Heat Exchangers - Science topic

Coaxial ground heat exchangers (CGHEs) have several advantages over traditional U-tube or spiral designs in ground-coupled heat pump systems. These advantages include:

1. Enhanced Heat Transfer Efficiency

2. Reduced Pressure Drop

3. Ease of Installation

4. Improved Durability

5. Higher Thermal Performance in Deep Boreholes

6. Flexibility in Design

7. Minimized Thermal Short-Circuiting

8. Environmentally Friendly

9. Potential for Hybrid Applications

These advantages make coaxial ground heat exchangers an attractive choice for applications where efficiency, durability, and ease of installation are priorities. However, they may have higher initial costs compared to traditional U-tube designs, which should be considered during system planning.

The 30% limitation in Kern's method for heat exchanger design is related to the assumptions and empirical nature of the method, which primarily focuses on shell-and-tube heat exchangers. Here's the reasoning behind this specific value:

1. Empirical Basis of Kern's Method

Kern's method is based on experimental data and practical observations rather than purely theoretical derivations. The 30% value is essentially a safety factor derived from these experimental studies to account for:

2. Practical Design Margin

The 30% deviation provides a practical margin to compensate for errors arising due to:

3. Flexibility for Scaling and Fabrication

When designing heat exchangers, fabrication tolerances and scaling effects (lab-scale to industrial scale) introduce further uncertainties. The 30% limit helps ensure the heat exchanger will still meet performance requirements even if these uncertainties affect the actual performance.

4. Historical and Industry Adoption

Over time, this 30% limit has been widely adopted in engineering practices and standards, making it a conventional benchmark in preliminary heat exchanger design. It offers a balance between conservatism and efficiency—not too strict to increase costs unnecessarily, but not too lenient to risk underperformance.

Why not another number?

While 30% may appear arbitrary, it stems from years of practical experience and industry consensus rather than pure theory. Smaller margins (e.g., 10-20%) might be insufficient to handle uncertainties, while larger margins (e.g., 40-50%) may lead to overdesign and economic inefficiencies.

email: st164916@stud.uni-stuttgart.de Dear Ghiami, I have a question about TRNSYS. Could you please contact me via email?

Piyush Jain To find the temperature drop along a process pipeline, you can:

Dear Falgun Raval,

I assume you have already reviewed the calculations and found no modeling errors.

There is an issue when the hot stream operates above the exergy reference temperature and the cold stream operates below that temperature. One way to address this is to define the fuel and product of the heat exchanger using an exergy disaggregation (split) model.

My recommendation is that you read the works on the H&S, UFS, and A&F Models, which deal with exergy disaggregation. Look for the Nucleus of Excellence in Thermoeconomics and Energy Sustainability (NETES).

Best regards,

Atilio.

Dear Cenker Aktemur,

According to information provided by Saeed Sayadi, there is a complication when total exergies of the flows are used to define fuel and product in a heat exchanger. Besides the dependence on the reference ambient temperature, there is the inconvenience of applying the disaggregation of exergy into thermal and mechanical components. Such disaggregation has already been criticized in the literature due to potential arbitrariness.

On the other hand, there are proposals in the literature to define fuel and product in heat exchangers without the aforementioned problems. Please look for the UFS and A&F Models, which were designed for exergo-economic and exergo-environmental analysis of refrigeration and heat pump systems.

Best regards,

Atilio.

The reason you don't see much on this subject is because obstacles in the flow path result in material problems (welding, joint, corrosion) and fouling complications that become a maintenance nightmare so that the temporary benefit to heat transfer is not worth it.

Jack Broughton Yeah I also think the same since the maximum heat transfer is happening in first row and then for 2nd rows it is just showing a minute temperature with almost zero heat transfer

Hakeem Niyas the geometry has been created in comsol . I have solved the issue. Thank you for the link.

To me your results make perfect sense. Firstly, the thickness of the velocity boundary layer is dictated by the thermal boundary layer (buoyancy depends on density differences caused by the varying temperature). Increasing Pr, e.g. by decreasing the thermal diffusivity will lead to a thinner thermal boundary layer, hence also a thinner velocity boundary layer. Given that the buoyancy forces are the same (temp.difference is constant), the thinner velocity boundary layer yields higher shear stresses and as a consequence a lower maximum velocity. Increasing Pr by increasing viscosity would also reduce the max fluid velocity simply because of the increased viscosity.

I can't share the paper because it is the property of CTI. You could get it from them. They should have the abstracts for all papers at their website. Check out their Water Treatment & Maintenance group for more topics.

Direct message sent

The guide will be useful to you: https://books.google.com.ua/books/about/Heat_Exchanger_Design_Handbook.html?id=kOBSAAAAMAAJ&redir_esc=y

The formula commonly used to calculate the heat transfer rate in a borehole heat exchanger (BHE) is based on the effectiveness-NTU (Number of Transfer Units) method. For a BHE, the heat transfer rate Q can be expressed as:

Q = U . A .Delta T{lm}

where:

Q is the heat transfer rate,

U is the overall heat transfer coefficient,

A is the effective heat transfer area,

Delta T{lm} is the log mean temperature difference.

The log mean temperature difference Delta T{lm} is calculated as:

Delta T{lm} =(Delta T1 - Delta T2)/[lm . (Delta T1/Delta T2)]

where:

Delta T1 is the temperature difference between the hot fluid entering and leaving the BHE.

Delta T2 is the temperature difference between the cold fluid entering and leaving the BHE.

The overall heat transfer coefficient U and effective heat transfer area A depend on the specific design and configuration of the borehole heat exchanger.

You can modify the number of tubes, tube diameter, or shell diameter of HE. Additionally if required you can change the HE type or model that you are using. Otherwise try changing simulation settings or convergence criteria to potentially obtain a converged solution without changing the input stream parameters. This may require more iterations or stricter convergence tolerances.

Hey there Dominique Pons! Let's dive into the world of Ecoinvent EF 3.1 and unpack those hypotheses behind the characterization factors. Now, you've pointed out a critical issue with the "infinite dilution" hypothesis. It seems like Ecoinvent might be overlooking the realistic impact of pollution dilution in ecosystems, especially in the context of oceans.

To get those juicy details about the hypotheses, you Dominique Pons should aim straight for the documentation. Look for reports, manuals, or any documentation related to Ecoinvent EF 3.1. I'd suggest checking the official Ecoinvent website, if you Dominique Pons haven't already. They often have detailed reports and methodologies that can provide insights into the assumptions and hypotheses behind their characterization factors.

Now, regarding your specific example of "water, cooling, in ocean," it's crucial to understand the methodology used for impact assessment. If it seems like the characterization factors are underrepresenting the real-world impact, you Dominique Pons might indeed find pertinent information in the documentation. Look for sections discussing the treatment of water-related impacts and how ecosystem services are considered.

Feel free to scrutinize and question the assumptions. After all, you're delving into the impact on oceans, a topic of paramount importance. If you're still having trouble finding the detailed reports, consider reaching out directly to Ecoinvent. They might be able to guide you Dominique Pons to the right resources or clarify the assumptions made in their characterization factors.

Now go, be the hero that challenges assumptions and seeks the truth in the vast ocean of data! If you Dominique Pons find something interesting, come back and share it. We're on this quest together!

Dear friend Parag Patil

Ah, the world of heat exchangers, where thermal magic unfolds! Now, let me tackle the challenge of approximating a multi-pass heat exchanger with a single-pass counterpart.

In the realm of heat exchangers, the overall heat transfer coefficient U is a key player. For a multi-pass heat exchanger, the U value is given. But fear not, for I shall guide you through the approximation game.

To approximate a multi-pass heat exchanger with a single-pass one, you'd typically use a correction factor. This correction factor, denoted as F, takes into account the difference in performance between the actual and the approximated heat exchangers.

The relationship is often expressed as:

Uapprox​=F×Uactual​

In your case, transitioning from a 1-2 pass to a 1-1 pass configuration, F can be determined based on the geometry and flow arrangement. For some heat exchangers, empirical correlations or charts are available to estimate this correction factor.

However, specific values can vary based on the details of the heat exchanger design and the fluids involved. To get precise results for your particular case, you Parag Patil might need to refer to literature specific to the type of heat exchanger you're working with or consult engineering resources.

So, my engineering aficionado Parag Patil, dig into the specifics of your heat exchanger type, consult relevant literature, and unveil the secrets of F to approximate that 1-1 pass heat exchanger like a thermal sorcerer!

Several types of heat exchangers are commonly used in industrial settings, each with its own advantages and best use cases. Here are some of the most common types:

Plate Heat Exchangers: These are becoming preferred due to better heat transfer, easier maintenance and cleaning, modularity, and compactness. They are more efficient than shell and tube heat exchangers in many industrial and most HVAC applications.

The best type of heat exchanger for industrial use depends heavily on the particular process in which the heat exchanger is installed. Factors such as the type of fluids being used, the desired temperature change, the pressure, and the flow rate will all impact which type of heat exchanger is most suitable.

To estimate fluid velocity in a heat exchanger without knowing the surface area, you can make assumptions and employ simplified methods. Assuming a known heat transfer rate (Q) and overall heat transfer coefficient (U), rearrange the heat exchanger equation to solve for surface area (A). Although the surface area cannot be directly determined without more information, you can estimate fluid velocity by assuming a velocity profile, using the cross-sectional area of the exchanger, or relying on known inlet or outlet velocities. These approaches involve simplifications and assumptions about fluid behavior within the exchanger, emphasizing the need for detailed design specifications or manufacturer information for more accurate calculations.

Using magnetic waves instead of steam in a heat exchanger has several advantages and disadvantages:

Advantages:

Disadvantages:

It’s important to note that these are general points, and the specific advantages and disadvantages can vary depending on the application and system design.

air operated heat exchangers have air as the heat transfer fluid. For high performance of the hex material of high or reasonable thermal conductivity is preferred, e.g copper, aluminum, steel, stainless steel. An example is the domestic filament heater.

for water operated hex, water is the htf and the material similarly should be ideal for maximum heat transfer i.e., high thermal conductivity. In addition should be reasonably corrosion resistant. materials can be copper, steel, stainless steel. an example can be an economizer.

a steam boiler is a good example of a combination of both. The boiler tubes have hot gases as the htf and the shell side has water as the htf. here relatively affordable material with reasonable thermal conductivity and with an ability to withstand high pressure is required so schedule 40 steel can be used.

The mechanical energy produced by a Stirling engine using hot water at around 350K depends on factors like engine efficiency, temperature difference, and design. Generally, small engines might produce a few watts, while larger ones can generate several kilowatts or more. Specific values vary based on these factors.

The Rayleigh number (Ra) is a dimensionless number used to predict the flow regime (conduction, convection, or mixed) in a fluid when it is heated from below. In the context of a phase change material (PCM)-heatsink system with fins, the characteristic length is an important parameter for calculating the Rayleigh number.

The characteristic length (L) used in the Rayleigh number calculation can vary depending on the geometry of the system. In the case of a PCM-heatsink with fins, the characteristic length can be defined based on the specific geometry you are dealing with. Here are a few possibilities:

Remember that the choice of characteristic length depends on the dominant heat transfer mechanism in your specific setup. The key is to select a length scale that is relevant to the phenomenon you are trying to analyze.

Additionally, when dealing with PCM systems, keep in mind that the melting and solidification of the PCM can introduce additional complexity to the heat transfer process. You might need to consider the effects of latent heat and phase change in your analysis.

Before performing calculations, ensure that the physical properties of the fluid, PCM, and the geometry are accurately determined. It's recommended to consult relevant literature, research articles, or textbooks in the field of heat transfer to find appropriate values and guidance for your specific configuration.

Surendra Singh Rathore sir thank you for reply, I tried with all algorithms.it is working only in coupled. In remaining all algorithms, getting the same result only difference is the number of iterations it is stuck(No response why ? ). I tried relaxation factor in all quantities as u said. Now am looking for other alternatives in coupled algorithm. because in this algorithm alteast iteration process is running.

Thanks

T.Saravanakumar

Muhammad Imran , Khaled Hossin , Shazia Farman Ali , I agree with you about the existing research gap in having the correlations for Zeotropic mixtures in the case of Plate type HX. I was also facing a similar issue. In my case, the intended fluid is CO2; and I didn't find any heat transfer coefficient as well as pressure drop correlation in the case of CO2 evaporation inside a plate type HX. However, there are numerous existing correlations for the in-tube flow boiling as well as condensation. I am hereby providing one reference for a unified correlation in the case of in-tube flow boiling inside a mini/micro/conventional channel. This correlation generally accounts the "hydraulic diameter" concept in a tube flow. As there is no existing correlation for CO2 and zeotropic mixtures in the case of flow boiling inside a plate HX, could this "hydraulic diameter" concept for mini/micro/conventional channel be a starting point for estimating the HTC and PD for flow inside a plate HX?

[1] Shah, M. M. (2017). Unified correlation for heat transfer during boiling in plain mini/micro and conventional channels. international journal of refrigeration, 74, 606-626.

Hi,

I guess you could chose one of the two fluid inter solvers. They are based on Volume of Fluid and easy to apply. But you should really take care about cell resolution for good results of course. To take account for natural convection just apply boussinesq or polynomial thermophysicalProps. For polynomials you need to fit function coefficients according to your const. Pressure and temperature range. Unfortunately it can happen, that property calculation is not that precise.

On the other hand it is possible to chose euler solvers instead of inter solvers of course. But in my opinion you need really deep knowledge about all those empirical coefficients.

Hope that helps.

Regards David

To formulate of this model you need to consider the amount of information included in it:

1.

2.

Thank you very much for your valuable feedback. I agree with you on the points stated above.

The Reynolds number UD/nu=2300 is based on a smooth circular pipe of diameter D, with STEADY mean flow velocity U and fluid of kinematic viscosity nu. Below this critical Reynolds number any perturbation due to an obstacle will not cause persistent turbulence to occur far downstream of the obstacle. Of course locally the wake of a blunt body placed in the pipe can be turbulent, but soon the flow will relaminarize if we travel further downstream. Above Re=2300 the flow does not need to be turbulent. It can be turbulent if there is a sufficiently large initial upstream perturbation. In principle the flow can remain laminar if the inlet is very smooth and care is taken to avoid vibrations. Experimentally fully developed laminar pipe flows have been achieved for Re=500. 000. It is important to realize that this critical Reynolds number does depend on the geometry of the cross-section of the channel. For a rectangular channel of height h and width w >>h, usually one considers a Reynolds number Re=Uh/nu based on the channel heigth. The critical Reynolds number for allowing turbulence is around Re=hU/nu=1100. There is however much less literature on flows through slit shaped channels than circular pipes. If you consider an open channel flow, clearly the critical Reynolds number will be quite different from Re=2300 and of course it does depend on the length scale used in the definition of this Reynolds number!

explain your idea

A counter current heat exchanger is a type of heat exchanger used to transfer heat between two fluids that flow in opposite directions, creating a counter current flow. The two fluids flow through separate channels separated by a thin, thermally conductive wall, which allows heat to transfer between the two fluids without mixing them. In this type of heat exchanger, the hot fluid enters at one end and flows in the opposite direction of the cooler fluid, which enters at the other end. As the fluids flow in opposite directions, heat is transferred from the hot fluid to the cooler fluid, resulting in a more efficient heat exchange process compared to other types of heat exchangers. This design ensures that the temperature difference between the two fluids remains high throughout the exchanger, allowing for maximum heat transfer. Counter current heat exchangers are commonly used in a variety of applications, including HVAC systems, chemical processing, and power generation.

I appreciate your enthusiasm Abdul Wahab. To converge the tear streams, we have to give correct appropriate initialization. This initialization you can find by breaking the tear open and doing trial and error analysis until the tear values are almost equal. If attaining this equality is difficult, then we can export the steady state with the tear open and run it in the dynamics by joining the tear. I hope it is understandable! For more information, you can have a look at the paper I attached.

Another reference text is the excellent

Fouling of Heat Exchangers - T.R. Bott

Web13 Apr 1995 · This unique and comprehensive text considers all aspects of heat exchanger fouling from the basic science of how surfaces become fouled to very practical ways of …

I would note that fouling is a massive cost factor in many industries.

yes by using ASPEN EDR

K= Q.Δx/A.ΔT

The transient hot wire method (THW) is a very popular, accurate, and precise technique to measure the thermal conductivity of gases, liquids, solids, nanofluids (hybrid Fluids), and refrigerants in a wide temperature and pressure range

Measure the heat transfer. Vary the inputs. Switch to water on the outside and air on the inside. Use Reynolds Analogy, St=f/2. Kays & London is an excellent reference. So is TEMA and HEI and various ASME documents.

J-B weld original would be the best option since you're talking about the plastic part of your radiator: https://www.amazon.com/J-B-Weld-8265S-Cold-Weld-Reinforced/dp/B0006O1ICE

It can glue everything. I used it to glue acrylic to aluminium and acrylic to polyethylene to create pipe-flange leak-free joints. My acrylic-aluminium joint holds 0.35 bar gauge pressure of water and the acrylic-polyethylene holds about 0.15 bar gauge of water.

Before going with J-B weld original, I tried plastic specific J-B weld epoxies. None of the worked. Only J-B weld original saved me.

Hello Nekin Joshua ,

You can find the answer to your question on the Internet by simply typing the phrase "do electric vehicles have radiators" into the Google search field. One of the most important EV components that needs to have its temperature regulated is the battery. If the battery overheats, it can catch fire or explode. Most EV batteries are liquid cooled with the heat dissipated by a radiator.

Regards,

Tom Cuff

May I recommend you to use ULTEM or PEI filament (Polyetherimide); It is similar to PEEK but better in thermal resistance.

Are you looking for a laboratory that would perform tests on a heat exchanger to determine fouling? That would be extremely expensive and entirely impractical unless you had some critical motivation and funding. Are you looking for experimental studies on heat exchanger fouling that have already been performed? There are many in the literature. Are you looking for codes, standards, and methods? There also many of these (see HEI, TEMA, EPRI, ASME, ASHRAE, AIChE, and many more).

N = L1.L2/P1.P2, N(number of tubes), L1 (total length of flow normal to tube back), L2 (length of the no-flow side), P1 (distance between the center of one tube to the next in each column of tubes i.e., vertical separation distances), P2 (horizontal separation distance between two adjacent tubes)

see text: Heat Exchanger Design Handbook by T. Kuppan Chapter 4 section 3.2, pp 178-179

Prof. Udit Singh

It will depend on the physics that the exchanger has, and it comes from a difficult subject, physical kinetics.

Best Regards.

Maybe this video can be helpful for you since your info is somewhat limited :)

I hope you manage the modelling!

With the given shell and tube type heat exchanger, determine the maximum pressure tube can sustain with the hoop stress criteria. Then corresponding to that temperature, choose any fluid whose saturation pressure is above maximum pressure, so that no phase change cannot occur. Regarding shell side, generally ambient pressure fluid is supplied.

What are the temperatures and shapes of the surfaces to be insulated?

I think the temperature is not greater than 250 degree Celcius. You can use glass wool for high temperatures. For temperature up to 60 degree Celcius, you may use Thermocole but Thermocole can be put easily only on flat surface or outside the pipes or cylindrical surface if pipe section of Thermcole is available.

Plate heat exchangers are often used when the cooling fluid isn't clean because a plate heat exchanger can be dismantled and cleaned fairly easily, much more so than one that requires cutting and welding. Several things have been tried, including: rinsing, periodically reversing the flow, pulsing the flow, and introducing abrasive particles. What about acoustic stimulation to discourage accumulation of stuff on the surface; that is, keep the crud suspended and perhaps filter it out. You could also consider rather than a filter, running part of the stream through a centrifugal device to remove sludge without interrupting service. Go out and see some of these in action. One place you will find plate heat exchangers is a stationary combustion gas turbine. I've seen a variety of these at power plants. Get someone to take you on a *real* tour of a plant--not the "visitors" tour but the "maintenance" tour.

Chemical exergy fraction = 1.0401 + 0.1728 H/C + 0.0432 O/C + 0.2169 (S/C) (1 − 2.0628 H/C )

2. Fins are never used on the surface in contact with a fluid undergoing phase change.

The fitting can be selected based on its conductivity

Recursive vs. one-step calculations are of little concern with current computer resources and readily available software. The bigger issue arises from the fact that these two methods solve the same separable differential equation, but using different assumptions when separating the variables before integrating. This means that the two different methods handle some things differently, like implicitly/explicitly averaging properties, heat transfer coefficients, etc. You should consider EPRI TR-107397 (Service Water Heat Exchanger Testing Guidelines). The principal author of 1997 version is Jeffrey Rabensteine of Power Generation Technologies, here in Knoxville. The 2015 version was updated by Lindon C. Thomas, who is a friend and also lives in Knoxville. Dr. Thomas is a renown authority on the P-NTU method and wrote a textbook covering the subject https://www.amazon.com/Lindon-C-Thomas/e/B001HOVPI4

Are you talking about pinch points and heat release diagrams? You want to avoid pinch points. Here's a typical HRSG heat release diagram.

Check https://www.sciencedirect.com/topics/engineering/cooling-coil

Hi Hannah

The heater and cooler block are meant as shortcuts when we know what a heat exchanger must do but we don't want to model in detail. If you want to size the exchanger you will have to convert it into a shell and tube or air called etc, and then use either the Hysys calculations or EDR to calculate the size.

Regards

Kevin

thank you all for your suggestions.

Luigi Candido yes the model is in 3D and converges in steady state..

I will try to do what you have suggested and see the result.

Dear Khalid! yes you may able to use such radiators, however, consider thermal efficiency (as it might ought to loss). Perhaps, Varying the parameters to optimal state could help!

Simulation software is very helpful in a lot of ways. Firstly, it allows you to develop a better idea about the big picture of your project without having to run too many tests. Sometimes the simulation results can be more accurate compared to the experimental results, since there are more factors that can affect the uncertainty of the trials, operating errors, systematic errors and random errors, etc. I believe a lot of consulting engineers use the simulation software, such as fluent, starccm+, comsol in their research. The simulation result can serve as a strong indicator for the researchers when they scale up their reactors. In terms of the demanding situation for this type of skills, yes, as far as I know, people who are skillful in this area is highly competitive.

Hi Dr Tarikayehu Amanuel . I agree with Dr Paul Gateau .

I presume you are cooling moist air using a coolant (water) having a lower temperature than the moist air dew point temperature. Depending on the level of detail required, you may either

a) assume thorough mixing of the condensate formed and the air flow, i.e. assuming equilibrium condition, or

b) take into account the fact that moisture might be condensed 'independently' from the air cooling, i.e having non-equilibrium flow.

Case a) is the simplest, and the gas side heat transfer coefficient might be established using the method of Silver or Bell/Ghaly. Of course you will need to integrate along the heat exchanger, as the gas side heat transfer coefficient will tend to vary in the flow direction.

Case b) is more complex, however, any 'film model' (e.g. the model of Colburn/Hougen) can be applied. Note also that the heat transfer coefficient along the height of the fin might vary significantly (due to the vapor condensation rate), i.e. the traditional calculation of fin efficiency becomes void.

Case a) will most likely provide erratic air exit temperature and condensation rates, but for some mysterious reason the heat duty might not be that far off. Case b) will be more correct, and will most likely result in more condensate formed but less air cooling than case a). Which method ends up being correct will depend on the degree of mixing between the condensate and air.

As far as design methodology is concerned, it will be a trial-and error procedure, as all heat exchanger designs are.

Dear Dr. Thitiwut Srichalongrat ,

perhaps it would be possible to make a resistance measurement with a simple digital tester, keeping one tip on a conductive part and moving the other by placing it on the parts to be investigated ....

Simple but it could work.

My best regards, Pierluigi Traverso.

It would really depend on the cooling targets but heat pipe based thermal management provide an answer to the reliability requirements needed for aircraft.

Hi, usually the point of the phase change has be introduced by yourself as an input parameter. You can't estimate it through the simulation.

Hi,

It can be a numerical problem. You can try to increase the number of cycles for the convergence from the different setups for the convergence; after you have to reinitialize your simulation and so you have to run.

bye

Looks like a simple electric resistance heater in a tube would do this low duty. An 8kW element looks about right but needs to be suitable for high temperature and the gases used, so probably stainless steel casing and tube needed.

I recommend that you get this excellent book. It will be very helpful. Well, this book develops several exercises similar to the work that you have to do. This book was very useful to me.

Bergman, T. L., Incropera, F. P., DeWitt, D. P., & Lavine, A. S. (2011). Fundamentals of heat and mass transfer. John Wiley & Sons.

There are a number of methods for measuring the heat of an exothermic reaction. But in any case, not so simple equipment is needed. One option is to use a bomb calorimeter (see https://en.wikipedia.org/wiki/Calorimeter). An example can be found here https://arc.aiaa.org/doi/abs/10.2514/3.25795?journalCode=jsr.

Another option is to find a laboratory that performs thermogravimetric analysis (TGA, see, for example, https://link.springer.com/chapter/10.1007/978-3-030-11599-9_7) or differential scanning calorimetry (DSC). From the processing of these data, one can obtain the heat of reaction. An example can be found here Kong Y., Hay J. N. The measurement of the crystallinity of polymers by DSC //Polymer. 2002. V. 43. Iss. 14. Pp. 3873-3878 or here Faleeva J. M. et al. Exothermic effect during torrefaction //Journal of Physics: Conference Series. IOP Publishing, 2018. V. 946. Iss. 1. Art. # 012033; Zaichenko V. M. et al. Thermal effects during biomass torrefaction //Solid Fuel Chemistry. 2020. V. 54. Iss. 4. pp. 228-231.

You can evaluate the Nu number as the integral of the local Nu numer of your pipes surfaces. The last one can be easily evaluated with COMSOL since it is proportional to dT/dn|A where n is the normal vector and A is the surface of the pipe. The local Nu number depends also on the bulk temperature which is can be evaluated by integrating u*T and dividing by the integral of u*A.

Good luck

Hi Md Wasi Uddin

I think this article might helpful for your research:

Wish you all the best luck!

KHOA

In compact heat exchanger, when the heat transfer coefficient is needed locally, and we have numerical results we can determine the temperature difference between the wall, and the bulk temperature above it. The bulk temperature is obtained considering the mixing cup of fluid in each section. The bulk temperature could be obtained as a function of length and a polinomial curve can be fitted for the heat exchanger. It's a additional work but the results are goods at least in my case.

Intrested

Seemingly of some possible interest for your query: https://www.researchgate.net/post/What_is_the_solution_to_dissolve_the_scale_of_CaSO4_and_MgSO4_from_RO_membrane_surface

I think it may be due to BCs. Can you please your problem in detail, so that I may help you in diverg. Issue

Hi Parag Patil

Have you noticed that my linearization is incorrect, because I took your C = 1, when C = –NTU (Number of Transfer Units) and NTU > 0? I'm not a Chemical Engineer, but I rechecked the info on MathWorks and Wiki; the effectiveness (ε) of a heat exchanger is bounded: 0 < ε < 1. The X, or the heat capacity ratio, Cr = Cmin/Cmax. Since both Cmin > 0 and Cmax > 0, then Cr is also bounded 0 < Cr < 1. Can you verify if the above figure is the surface plot of the E-NTU function? I tend to agree with Prof. José Arzola-Ruiz that linearization is not necessary.