Question on Mass transfer coefficient (Sc Number)

[sero2000]

Homework Statement

What is the mass transfer coefficient for natural convection from rock salt (assume flow is over a horizontal cylinder (salt crystal) of length 2cm, diameter 0.5cm).

Given:

Temperature = 24degrees
Density of salt 2165kg/m^3
Density of mixture when salt concentration is saturated = 1310kg/m^3

Homework Equations

Sh = C2 (Gr.Sc)^p
Sc = Kinematic viscosity/Diffusivity

The Attempt at a Solution

I am having trouble finding the correct diffusivity to use for the Sc number. I have previously calculated the maximium concentration of the salt in the water. Which is 6kmol/m^3 and i also a table of values for the diffusivity for different solute concentrations.

So the qn is do i use the maximium concentration of salt to find my diffusivity or do I have to use the actual concentration? Thats because I am not given the volume of the solvent even though i am able to find the mass of the solute by finding the volume of solute x the density.

A great big load of thanks in advance.

 

[Chestermiller]

I assume what you mean by maximum concentration is the concentration of an aqueous solution saturated with salt. That is certainly the concentration at the rock salt interface. This is the appropriate diffusivity value to use. I also assume that, far from the rock salt, the concentration of the salt in the solution is zero.

Chet

 

[sero2000]

I assume what you mean by maximum concentration is the concentration of an aqueous solution saturated with salt. That is certainly the concentration at the rock salt interface. This is the appropriate diffusivity value to use. I also assume that, far from the rock salt, the concentration of the salt in the solution is zero.

Chet

Hi there, thanks!. Another question though, for the grashof number, I am given the formula as

Gr = [g ( Densitybulk - Densitysurface)]/film density x Kinematic viscosity.

So I found the density of the bulk which is 1000kg/m^3 and the density of the surface layer which is 2156kg/m^3. For the film density I just took the sum of the 2 densities and divided by 2.

Question is, for the kinematic viscosity, do i use the dynamic viscosity of the bulk fluid at 24°C which is 855x10^-6 and divide by it's density which is 1000kg/m^3 or do I divide it by the film density?

 

[Chestermiller]

Hi there, thanks!. Another question though, for the grashof number, I am given the formula as

Gr = [g ( Densitybulk - Densitysurface)]/film density x Kinematic viscosity.

So I found the density of the bulk which is 1000kg/m^3 and the density of the surface layer which is 2156kg/m^3. For the film density I just took the sum of the 2 densities and divided by 2.

You don't use the density of the solid salt. You use the density of the saturated aqueous salt solution.

Question is, for the kinematic viscosity, do i use the dynamic viscosity of the bulk fluid at 24°C which is 855x10^-6 and divide by it's density which is 1000kg/m^3 or do I divide it by the film density?

I would divide by the film density. What does your book recommend? It doesn't matter much because, if I remember correctly, p = 0.25.

Chet

 

[sero2000]

You don't use the density of the solid salt. You use the density of the saturated aqueous salt solution.

I would divide by the film density. What does your book recommend? It doesn't matter much because, if I remember correctly, p = 0.25.

Chet

Is there a reason we use the saturated aqueous salt solution density? Does it have something to do with the interface?

My notes don't really say much about all these. It just mentions use properties at the film density. I borrowed a textbook from the library but it does not explain much as well. I just find it weird that I am taking the dynamic viscosity of water divided by the density of something that is not water.

 

[Chestermiller]

Is there a reason we use the saturated aqueous salt solution density? Does it have something to do with the interface?

The equations you are using apply to mass transfer in the liquid phase.

My notes don't really say much about all these. It just mentions use properties at the film density. I borrowed a textbook from the library but it does not explain much as well. I just find it weird that I am taking the dynamic viscosity of water divided by the density of something that is not water.

How different is the viscosity of saturated salt water from the viscosity of pure water?