Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase

Go Liquid Phase Mass Transfer Coefficient = Overall Liquid Phase Mass Transfer Coefficient/Fractional Resistance Offered by Liquid Phase

Fractional Resistance Offered by Gas Phase

Go Fractional Resistance Offered by Gas Phase = (1/Gas Phase Mass Transfer Coefficient)/(1/Overall Gas Phase Mass Transfer Coefficient)

Overall Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase

Go Overall Gas Phase Mass Transfer Coefficient = Gas Phase Mass Transfer Coefficient*Fractional Resistance Offered by Gas Phase

Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase

Go Gas Phase Mass Transfer Coefficient = Overall Gas Phase Mass Transfer Coefficient/Fractional Resistance Offered by Gas Phase

Mass Transfer Coefficient by Surface Renewal Theory

Go Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate)

Surface Renewal Rate by Surface Renewal Theory

Go Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient (DAB)

Diffusivity by Surface Renewal Theory

Go Diffusion Coefficient (DAB) = (Convective Mass Transfer Coefficient^2)/Surface Renewal Rate

Mass Transfer Coefficient by Film Theory

Go Convective Mass Transfer Coefficient = Diffusion Coefficient (DAB)/Film Thickness

Film Thickness by Film Theory

Go Film Thickness = Diffusion Coefficient (DAB)/Convective Mass Transfer Coefficient

Diffusivity by Film Theory

Go Diffusion Coefficient (DAB) = Convective Mass Transfer Coefficient*Film Thickness

< 25 Important Formulas in Mass Transfer Coefficient, Driving Force and Theories Calculators

Convective Mass Transfer Coefficient through Liquid Gas Interface

Go Convective Mass Transfer Coefficient = (Mass Transfer Coefficient of Medium 1*Mass Transfer Coefficient of Medium 2*Henry's Constant)/((Mass Transfer Coefficient of Medium 1*Henry's Constant)+(Mass Transfer Coefficient of Medium 2))

Logarithmic Mean Partial Pressure Difference

Go Logarithmic Mean Partial Pressure Difference = (Partial Pressure of Component B in Mixture 2-Partial Pressure of Component B in Mixture 1)/(ln(Partial Pressure of Component B in Mixture 2/Partial Pressure of Component B in Mixture 1))

Logarithmic Mean of Concentration Difference

Go Logarithmic Mean of Concentration Difference = (Concentration of Component B in Mixture 2-Concentration of Component B in Mixture 1)/ln(Concentration of Component B in Mixture 2/Concentration of Component B in Mixture 1)

Convective Mass Transfer Coefficient

Go Convective Mass Transfer Coefficient = Mass Flux of Diffusion Component A/(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)

Liquid Phase Mass Transfer Coefficient by Two Film Theory

Go Overall Liquid Phase Mass Transfer Coefficient = 1/((1/(Gas Phase Mass Transfer Coefficient*Henry's Constant))+(1/Liquid Phase Mass Transfer Coefficient))

Convective Mass Transfer Coefficient for Simultaneous Heat and Mass Transfer

Go Convective Mass Transfer Coefficient = Heat Transfer Coefficient/(Specific Heat*Density of Liquid*(Lewis Number^0.67))

Gas Phase Mass Transfer Coefficient by Two Film Theory

Go Overall Gas Phase Mass Transfer Coefficient = 1/((1/Gas Phase Mass Transfer Coefficient)+(Henry's Constant/Liquid Phase Mass Transfer Coefficient))

Heat Transfer Coefficient for Simultaneous Heat and Mass Transfer

Go Heat Transfer Coefficient = Convective Mass Transfer Coefficient*Density of Liquid*Specific Heat*(Lewis Number^0.67)

Average Mass Transfer Coefficient by Penetration Theory

Go Average Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient (DAB)/(pi*Average Contact Time))

Convective Mass Transfer Coefficient of Flat Plate in Combined Laminar Turbulent Flow

Go Convective Mass Transfer Coefficient = (0.0286*Free Stream Velocity)/((Reynolds Number^0.2)*(Schmidt Number^0.67))

Convective Mass Transfer Coefficient of Flat Plate Laminar Flow using Reynolds Number

Go Convective Mass Transfer Coefficient = (Free Stream Velocity*0.322)/((Reynolds Number^0.5)*(Schmidt Number^0.67))

Fractional Resistance Offered by Liquid Phase

Go Fractional Resistance Offered by Liquid Phase = (1/Liquid Phase Mass Transfer Coefficient)/(1/Overall Liquid Phase Mass Transfer Coefficient)

Convective Mass Transfer Coefficient of Flat Plate Laminar Flow using Drag Coefficient

Go Convective Mass Transfer Coefficient = (Drag Coefficient*Free Stream Velocity)/(2*(Schmidt Number^0.67))

Convective Mass Transfer Coefficient of Flat Plate Laminar Flow using Friction Factor

Go Convective Mass Transfer Coefficient = (Friction Factor*Free Stream Velocity)/(8*(Schmidt Number^0.67))

Liquid Phase Mass Transfer Coefficient using Fractional Resistance by Liquid Phase

Go Liquid Phase Mass Transfer Coefficient = Overall Liquid Phase Mass Transfer Coefficient/Fractional Resistance Offered by Liquid Phase

Fractional Resistance Offered by Gas Phase

Go Fractional Resistance Offered by Gas Phase = (1/Gas Phase Mass Transfer Coefficient)/(1/Overall Gas Phase Mass Transfer Coefficient)

Gas Phase Mass Transfer Coefficient using Fractional Resistance by Gas Phase

Go Gas Phase Mass Transfer Coefficient = Overall Gas Phase Mass Transfer Coefficient/Fractional Resistance Offered by Gas Phase

Mass Transfer Boundary Layer Thickness of Flat Plate in Laminar Flow

Go Mass Transfer Boundary Layer Thickness at x = Hydrodynamic Boundary Layer Thickness*(Schmidt Number^(-0.333))

Mass Transfer Stanton Number

Go Mass Transfer Stanton Number = Convective Mass Transfer Coefficient/Free Stream Velocity

Average Sherwood Number of Combined Laminar and Turbulent Flow

Go Average Sherwood Number = ((0.037*(Reynolds Number^0.8))-871)*(Schmidt Number^0.333)

Local Sherwood Number for Flat Plate in Turbulent Flow

Go Local Sherwood Number = 0.0296*(Local Reynolds Number^0.8)*(Schmidt Number^0.333)

Local Sherwood Number for Flat Plate in Laminar Flow

Go Local Sherwood Number = 0.332*(Local Reynolds Number^0.5)*(Schmidt Number^0.333)

Average Sherwood Number of Internal Turbulent Flow

Go Average Sherwood Number = 0.023*(Reynolds Number^0.83)*(Schmidt Number^0.44)

Sherwood Number for Flat Plate in Laminar Flow

Go Average Sherwood Number = 0.664*(Reynolds Number^0.5)*(Schmidt Number^0.333)

Average Sherwood Number of Flat Plate Turbulent Flow

Go Average Sherwood Number = 0.037*(Reynolds Number^0.8)

Mass Transfer Coefficient by Surface Renewal Theory Formula

Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate)
k_L = sqrt(D_AB*s)

What is Surface Renewal Theory ?

The surface renewal theory, developed by Danckwerts, applies mathematics of the penetration theory to a more plausible situation, where the liquid is pictured as two regions, a large well mixed bulk region and an interfacial region, which is renewed so fast that it behaves as a thick film.

What are the assumptions of Surface Renewal Theory?

The basic assumptions of the theory are (1) liquid elements at the interface are being randomly swapped by fresh elements from the bulk; (2) At any moment, each of the liquid elements at the interface has the same probability of being substituted by a fresh element; (3) mass transfer from the gas into the liquid element during its stay at the interface takes place under unsteady-state conditions.

How to Calculate Mass Transfer Coefficient by Surface Renewal Theory?

Mass Transfer Coefficient by Surface Renewal Theory calculator uses Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate) to calculate the Convective Mass Transfer Coefficient, The Mass Transfer Coefficient by Surface Renewal Theory formula is used to calculate the mass transfer coefficient in mass transfer based on surface renewal theory using diffusivity and surface renewal rate. Convective Mass Transfer Coefficient is denoted by k_L symbol.

How to calculate Mass Transfer Coefficient by Surface Renewal Theory using this online calculator? To use this online calculator for Mass Transfer Coefficient by Surface Renewal Theory, enter Diffusion Coefficient (DAB) (D_AB) & Surface Renewal Rate (s) and hit the calculate button. Here is how the Mass Transfer Coefficient by Surface Renewal Theory calculation can be explained with given input values -> 0.009165 = sqrt(0.007*0.012).

FAQ

What is Mass Transfer Coefficient by Surface Renewal Theory?

The Mass Transfer Coefficient by Surface Renewal Theory formula is used to calculate the mass transfer coefficient in mass transfer based on surface renewal theory using diffusivity and surface renewal rate and is represented as k_L = sqrt(D_AB*s) or Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate). 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 & Surface Renewal Rate is the fractional rate or frequency of surface renewal.

How to calculate Mass Transfer Coefficient by Surface Renewal Theory?

The Mass Transfer Coefficient by Surface Renewal Theory formula is used to calculate the mass transfer coefficient in mass transfer based on surface renewal theory using diffusivity and surface renewal rate is calculated using Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient (DAB)*Surface Renewal Rate). To calculate Mass Transfer Coefficient by Surface Renewal Theory, you need Diffusion Coefficient (DAB) (D_AB) & Surface Renewal Rate (s). With our tool, you need to enter the respective value for Diffusion Coefficient (DAB) & Surface Renewal Rate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Convective Mass Transfer Coefficient?

In this formula, Convective Mass Transfer Coefficient uses Diffusion Coefficient (DAB) & Surface Renewal Rate. We can use 9 other way(s) to calculate the same, which is/are as follows -

Convective Mass Transfer Coefficient = Diffusion Coefficient (DAB)/Film Thickness
Convective Mass Transfer Coefficient = Mass Flux of Diffusion Component A/(Mass Concentration of Component A in Mixture 1-Mass Concentration of Component A in Mixture 2)
Convective Mass Transfer Coefficient = Heat Transfer Coefficient/(Specific Heat*Density of Liquid*(Lewis Number^0.67))
Convective Mass Transfer Coefficient = (0.0286*Free Stream Velocity)/((Reynolds Number^0.2)*(Schmidt Number^0.67))
Convective Mass Transfer Coefficient = (Drag Coefficient*Free Stream Velocity)/(2*(Schmidt Number^0.67))
Convective Mass Transfer Coefficient = (Friction Factor*Free Stream Velocity)/(8*(Schmidt Number^0.67))
Convective Mass Transfer Coefficient = (Free Stream Velocity*0.322)/((Reynolds Number^0.5)*(Schmidt Number^0.67))
Convective Mass Transfer Coefficient = (Mass Transfer Coefficient of Medium 1*Mass Transfer Coefficient of Medium 2*Henry's Constant)/((Mass Transfer Coefficient of Medium 1*Henry's Constant)+(Mass Transfer Coefficient of Medium 2))
Convective Mass Transfer Coefficient = Diffusion Coefficient (DAB)/Film Thickness

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