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Surface Renewal Rate based on Surface Renewal Theory Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient
s = (kL^2)/DAB
This formula uses 2 Variables
Variables Used
Convective Mass Transfer Coefficient - 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. (Measured in Meter per Second)
Diffusion Coefficient - The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 s under the influence of a gradient of one unit. (Measured in Square Meter Per Second)
STEP 1: Convert Input(s) to Base Unit
Convective Mass Transfer Coefficient: 0.0095 Meter per Second --> 0.0095 Meter per Second No Conversion Required
Diffusion Coefficient: 0.005 Square Meter Per Second --> 0.005 Square Meter Per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
s = (kL^2)/DAB --> (0.0095^2)/0.005
Evaluating ... ...
s = 0.01805
STEP 3: Convert Result to Output's Unit
0.01805 1 Per Second --> No Conversion Required
FINAL ANSWER
0.01805 1 Per Second <-- Surface Renewal Rate
(Calculation completed in 00.000 seconds)

7 Mass Transfer Theories Calculators

Penetration Theory of Mass Transfer
Convective Mass Transfer Coefficient = 2*sqrt(Diffusion Coefficient/(pi*Contact Time)) Go
Contact Time based on Penetration Theory
Contact Time = (4*Diffusion Coefficient)/((Convective Mass Transfer Coefficient^2)*pi) Go
Mass Transfer Coefficient based on Surface Renewal Theory
Convective Mass Transfer Coefficient = sqrt(Diffusion Coefficient*Surface Renewal Rate) Go
Surface Renewal Rate based on Surface Renewal Theory
Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient Go
Mass Transfer Coefficient based on Film Theory
Convective Mass Transfer Coefficient = Diffusion Coefficient/Film Thickness Go
Film Thickness based on Film Theory
Film Thickness = Diffusion Coefficient/Convective Mass Transfer Coefficient Go
Diffusivity Based on Film Theory
Diffusion Coefficient = Convective Mass Transfer Coefficient*Film Thickness Go

Surface Renewal Rate based on Surface Renewal Theory Formula

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

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; and (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 Surface Renewal Rate based on Surface Renewal Theory?

Surface Renewal Rate based on Surface Renewal Theory calculator uses Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient to calculate the Surface Renewal Rate, The Surface Renewal Rate based on Surface Renewal Theory formula is used to calculate the surface renewal rate in mass transfer based on surface renewal theory using diffusivity and mass transfer coefficient. Surface Renewal Rate is denoted by s symbol.

How to calculate Surface Renewal Rate based on Surface Renewal Theory using this online calculator? To use this online calculator for Surface Renewal Rate based on Surface Renewal Theory, enter Convective Mass Transfer Coefficient (kL) & Diffusion Coefficient (DAB) and hit the calculate button. Here is how the Surface Renewal Rate based on Surface Renewal Theory calculation can be explained with given input values -> 0.01805 = (0.0095^2)/0.005.

FAQ

What is Surface Renewal Rate based on Surface Renewal Theory?
The Surface Renewal Rate based on Surface Renewal Theory formula is used to calculate the surface renewal rate in mass transfer based on surface renewal theory using diffusivity and mass transfer coefficient and is represented as s = (kL^2)/DAB or Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient. 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 & The Diffusion Coefficient (DAB) is the amount of a particular substance that diffuses across a unit area in 1 s under the influence of a gradient of one unit.
How to calculate Surface Renewal Rate based on Surface Renewal Theory?
The Surface Renewal Rate based on Surface Renewal Theory formula is used to calculate the surface renewal rate in mass transfer based on surface renewal theory using diffusivity and mass transfer coefficient is calculated using Surface Renewal Rate = (Convective Mass Transfer Coefficient^2)/Diffusion Coefficient. To calculate Surface Renewal Rate based on Surface Renewal Theory, you need Convective Mass Transfer Coefficient (kL) & Diffusion Coefficient (DAB). With our tool, you need to enter the respective value for Convective Mass Transfer Coefficient & Diffusion Coefficient 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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