Temperature of fluid flowing through pipe

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Discussion Overview

The discussion revolves around the mathematical relationship for temperature change in a fluid flowing through a pipe. Participants explore various parameters that may influence this temperature change, including fluid properties and flow conditions, and consider both theoretical and practical applications, particularly in automotive contexts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning
  • Experimental/applied

Main Points Raised

  • Some participants propose that key parameters affecting temperature change include cross-sectional diameter, viscosity, volumetric flow rate, specific heat, length of the pipe, density, and thermal conductivity of the fluid.
  • Others mention the importance of the thermal properties of the pipe itself and suggest that heat transfer resistance within the pipe and through the pipe wall must be considered.
  • A participant highlights the need for a frame of reference, particularly in the context of exhaust pipes and radiator hoses, suggesting that velocity and specific heat are not the only factors involved.
  • There is a discussion about Fanno flow analysis and its relevance to understanding flow exit velocity and temperature change.
  • Some participants express uncertainty about the applicability of the equation Q = mcΔT for fluids in motion, questioning its relevance in the context of heating by an engine.
  • References to textbooks such as "Transport Phenomena" and "Heat Transmission" are made, with participants seeking specific chapters relevant to their inquiries.
  • One participant indicates they found the equation they were looking for in a textbook but expresses a desire for further assistance.
  • There is a query about the distinction between energy and power in relation to temperature difference, particularly in continuously heated fluids.

Areas of Agreement / Disagreement

Participants generally agree on the importance of various parameters affecting temperature change, but multiple competing views remain regarding the specific relationships and equations applicable to different scenarios, particularly in automotive applications. The discussion remains unresolved on several technical points.

Contextual Notes

Limitations include the dependence on specific definitions of parameters and the complexity of heat transfer phenomena in practical applications, which may not be fully captured by simple equations. Some participants note that the equations discussed may not provide a direct mathematical relation for all scenarios.

  • #121
You can always put the data in as discrete values in a table that you can interpolate.

There are certainly many sites which will allow me to find an equation using polynomial interpolation. But I would imagine that such a basic study of the physical parameters of important (common) gases like N2, CO2 and H2O should have been available now in literature.

But I will do what you are saying. Is it good if I tabulate the results in intervals of 20 degrees, or is that too much, or too less?
 
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  • #123
Hi Chet,

In the stage where we are calculating the Nusselt number for the gas, is there a better way to come up with the proportionality constant instead of the graph in BSL? I mean, in my code, I want to actually get the value of the ordinate.

Now, ordinate axis has a complicated looking equation on it which uses the heat transfer coefficient (which we wouldn't have at that point). My question is : Is there a way to calculate the ordinate value instead of looking up the graph?
 
  • #124
Actually, the ordinate is simply Nu/(RePr^(1/3)). No equation is involved. I would fit a piecewise linear variation to the curve, as a function of Re. I would do the fit in the logs. So, once you know Re, you know Nu.

Chet
 
  • #125
But what is this linear variation exactly? What is the equation for it?

The graph in BSL doesn't have a very good resolution. The line of the sketch is not fine, its pretty thick and the ordinate axis is not calibrated.
 
  • #126
In the code I have for now, I am using 0.004 as the proportionality constant. However, there is another issue. The temperature of gas variable seems pretty high.

I put dummy values :

RPM : 88
temperature of pipe wall : 125 C (398 K)
ambient temperature : 35 C (308 K)
mileage : 28 mpg
x : 10 cm (0.1 m)
d : 7 cm (0.07 m)

I get the gas temperature as 1135 K (862 C). Are these values reasonable? If the temperature is 862 C, I imagine the pipe would start to melt?
 
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  • #127
Jay_ said:
In the code I have for now, I am using 0.004 as the proportionality constant. However, there is another issue. The temperature of gas variable seems pretty high.

I put dummy values :

RPM : 88
temperature of pipe wall : 125 C (398 K)
ambient temperature : 35 C (308 K)
mileage : 28 mpg
x : 10 cm (0.1 m)
d : 7 cm (0.07 m)

I get the gas temperature as 1135 K (862 C). Are these values reasonable? If the temperature is 862 C, I imagine the pipe would start to melt?
No. It doesn't seem reasonable. What were your values of h1 and h2?

Chet
 
  • #128
Jay_ said:
But what is this linear variation exactly? What is the equation for it?

The graph in BSL doesn't have a very good resolution. The line of the sketch is not fine, its pretty thick and the ordinate axis is not calibrated.
Use 0.004 from 4000 to 10000, and 0.003 at 60000, with a linear fit on the log of the ordinate between 10000 and 60000.

I hate to bring this up at such a late date, but for the gas flow in the pipe, the figure assumes that the gas velocity profile is fully developed (parabolic) at the entrance to the pipe (exit of the muffler). But, for such a short pipe, this is unlikely to be the case. It will be closer to a flat velocity profile, with a boundary layer on the inside wall of the pipe. Under these circumstances, the correct correlation to use is the flat plate approximation (even inside the pipe), with the free stream gas velocity taken equal to the mass flow rate in the pipe divided by the gas density times the cross sectional area. I am recommending that you run a quick scouting calculation to see what value you get for h1 using this approach.

Chet
 
  • #129
Use 0.004 from 4000 to 10000, and 0.003 at 60000, with a linear fit on the log of the ordinate between 10000 and 60000.

Okay. So that fixes it.

Regarding your second paragraph - are you saying I need to calculate the Reynolds number, Nusselt number and heat transfer coefficient for the inside the same way I did for the outside and see what results I get.

In this case, I would need the density of the gas mixture because the Reynolds equation requires it. And the velocity would be the velocity of the gas? And then I use 0.332(Re^0.5)(Pr^(1/3)) ?
 
  • #130
Jay_ said:
Okay. So that fixes it.
Yes.
Regarding your second paragraph - are you saying I need to calculate the Reynolds number, Nusselt number and heat transfer coefficient for the inside the same way I did for the outside and see what results I get.
Yes, just to see.
In this case, I would need the density of the gas mixture because the Reynolds equation requires it. And the velocity would be the velocity of the gas?

No. You don't need the density. ρv=w/A.
And then I use 0.332(Re^0.5)(Pr^(1/3)) ?
Yes
 
  • #131
Okay. I made a huge blunder. When calculating the speed of the flat plate for hout, I multiplied the RPM data with the diameter of the pipe, it should the diameter of the tire!

Now I get hout = 10.7, and hin = 3.66. Do these values sound reasonable in SI units?

This time the dummy data was similar :

RPM : 88
temperature of pipe wall : 125 C (398 K)
ambient temperature : 35 C (308 K)
mileage : 28 mpg
tire diameter : 26 inches (0.6604 m) (The one I missed out!)
x : 10 cm (0.1 m)
d : 7 cm (0.07 m)

I get gas temperature to be 661 K (388 C)
 
  • #132
The car speed seems very low, and those h's seem very low. Please show the details of the calculations.

Chet
 
  • #133
I input the car speed. 88 RPM is slow, but a car can move at that speed right? In mph this speed is 6.8, which is indeed very slow. I increased the RPM to 400, which makes the speed in in mph as 30.94 (tire diameter is 26 inches).

Its hard to show the whole code. But I have attached a screen shot of the values (all are supposed to be in S.I. units). The ones that look odd, should probably tell me where I made a mistake?

I have attached a word file to this. The funny thing is, when I keep the pipe temperature the same (125 C) and increase the speed of the car (from 88 rpm to 400 rpm), the gas temperature inside decreases! I also found that this 'saturates' to the value of the pipe temperature (125 C), if I increase the speed indefinitely. I made rpm 1010 and then 1020 and found it comes to the pipe temperature in both instances.

In any case, below (in the attached .docx file) is the data I got for 400 rpm. Everything should be in S.I. units. So could you see which is odd?
 

Attachments

Last edited:
  • #134
Jay_ said:
I input the car speed. 88 RPM is slow, but a car can move at that speed right? In mph this speed is 6.8, which is indeed very slow. I increased the RPM to 400, which makes the speed in in mph as 30.94 (tire diameter is 26 inches).

Its hard to show the whole code. But I have attached a screen shot of the values (all are supposed to be in S.I. units). The ones that look odd, should probably tell me where I made a mistake?

I have attached a word file to this. The funny thing is, when I keep the pipe temperature the same (125 C) and increase the speed of the car (from 88 rpm to 400 rpm), the gas temperature inside decreases! I also found that this 'saturates' to the value of the pipe temperature (125 C), if I increase the speed indefinitely. I made rpm 1010 and then 1020 and found it comes to the pipe temperature in both instances.

In any case, below (in the attached .docx file) is the data I got for 400 rpm. Everything should be in S.I. units. So could you see which is odd?
It's very hard to tell without seeing the details of the calculations. One way of checking, of course, is to do the calculation by hand, which shouldn't take too much effort. So bite the bullet.

The heat transfer coefficient inside looks lower than what you calculated before for the same car speed, and the Re looks higher. Why? The Pr outside should be 0.69, shouldn't it? The Pr inside looks a little high (maybe), since the outside gas is mostly N2.

Chet
 
  • #135
The inside and outside gases are mostly N2. If the Pr values are wrong, then the cp, k and mu values may be wrong. I will check my functions.

The values may be slightly off because I am deriving them from the temperature polynomial function for cp, k, mu, rho (density) etc.
 
  • #136
Calculations :

This is the simple code I put in MATLAB :

Code: 
rpm = 400; %input('Enter RPM data :\n');
T_pipe = 125; %input('\nEnter pipe temperature in deg. celsius :\n');
d = 7; %input('\nEnter diameter of pipe in centimeters : \n');
x = 10; %input('\nEnter distance of sensor from pipe end in centimeters : \n');
T_amb = 35; %input('\nEnter ambient temperature in deg. celsius :\n');
mpg = 28; %input('\nEnter mileage for the given drive cycle in miles per gallon: \n');
D = 26; %input('\nEnter the diameter of the tire in inches: \n');

D = D*2.54/100;
d = d/100;
x = x/100;
T_pipe = T_pipe + 273.15;
T_amb = T_amb + 273.15;
v = pi*D*rpm/60;
mph = 2.23694*v;
V_fuel = mph/(3600*mpg);
M_fuel = 6.073*V_fuel;

m_gas = 0.45359*15.7*M_fuel;

T_gas = 2.5*T_pipe;
T_gas_est = 0;

while (abs(T_gas - T_gas_est) > 0.2)

T_gas_est = T_gas;
Tf_in = mean([T_gas_est T_pipe]);
Tf_out = mean([T_amb T_pipe]);

sig_phi = SIGMA_PHI(Tf_in);                   % I can post HOW these functions are defined if needed
u_gas = VISCOSITY_GAS(Tf_in, sig_phi);   % SIGMA_PHI and all these are based from the mixing 
k_gas = THERMAL_GAS(Tf_in, sig_phi);      % rules in BSL
cp_gas = SPECIFIC_HEAT_GAS(Tf_in);

Re_in = (4*m_gas)/(u_gas*pi*d);
Pr_in = cp_gas*u_gas/k_gas;

Nu_in = 0.004*(Re_in)*(Pr_in^(1/3));  % Find equation for ordinate!
h_in = Nu_in*k_gas/d;

rho_air = DENSITY_AIR(Tf_out);       % I can post HOW these functions are defined if needed
u_air = VISCOSITY_AIR(Tf_out);
k_air = THERMAL_AIR(Tf_out);
cp_air = SPECIFIC_HEAT_AIR(Tf_out);

Re_out = (v*rho_air*x)/u_air;
Pr_out = (cp_air*u_air)/k_air;

Nu_out = 0.332*(Re_out^(1/2))*(Pr_out^(1/3));

h_out = Nu_out*k_air/x;

T_gas = (h_out/h_in)*(T_pipe - T_amb) + T_pipe;

end

Its pretty straight forward what we did, but merely put as code. Now the functions for obtaining the physical parameters of the gas and that of air, I took from the sources we discussed and I have them as polynomials in temperature. That's why I put the input as Tf_in (for the gases) and Tf_out (for air), these are basically the film temperatures.

Also, I changed the temperature from 125 C to 250 C, like we did earlier and I got a temperature of 527 C for the gas. Seems okay to me. Do you feel its all right?
 
Last edited:
  • #137
Okay, I just put the code in which T_pipe is still 125 C, sorry! Below I have attached the data I got for T_pipe being 250 C and I changed the rpm to 455 because it corresponds to the value of 35 mph we had considered earlier.

Code: 
rpm = 455; %input('Enter RPM data :\n');
T_pipe = 250; %input('\nEnter pipe temperature in deg. celsius :\n');
d = 7; %input('\nEnter diameter of pipe in centimeters : \n');
x = 10; %input('\nEnter distance of sensor from pipe end in centimeters : \n');
T_amb = 35; %input('\nEnter ambient temperature in deg. celsius :\n');
mpg = 28; %input('\nEnter mileage for the given drive cycle in miles per gallon: \n');
D = 26; %input('\nEnter the diameter of the tire in inches: \n');

D = D*2.54/100;
d = d/100;
x = x/100;
T_pipe = T_pipe + 273.15;
T_amb = T_amb + 273.15;
v = pi*D*rpm/60;
mph = 2.23694*v;
V_fuel = mph/(3600*mpg);
M_fuel = 6.073*V_fuel;

m_gas = 0.45359*15.7*M_fuel;

T_gas = 2.5*T_pipe;
T_gas_est = 0;

while (abs(T_gas - T_gas_est) > 0.01)

T_gas_est = T_gas;
Tf_in = mean([T_gas_est T_pipe]);
Tf_out = mean([T_amb T_pipe]);

sig_phi = SIGMA_PHI(Tf_in);
u_gas = VISCOSITY_GAS(Tf_in, sig_phi);
k_gas = THERMAL_GAS(Tf_in, sig_phi);
cp_gas = SPECIFIC_HEAT_GAS(Tf_in);

Re_in = (4*m_gas)/(u_gas*pi*d);
Pr_in = cp_gas*u_gas/k_gas;

Nu_in = 0.004*(Re_in)*(Pr_in^(1/3));  % Find equation for ordinate!
h_in = Nu_in*k_gas/d;

rho_air = DENSITY_AIR(Tf_out);
u_air = VISCOSITY_AIR(Tf_out);
k_air = THERMAL_AIR(Tf_out);
cp_air = SPECIFIC_HEAT_AIR(Tf_out);

Re_out = (v*rho_air*x)/u_air;
Pr_out = (cp_air*u_air)/k_air;

Nu_out = 0.332*(Re_out^(1/2))*(Pr_out^(1/3));

h_out = Nu_out*k_air/x;

T_gas = (h_out/h_in)*(T_pipe - T_amb) + T_pipe;

end

I get the value of the temperature of gas = 511 C. Does it seem okay? When we did calculations earlier, we didn't actually use the mixing rules in BSL. One thing that bothers me is that the temperature is the same 250 C, and when I change the speed higher, I get a LOWER temperature value (527 C @ 400 rpm, as opposed to 511 C @ 455 rpm).
 

Attachments

  • #138
Jay_ said:
Calculations :

This is the simple code I put in MATLAB :

Code: 
rpm = 400; %input('Enter RPM data :\n');
T_pipe = 125; %input('\nEnter pipe temperature in deg. celsius :\n');
d = 7; %input('\nEnter diameter of pipe in centimeters : \n');
x = 10; %input('\nEnter distance of sensor from pipe end in centimeters : \n');
T_amb = 35; %input('\nEnter ambient temperature in deg. celsius :\n');
mpg = 28; %input('\nEnter mileage for the given drive cycle in miles per gallon: \n');
D = 26; %input('\nEnter the diameter of the tire in inches: \n');

D = D*2.54/100;
d = d/100;
x = x/100;
T_pipe = T_pipe + 273.15;
T_amb = T_amb + 273.15;
v = pi*D*rpm/60;
mph = 2.23694*v;
V_fuel = mph/(3600*mpg);
M_fuel = 6.073*V_fuel;

m_gas = 0.45359*15.7*M_fuel;

T_gas = 2.5*T_pipe;
T_gas_est = 0;

while (abs(T_gas - T_gas_est) > 0.2)

T_gas_est = T_gas;
Tf_in = mean([T_gas_est T_pipe]);
Tf_out = mean([T_amb T_pipe]);

sig_phi = SIGMA_PHI(Tf_in);                   % I can post HOW these functions are defined if needed
u_gas = VISCOSITY_GAS(Tf_in, sig_phi);   % SIGMA_PHI and all these are based from the mixing 
k_gas = THERMAL_GAS(Tf_in, sig_phi);      % rules in BSL
cp_gas = SPECIFIC_HEAT_GAS(Tf_in);

Re_in = (4*m_gas)/(u_gas*pi*d);
Pr_in = cp_gas*u_gas/k_gas;

Nu_in = 0.004*(Re_in)*(Pr_in^(1/3));  % Find equation for ordinate!
h_in = Nu_in*k_gas/d;

rho_air = DENSITY_AIR(Tf_out);       % I can post HOW these functions are defined if needed
u_air = VISCOSITY_AIR(Tf_out);
k_air = THERMAL_AIR(Tf_out);
cp_air = SPECIFIC_HEAT_AIR(Tf_out);

Re_out = (v*rho_air*x)/u_air;
Pr_out = (cp_air*u_air)/k_air;

Nu_out = 0.332*(Re_out^(1/2))*(Pr_out^(1/3));

h_out = Nu_out*k_air/x;

T_gas = (h_out/h_in)*(T_pipe - T_amb) + T_pipe;

end

Its pretty straight forward what we did, but merely put as code. Now the functions for obtaining the physical parameters of the gas and that of air, I took from the sources we discussed and I have them as polynomials in temperature. That's why I put the input as Tf_in (for the gases) and Tf_out (for air), these are basically the film temperatures.

Also, I changed the temperature from 125 C to 250 C, like we did earlier and I got a temperature of 527 C for the gas. Seems okay to me. Do you feel its all right?
Hi Jay,

I feel that it's not of value (to you) for me to help troubleshoot and debug your program. That's experience that you should be getting. But, I will offer this piece of advice:
If you are using polynomials to evaluate the physical properties, make sure you are either using double precision (16 digets), or the specific algorithm that minimizes roundoff error.

Chet
 
  • #139
Okay. But do you think the values are not correct? I would only need to troubleshoot if that's the case right?
 
  • #140
Jay_ said:
Okay. But do you think the values are not correct? I would only need to troubleshoot if that's the case right?
You don't need my help to answer this. Just do the calculations by hand. It should only take about 20 minutes, and then you'll be sure.

Chet
 
  • #141
The values seem correct to me. I did the calculations by hand before and verified them in the code (like the mixing rules for instance). But since I haven't done this before, I wanted you to check if the values are inside the typical values.
 
  • #142
Jay_ said:
The values seem correct to me. I did the calculations by hand before and verified them in the code (like the mixing rules for instance). But since I haven't done this before, I wanted you to check if the values are inside the typical values.
Well done!

What about the calculated physical properties (conductivity, viscosity, heat capacity) as a function of temperature from your relationships? Do they match up as closely as you would like with the values in tables, or from graphs. For example, there are graphs of heat capacity as a function of temperature in some books. Is that a close enough match for you? Density, of course, comes from the ideal gas law, so that's no problem, right?

Chet
 
  • #143
I just did a random check. I checked it for viscosity of CO2 at two different temperatures. And heat capacities for Air and apart from that I kept faith in the equations because they seem to be from credible sources. The equations from Perry I double checked for each of them at random temperatures.
 
  • #144
Then it looks like you're ok.

Chet
 
  • #145
Hey Chet,

Congratulations on becoming Mentor, you have certainly been mine through this, and I will mention you the report.

I am back here because I am still feeling dicey about the equation for the Nusselt number inside the pipe.

In the pdf attached, they seem to use the Seider-Tate relation (Page 3, eq. (1)). I would have overlooked it, but its the proportionality constant values. We are using 0.003 to 0.004, and they Seider-Tate uses a value as high as 0.027, almost 6 to 9 times as high!

Since, we have put all this effort, I don't want us to mess up on this one aspect. You mentioned that these equations are based off on collected data, but I can't imagine why the proportionality constants would vary so much.
 
  • #146
Jay_ said:
Hey Chet,

Congratulations on becoming Mentor, you have certainly been mine through this, and I will mention you the report.

Thanks very much.
I am back here because I am still feeling dicey about the equation for the Nusselt number inside the pipe.

In the pdf attached, they seem to use the Seider-Tate relation (Page 3, eq. (1)). I would have overlooked it, but its the proportionality constant values. We are using 0.003 to 0.004, and they Seider-Tate uses a value as high as 0.027, almost 6 to 9 times as high!

Since, we have put all this effort, I don't want us to mess up on this one aspect. You mentioned that these equations are based off on collected data, but I can't imagine why the proportionality constants would vary so much.

Seider-Tate will always give a lower value of Nu than 0.004 (within its Re range of applicability). Also, check out the exponent on the Re in Seider-Tate. If you're not sure about all this, just calculate the Nu both ways for different Re's and compare them.

Chet
 
  • #147
What use it it comparing them? Let's take the value we got 6717 for Re, and 0.68 for Pr.

BSL gives me : Nu = 23.627,
Seider-Tate gives me : Nu = 27.37

Okay, I assumed the values are going to be much different. In any case, which one do I consider and why?
 
  • #148
What's the required Re range for Seider-Tate?

Chet
 
  • #149
Wikipedia says it must be above 10,000. Let's consider that Re = 10000.

Taking the log of the Nusselt number equations in both cases :

BSL : log(Nu) - (1/3)*log(Pr) = log(0.004) + log(10,000) = 1.60206

Seider-Tate : log(Nu) - (1/3)*log(Pr) = log(0.027) + 0.8*log(10,000) = 1.63136

Is that difference acceptable? The disturbing thing about that graph in BSL is :

1. The line of the graph is thick, leading to inaccuracies
2. At Re = 60,000 the line is actually below 0.003, which is another inaccuracy. At Re = 10,000 also, its below 0.004 - that means the Nusselt numbers are smaller than calculated - that would have been comforting. But the problem being that the Nu by Seider-Tate comes to be bigger. If it came to be smaller, I could have thought of it as the inaccuracy in the line of the graph (and my vision).

-------------------------------------------------------------------------------------

Also!

Since I have temperature based polynomials for the viscosity of the gas, I could as well include the viscosity factor in the calculations right?

viscosity factor = (mu_bulk/mu_boundary_layer)

Correct?

Here, the temperature of the bulk gas is the T_gas_estimated, and the denominator is the INNER film temperature right? I am just going to include the (viscosity factor)^0.14 in the Nusselt number equation.

And which would be a better pick, Seider-Tate or BSL? If Sieder-Tate is more accurate, I want to use BSL for Nusselt numbers up to the value of 10,000 and then use Sedier-Tate from there on. But which is more accurate in your opinion?
 
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  • #150
Jay_ said:
Wikipedia says it must be above 10,000. Let's consider that Re = 10000.

Taking the log of the Nusselt number equations in both cases :

BSL : log(Nu) - (1/3)*log(Pr) = log(0.004) + log(10,000) = 1.60206

Seider-Tate : log(Nu) - (1/3)*log(Pr) = log(0.027) + 0.8*log(10,000) = 1.63136

Is that difference acceptable?
The difference in Nu is only 7%. This compares with the 20-30% uncertainty cited in BSL for these correlations.
The disturbing thing about that graph in BSL is :

1. The line of the graph is thick, leading to inaccuracies
2. At Re = 60,000 the line is actually below 0.003, which is another inaccuracy. At Re = 10,000 also, its below 0.004 - that means the Nusselt numbers are smaller than calculated - that would have been comforting. But the problem being that the Nu by Seider-Tate comes to be bigger. If it came to be smaller, I could have thought of it as the inaccuracy in the line of the graph (and my vision).

In my judgement, you're splitting hairs, and asking for more accuracy from the correlations than is realistic. Furthermore, remember that the uncertainty in the outside heat transfer coefficient is much larger than this, so why are you torturing yourself in pursuit of just a few of percent more accuracy.

-------------------------------------------------------------------------------------

Also!

Since I have temperature based polynomials for the viscosity of the gas, I could as well include the viscosity factor in the calculations right?

viscosity factor = (mu_bulk/mu_boundary_layer)

Correct?
Yes. But, check BSL's description to be sure.
Here, the temperature of the bulk gas is the T_gas_estimated, and the denominator is the INNER film temperature right? I am just going to include the (viscosity factor)^0.14 in the Nusselt number equation.

And which would be a better pick, Seider-Tate or BSL? If Sieder-Tate is more accurate, I want to use BSL for Nusselt numbers up to the value of 10,000 and then use Sedier-Tate from there on. But which is more accurate in your opinion?
In my opinion, again, you're splitting hairs. The correlation in BSL appears in many other books, and BSL indicate that it is based on Seider and Tate's data. They even give an equation with a 0.027 instead of 0.026. Any of these choices that you describe is adequate, and they all have about the same degree of accuracy.

Several posts ago, I asked you to consider applying the flat plate approximation to the exhaust gas flow inside the tube (with the leading edge at the exit of the muffler) to see how the value of the heat transfer coefficient compares. This is because the Seider -Tate and BSL correlations for internal flow are based on fully developed velocity profiles in the pipe, while, in your case, the region of interest is in the hydrodynamic entrance region of the pipe, where the velocity profile is still developing. Have you had a chance to check this out yet?

Chet
 

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Doublet flow in Fluid Dynamics between two spheres or cylinders
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