11 replies to this topic

[firefox23]

Hi, I have an exercise to complete on heat and mass transfer fundamentals and am struggling with a question on heat transfer coefficients. i have attached all of the information and data I have been give and have completed steps a and b. However, I am struggling with the set up and approach for step c. For step a I derived the overall heat transfer efficient U as q/(Tb - Tcw) where Tb is the bulk liquid temperature and Tcw is the coolant temperature. Any help would be much appreciated   IMG_1244.JPG   119.59KB   0 downloads  IMG_1245.JPG   105.53KB   0 downloads  IMG_1246.JPG   115.41KB   0 downloads

[Francisco Angel]

Hi firefox23:

You are not wrong, because you can say:
 

U = q / (Tb-Tcw)

 

assuming q is heat transfer rate divided by area. But in this problem I think the point is that you express the overall heat transfer coefficient as a sum of resistances in series:

 

1/U_overall = 1/U_solids(brass, maybe steel) + 1/U_testsolution + 1/U_coolant

 

You must know from your classes how to determine each of those contributions. Also a correlation is given to calculate the U_testsolution contribution in terms of Reynolds and Prandtl numbers.

In part b they say basically, input the physical property values in the expression obtained in part a and obtain the numerical values of U_testsolution.

Finally in part c they give you the value of U_coolant and ask you to calculate the overall heat transfer value.

Best regards.

Edited by Francisco Angel, 27 February 2017 - 05:56 PM.

[firefox23]

 IMG_1342.JPG   101.69KB   0 downloadsHi,

 

 

Francisco Angel:

 

Thanks for your help it cleared a lot of things up for me. I have now got to the last part of d) and am struggling with finding the evolution of temperature of the can base - foulant interface, which I have called Tfb, and the foulant - solution interface, which I have called Tfs. I have attached equations which I tried to use but I do not think are correct. I think the equation for Tfb may be correct but am unsure about how to find Tfs. Any more assistance would be greatly appreciated!

[firefox23]

Also the values I found for U_coolant for part b were in the range 190 - 277, but the value stated in c is 400 which is outside of the temperature range 10 - 60 degrees. Have i calcualted these h values wrong do you think?

[Francisco Angel]

Dear firefox:

 

I edited my first post.  I made a typo there.  The correlation given to you is used to calculate the solution heat transfer coefficient, part b is also about calculating the solution heat transfer coefficient using that correlation. The value 400 given in the problem corresponds to the coolant, so both values refer to different things.

 

In the pages you attached in your first post, part d was not shown.  Can you attach it?

 

Best regards.

[firefox23]

Apologies I have now attached the rest of the questions. I have also attached some of the data provided.  The value I found for Uclean in part b was 199.479, which I hope is correct.

 

 IMG_1345.JPG   256.12KB   0 downloads  IMG_1344.JPG   121.78KB   0 downloadsHi,

[Francisco Angel]

IMG_1345.JPGIMG_1344.JPG

 

 

Hi firefox23:

You are not wrong, because you can say:
 

U = q / (Tb-Tcw)

 

assuming q is heat transfer rate divided by area. But in this problem I think the point is that you express the overall heat transfer coefficient as a sum of resistances in series:

 

1/U_overall = 1/U_solids(brass, maybe steel) + 1/U_testsolution + 1/U_coolant

 

You must know from your classes how to determine each of those contributions. Also a correlation is given to calculate the U_coolant contribution in terms of Reynolds and Prandtl numbers.

In part b they say basically, input the physical property values in the expression obtained in part a and obtain the numerical values of U_coolant.

Finally in part c they give you the value of U_coolant and ask you to calculate the overall heat transfer value.

Best regards.

Also the values I found for U_coolant for part b were in the range 190 - 277, but the value stated in c is 400 which is outside of the temperature range 10 - 60 degrees. Have i calcualted these h values wrong do you think?

 

Dear firefox:

I edited my first post, I made a typo there, the correlation given to you is used to calculate the solution heat transfer coefficient, part b is also about calculating the solution heat transfer coefficient using that correlation. The value 400 given in the problem corresponds to the coolant, so both values refer to different things.

In the pages you attached in your firts post, part d was not shown, can you attach it?

Best regards.

 

Hi,

 

Apologies I have now attached the rest of the questions. I have also attached some of the data provided. The value I found for Uclean in part b was 199.479, which I hope is correct.

Dear firefox:

As suggested in part e, to calculate the resistance of the test solution you need to apply an interative procedure, because the correlation uses the physical properties at the film temperature, so in part b you would go like this:

 

i) Guess film temperature, say bulk temperature of the test solution.

ii) Calculate heat transfer resistances, don't forget the resistance of the heat flux sensor!

iii) Determine the heat flux value.

iv) Use the value of heat flux to determine the intermediate temperatures.

v) Compare the calculated film temperature with the guessed value, and update the guess if necessary, that means returning to step i).

 

As for the value of 199.479 you obtained, I try to not give students all the work done when replying in the forum, that means in most cases I would not plug the values in a spreadsheet myself, just give you indications, please understand my point of view.

 

As for the procedure to calculate intermediate temperatures, it is like this (I will denote T(a, b )as the temperature at the interface betweeen a and  b .

1) You write heat transfer equation for every layer:

 

T(bulk)- T(bulk,fouling) = q / U(bulk)

T(bulk,fouling)-T(fouling,stainlesssteel) = q / U(fouling)

T(fouling,stainlesssteel) - T (brass,stainlesssteel) =  q / U (stainlesssteel)

T (brass,stainlesssteel)- T(brass, coolant) = q / U (brass, heat sensor) I included here the heat flux sensor resistance.

T(brass, coolant)- T(coolant) = q / U(coolant)

 

2) You use the facts that:

   i) You know the "start" and "final" temperatures, say T(coolant) and T(bulk).

   ii) Heat flux is the same in every layer (not necessarily correct if transient problem).

   iii) You know how to calculate "U" values.

 

  Then sum all the previous equations, note that intermediate temperatures cancel out.

 

T(bulk)- T(coolant) = q * ( 1/U(bulk)+1/ U(fouling)+1/ U (stainlesssteel)+1/ U (brass, heat sensor)+1/ U(coolant))

 

From the previous equation you can determine the value of "q". Now you use that value to sustitute in every "layer" equation to determine the value of every intermediate temperature.

 

Hope that helps. Best regards.

Edited by Francisco Angel, 27 February 2017 - 06:46 PM.

[firefox23]

 

IMG_1345.JPGIMG_1344.JPG

 

 

Hi firefox23:

You are not wrong, because you can say:
 

U = q / (Tb-Tcw)

 

assuming q is heat transfer rate divided by area. But in this problem I think the point is that you express the overall heat transfer coefficient as a sum of resistances in series:

 

1/U_overall = 1/U_solids(brass, maybe steel) + 1/U_testsolution + 1/U_coolant

 

You must know from your classes how to determine each of those contributions. Also a correlation is given to calculate the U_coolant contribution in terms of Reynolds and Prandtl numbers.

In part b they say basically, input the physical property values in the expression obtained in part a and obtain the numerical values of U_coolant.

Finally in part c they give you the value of U_coolant and ask you to calculate the overall heat transfer value.

Best regards.

Also the values I found for U_coolant for part b were in the range 190 - 277, but the value stated in c is 400 which is outside of the temperature range 10 - 60 degrees. Have i calcualted these h values wrong do you think?

 

Dear firefox:

I edited my first post, I made a typo there, the correlation given to you is used to calculate the solution heat transfer coefficient, part b is also about calculating the solution heat transfer coefficient using that correlation. The value 400 given in the problem corresponds to the coolant, so both values refer to different things.

In the pages you attached in your firts post, part d was not shown, can you attach it?

Best regards.

 

Hi,

 

Apologies I have now attached the rest of the questions. I have also attached some of the data provided. The value I found for Uclean in part b was 199.479, which I hope is correct.

Dear firefox:

As suggested in part e, to calculate the resistance of the test solution you need to apply an interative procedure, because the correlation uses the physical properties at the film temperature, so in part b you would go like this:

 

i) Guess film temperature, say bulk temperature of the test solution.

ii) Calculate heat transfer resistances, don't forget the resistance of the heat flux sensor!

iii) Determine the heat flux value.

iv) Use the value of heat flux to determine the intermediate temperatures.

v) Compare the calculated film temperature with the guessed value, and update the guess if necessary, that means returning to step i).

 

As for the value of 199.479 you obtained, I try to not give students all the work done when replying in the forum, that means in most cases I would not plug the values in a spreadsheet myself, just give you indications, please understand my point of view.

 

As for the procedure to calculate intermediate temperatures, it is like this (I will denote T(a, b )as the temperature at the interface betweeen a and  b .

1) You write heat transfer equation for every layer:

 

T(bulk)- T(bulk,fouling) = q / U(bulk)

T(bulk,fouling)-T(fouling,stainlesssteel) = q / U(fouling)

T(fouling,stainlesssteel) - T (brass,stainlesssteel) =  q / U (stainlesssteel)

T (brass,stainlesssteel)- T(brass, coolant) = q / U (brass, heat sensor) I included here the heat flux sensor resistance.

T(brass, coolant)- T(coolant) = q / U(coolant)

 

2) You use the facts that:

   i) You know the "start" and "final" temperatures, say T(coolant) and T(bulk).

   ii) Heat flux is the same in every layer (not necessarily correct if transient problem).

   iii) You know how to calculate "U" values.

 

  Then sum all the previous equations, note that intermediate temperatures cancel out.

 

T(bulk)- T(coolant) = q * ( 1/U(bulk)+1/ U(fouling)+1/ U (stainlesssteel)+1/ U (brass, heat sensor)+1/ U(coolant))

 

From the previous equation you can determine the value of "q". Now you use that value to sustitute in every "layer" equation to determine the value of every intermediate temperature.

 

Hope that helps. Best regards.

 

Hi,

 

Of course I completely understand its more important for me to work through it by myself. That all makes sense I've now worked through part d. I now think I may have misunderstood part b.in order to find U_Bulk  need to use equation  given to me. The initial surface temperature, Ts is also a function of this U value so am I correct in thinking that i need to create a circular reference on excel to find U_Bulk, U_clean and Ts? 

[Francisco Angel]

Hi,

 

Of course I completely understand its more important for me to work through it by myself. That all makes sense I've now worked through part d. I now think I may have misunderstood part b.in order to find U_Bulk  need to use equation  given to me. The initial surface temperature, Ts is also a function of this U value so am I correct in thinking that i need to create a circular reference on excel to find U_Bulk, U_clean and Ts? 

 

 

You are right, it was my error to suggest that you must use an iterative procedure in part b. In part b you can calculate directly using the correlation because a temperature interval is given to you.

In part c you need to use the iterative procedure that I outlined in my previous post, because you need to calculate U_testsolution using the surface temperature, which is unknown at first. A circular reference is by definition an error on excel so it is not the way to go. As I explained before the procedure is like this:

 

Guess T_s -> Calculate U_testsolution -> Calculate q -> Using q to calculate T_s

 

The criteria for convergence is the equality of the guessed and calculated value of T_s.  You can implement this in a variety of ways. For example if you input a guessed value of T_s at one cell, and then calculate U_testsolution, q and "T_s calculated" as dependent cells, you can:

 

* Repeteadly paste the value of "T_s calculated" cell on the cell that contains the guessed T_s value until you consider that convergence as been reached (Is important that you only paste the "value", check "past special" options, or an error circular reference will be raised).

*Use the value of "T_s calculated" to perfom another iteration of the calculation of U_bulk, q and T_s, say advancing one iteration by row at excel until you consider the calculation converged.

*Use the solver to adjust the "T_s guessed"  value to equate it to the "T_s calculated" value, for example minimizing the difference of both values, raised to second power.

*Create a small VBA script that makes the the "copy only the value" operation until a convergence criteria is satisfied (using a WHILE loop for example).

*Create a VBA script that handles all the calculation internally and only outputs the converged results.

 

Etc, etc.

 

Solution utilizing code are more scallable in my opinion. Also remember that in part e you will need to use the iterative procedure again.

 

Best regards.

[firefox23]

 

Hi,

 

Of course I completely understand its more important for me to work through it by myself. That all makes sense I've now worked through part d. I now think I may have misunderstood part b.in order to find U_Bulk  need to use equation  given to me. The initial surface temperature, Ts is also a function of this U value so am I correct in thinking that i need to create a circular reference on excel to find U_Bulk, U_clean and Ts? 

 

 

You are right, it was my error to suggest that you must use an iterative procedure in part b. In part b you can calculate directly using the correlation because a temperature interval is given to you.

In part c you need to use the iterative procedure that I outlined in my previous post, because you need to calculate U_testsolution using the surface temperature, which is unknown at first. A circular reference is by definition an error on excel so it is not the way to go. As I explained before the procedure is like this:

 

Guess T_s -> Calculate U_testsolution -> Calculate q -> Using q to calculate T_s

 

The criteria for convergence is the equality of the guessed and calculated value of T_s.  You can implement this in a variety of ways. For example if you input a guessed value of T_s at one cell, and then calculate U_testsolution, q and "T_s calculated" as dependent cells, you can:

 

* Repeteadly paste the value of "T_s calculated" cell on the cell that contains the guessed T_s value until you consider that convergence as been reached (Is important that you only paste the "value", check "past special" options, or an error circular reference will be raised).

*Use the value of "T_s calculated" to perfom another iteration of the calculation of U_bulk, q and T_s, say advancing one iteration by row at excel until you consider the calculation converged.

*Use the solver to adjust the "T_s guessed"  value to equate it to the "T_s calculated" value, for example minimizing the difference of both values, raised to second power.

*Create a small VBA script that makes the the "copy only the value" operation until a convergence criteria is satisfied (using a WHILE loop for example).

*Create a VBA script that handles all the calculation internally and only outputs the converged results.

 

Etc, etc.

 

Solution utilizing code are more scallable in my opinion. Also remember that in part e you will need to use the iterative procedure again.

 

Best regards.

 

Thanks, that all makes sense although I don't know why i need to find values for q when these are provided? Would I be able to guess the T_s value for each provided q value and then calculate U_Bulk and T_s and use solver to minimise the difference between guessed and calculated values?

[Francisco Angel]

 

Thanks, that all makes sense although I don't know why i need to find values for q when these are provided? Would I be able to guess the T_s value for each provided q value and then calculate U_Bulk and T_s and use solver to minimise the difference between guessed and calculated values?

 

 Yes you are right, I thought that the values provided to you were U(t) according to :
 

R_f(t) = 1 / U(t) -1 / U_clean

 

 in section d. I didn't know that instead the values of heat flux were provided. So in this case, if you know heat flux, I think you can proceed directly from the upper layer, calculating temperatures at the different interfaces, until you reach the stainless steel - foulant interface. There you would probably need an iteration, because the temperature of the foulant-test solution interface, required to calculate the test solution heat transfer coefficient, is unknown.

I think at this point you understand the problem better than I .

Best regards.

[firefox23]

 

 

Thanks, that all makes sense although I don't know why i need to find values for q when these are provided? Would I be able to guess the T_s value for each provided q value and then calculate U_Bulk and T_s and use solver to minimise the difference between guessed and calculated values?

 

 Yes you are right, I thought that the values provided to you were U(t) according to :
 

R_f(t) = 1 / U(t) -1 / U_clean

 

 in section d. I didn't know that instead the values of heat flux were provided. So in this case, if you know heat flux, I think you can proceed directly from the upper layer, calculating temperatures at the different interfaces, until you reach the stainless steel - foulant interface. There you would probably need an iteration, because the temperature of the foulant-test solution interface, required to calculate the test solution heat transfer coefficient, is unknown.

I think at this point you understand the problem better than I .

Best regards.

 

Great, thanks so much for all your help! i think I now understand the problem, although I am having some issues with solver but nothing i can't work through I don't think! Thanks again