Heat loss/gain takes place from a pipe carrying hotter/ colder fluid than ambient temperature. Insulation reduces the heat loss to surroundings. Heat loss depends upon number of factors like insulation thickness, ambient temperature, wind speed etc. This article shows how to calculate heat loss from an insulated pipe and a bare pipe to surroundings.

**Example**

* A 3″ Carbon steel pipe is carrying hot oil at 180°C and insulated with 50 mm thick calcium silicate insulation. Insulation is cladded with a sheet with surface emissivity of 0.9. Ambient temperature is 28°C and wind velocity is 3.5 m/s. Calculate surface temperature and heat loss from insulated and bare pipe.
*

Overall heat transfer coefficient of an insulated pipe is defined as following.

where, k_{PIPE}, k_{INSULATION} are thermal conductivity of pipe and insulation. h_{in} is heat transfer coefficient for fluid flowing in pipe and h_{air} is heat transfer coefficient due to air flowing outside the pipe. The first two terms of denominator in above equation are generally smaller compared to remaining terms and can be neglected. For this example first term due to pipe fluid is ignored.

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### Air Side Heat Transfer Coefficient, h_{AIR}

Air side heat transfer is due to combined effect of convection and radiation. Assume a temperature at cladding surface *t_surface* and steel pipe surface *t_interface*. Calculate average air film temperature as following.

` t_average = ( t_surface + t_ambient )/ 2`

Estimate thermodynamic properties of air like thermal conductivity (k), viscosity (μ), expansion coefficient (β = 1/t_average), air density (ρ), kinematic viscosity (ν), specific heat (Cp) and thermal diffusivity (α) at average air film temperature. These properties are available in literature in form of tables, these can be fitted into a polynomial form using excel’s LINEST function. Reynolds’s number (Re), Prandtl number (Pr) and Rayleigh number (Ra) are calculated based on above properties.

### h_radiation

Heat transfer coefficient due to radiation is calculated using following relation.

` h_radiation = σ ε (t_surface`^{4} - t_ambient^{4})/ (t_surface - t_ambient)

where σ is Stefan Boltzmann coefficient and ε is emissivity for cladded surface.

### h_convection

Convective heat transfer coefficient comprises of forced and free convection. Forced convection can be modeled based on correlation by Churchill and Bernstein.

` h_forced = Nu.k_air / D3`

Free convection is calculated based on correlation by Churchill and Chu.

` h_free = Nu.k_air / D3`

Combined heat transfer coefficient due to forced and free convection is calculated using following relation.

`Nu_combined = ( Nu_forced`

^{4}+ Nu_free^{4})^{0.25}`h_convection = Nu_combined.k_air / D3`

Air side heat transfer coefficient is calculated as following.

` h_air = h_radiation + h_convection`

### Overall Heat Transfer Coefficient, U

Thermal conductivity for insulation material and pipe is available in literature and depends upon temperature. It can be fitted into a polynomial equation using LINEST function in excel. Heat transfer resistance due to pipe and insulation is calculated using following relation.

`r_pipe = D3.ln(D2/D1) / 2.k_pipe`

`r_insulation = D3.ln(D3/D2) / 2.k_insulation`

Overall heat transfer coefficient is calculated as.

`r_overall = r_pipe + r_insulation + 1/h_air`

`U = 1/r_overall`

Heat flowing through insulation is estimated.

` Q = (t_operating - t_ambient)/r_overall`

A revised estimate for interface and surface temperature is made.

`t_interface = t_operating - Q.r_pipe`

`t_surface = t_interface - Q.r_insulation`

Above steps are repeated with these new estimates till there is negligible difference in temperature.

Heat loss per unit length of pipe is estimated as following.

` Heat`_{Loss} = πD3 Q

### Bare Pipe

For heat loss from bare pipe all above steps are repeated with resistance due to insulation not considered.

`r_pipe = D2.ln(D2/D1) / 2.k_pipe`

`r_overall = r_pipe + 1/h_air`

For this example surface temperature and heat loss are as following.

In the calculation of the overall heat transfer coefficient. We have 4 resistance: fluid, pipe, insulation and air. , I think it is required the Hconvection of the fluid, doesn’t it? I don’t know a correlation inside the pipe but I think it is required. does anybody agree with me?

For above calculations, resistance due to fluid is ignored as it is generally small compared to other terms for turbulent flow inside pipe. But Hconvection can always be added in overall heat transfer coefficient as mentioned below :

Do you have an example made up for multiple layers of insulation? That would be very helpful if you do. I’ve been trying to come up with my own spreadsheet and am having a hard time matching the results of another program that has to be purchased. Any help you can provide would be great

Hi, for Heat Loss From An Insulated Pipe spreadsheet, can you please let me know what the five cases shown on the calculation sheet are? For the first case (cell G20), surface temperature is equal to Ambient Temperature + 1. For the second case (cell H20), surface temperature equal to cell G56. and so on for the other three cases. What do these 5 cases represent?

thank you.

Tom

Iteration is required to calculate surface temperature, as a first guess it is taken as ambient temperature + 1, later on it is recalculated in the calculation and used as initial value for next iteration. 5 cases represent iteration with different surface temperatures. After 5 iterations when there is no change in surface temperature, it gives the final calculated value.

much appreciated.

Regards

Tom

In case the pipe is buried in underground, how can I calculate the heat loss?

Do I just apply thermal conductivity of soil instead of air?

how can I assume heat transfer area for soil?

Please, give me your answer.

Soil will act as insulating material and its thermal conductivity can be used for heat transfer calculation.

Can I use this calculation sheet under the heat gain case with colder fluid in the pipe ?

Thank you

Same calculation can be used for colder fluid in pipe.

I think the following equation maybe some mistake:

h_radiation = σ ε (t_average4 – t_ambient4)/ (t_average – t_ambient)

If ε is emissivity for cladded surface. Then I think the equation should be like this:

h_radiation = σ ε (t_surface4 – t_ambient4)/ (t_surface4 – t_ambient)

In this equation, we calculate the radiation heat transferring between cladding surface and the ambient.

Do you agree with me ? @CheGuide

Thanks

Thanks for finding the error in equation, we have corrected the formula and the attached spreadsheet.

WHAT IS THE DENSITY OF MINERAL WOOL IN THE THE HEAT LOSS CALCULATOR? PLEASE DO REPLY.

Mineral wool density is 430 kg/m3

Thank you so much for answering.

Sir, I want to calculate the heat loss at density 120 kg/cu. m and 150 kg/cu.m of the insulation material and having pressure 3 kg/sq. cm. of oil.

So how can I do that?

can you please tell me the relation between density and heat transfer because it will be easy for me to calculate.

Heat transfer depends on thermal conductivity of insulation material and not on density. In above equations density of insulation is not used.

sir can you please confirm it is 430 kg /cu. m.

We have taken a sample insulation material available in the reference text book “Fundamentals of Heat and Mass Transfer (2007), Frank P Incropera”. You need to find and consider properties of insulation material being used.

sir also clarify the unit of heat loss BTU/h/ft used in the calculator…that it BTU/h/ft or BTU/h/ sq. ft

Calculator gives heat loss per unit length of pipe.

Thank you so much for answering my questions and sharing your knowledge.

This spreadsheet is nicely done. I like the curve fitting.

1) This spreadsheet will work for compressible fluid (air) in the pipe. Correct? (Perhaps adding the convective thermal resistance on the inside of the pipe would be wise in that case).

2) It appears that k_pipe cells G88:K88 are missing the ^4 term from the Properties tab, although the number appears to be negligible. Please confirm that the ^4 term should be added.

3) What is the purpose of cells G19:K20? I20:K:30 say NA. None of these appear to be used by other cells. The same question applies ot the 2nd & 3rd rows of curve fitting coefficients on the Air_Properties sheet.

4) I suggest adding a short note near the 1st instance, indicating that the “.” in your equations indicates multiplication. For instance, it would help people to easily understand ” r_pipe = D3.ln(D2/D1) / 2.k_pipe”. It’s easy enough to figure out when you already know what the equation would look like, but for those who don’t…

Please ignore question 2 above. I see that the insulation and air properties use a 4th order polynomial fit, but the pipe uses a 3rd order fit. Adding a ^4 term is not needed.

In the second and consequtive iteration the surface temperature of the bare pipe is taken from the calculated interface temperature.

Is it not better to calculate this in each iteration using:

Interface Temp – Heat Flow x Insulation Resistance