Skip to main content
SpringerLink
Log in

Description and Analytical Modeling for a Solid Block Cross-flow High Temperature Heat Exchanger

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

In this report, the design specifics, and performance modeling results, for a simple, solid metal block, liquid–liquid cross-flow heat exchanger, intended for high temperature applications, are given. The design consists of a solid block of metal, with cylindrical channels providing the cross-flow passageways for two non-mixing liquids. In this design, all flow channels are separated by a certain minimum thickness of the host solid block material. This particular design is limited by the length of pores that can be machined from a solid block. In this study, a simple heat transfer model, appropriate for such an exchanger, was used to estimate what values of effectiveness might be obtainable while keeping the size of the exchanger as compact as possible. The effects of channel length and spacing, liquid specific heat and viscosity and block material conductivity on exchanger effectiveness are considered and results reported. The model predicts that for a cubic exchanger of side length 8.25 cm with 50 channels per side at a diameter of 3.0 mm each, for a particular high temperature situation using molten salts, with an inlet and outlet temperature difference of around 170 K, an effectiveness of 0.4 can be achieved with a total mass flow rate of 0.5 kg\(\cdot\)s\(^{-1}\) along with a Reynolds number of less than 2000.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data Availability

Not applicable.

Abbreviations

\(\alpha\) :

Linear expansion coefficient (1/C\(^{\text {o}}\))

\(c_c\) :

Cold side liquid specific heat (J\(\cdot\)mol\(^{-1}\) \(\cdot\)K\(^{-1}\))

\(c_h\) :

Hot side liquid specific heat (J\(\cdot\)mol\(^{-1}\) \(\cdot\)K\(^{-1}\))

D :

Channel diameter (m)

\(\epsilon\) :

Exchanger effectiveness

f :

Friction coefficient

g :

Acceleration due to gravity magnitude (m\(\cdot\)s\(^{-2}\))

\(h_H\) :

Hot channel heat transfer coefficient (W\(\cdot\)m\(^{-2}\) \(\cdot\)K\(^{-1}\))

\(h_C\) :

Cool channel heat transfer coefficient (W\(\cdot\)m\(^{-2}\) \(\cdot\)K\(^{-1}\))

k :

Thermal conductivity (W\(\cdot\)m\(^{-1}\) \(\cdot\)K\(^{-1}\))

\(l_o\) :

Length before thermal expansion (m)

L :

Distance between channels (m)

Lt, w :

Exchanger length/width (m)

\(\dot{m}_c\) :

Cool side mass flow rate (kg\(\cdot\)s\(^{-1}\))

\(\dot{m}_h\) :

Hot side mass flow rate (kg\(\cdot\)s\(^{-1}\))

N :

Number of channels in layer

\(\Delta P\) :

Channel pressure drop (Pa)

\(P_d\) :

Power density (W\(\cdot\)m\(^{-3}\))

\(P_p\) :

Pumping power (W)

\(\rho\) :

Mass density (kg\(\cdot\)m\(^{-3}\))

\(R_e\) :

Reynolds number

S :

Shape factor (m)

\(T_C\) :

Cool side inlet temperature (K)

\({T_C}_f\) :

Cool side final temperature (K)

\(T_H\) :

Hot side inlet temperature (K)

\({T_H}_f\) :

Hot side final temperature (K)

v :

Flow speed (m\(\cdot\)s\(^{-1}\))

z :

Distance between layers (m)

References

  1. K. Jin, A.B. Krishna, K.Z. Wong, P.S. Ayyaswamy, I. Catton, T.S. Fisher, Thermohydraulic experiments on a supercritical carbon dioxide-air microtube heat exchanger. Int. J. Heat Mass Transf. 203, 123840 (2023). https://doi.org/10.1016/j.ijheatmasstransfer.2022.123840

    Article  Google Scholar 

  2. A.B. Krishna, K. Jin, P.S. Ayyaswamy, I. Catton, T.S. Fisher, Technoeconomic optimization of superalloy supercritical CO\(_2\) microtube shell-and-tube-heat exchangers. Appl. Therm. Eng. 220, 119578 (2023). https://doi.org/10.1016/j.applthermaleng.2022.119578

    Article  Google Scholar 

  3. R.K. Shah, D.P. Sekulić, Heat exchangers, in Handbook of Heat Transfer, 3rd edn., ed. by W.M. Rohsenow, J.P. Hartnett, Y.I. Cho (McGraw-Hill, New York, 1998)

    Google Scholar 

  4. S.S. Arasavelli, R. Konijeti, G.R. Budda, Influence of transverse vibrations on convective heat transfer in parallel flow tube-in-tube heat exchanger. Heat Transf. 50, 1985–2006 (2021). https://doi.org/10.1002/htj.21965

    Article  Google Scholar 

  5. G. Çakmak, H.L. Yücel, Z. Argunhan, C. Yildiz, Experimental investigation of thermal performance in a concentric-tube heat exchanger with wavy inner pipe. Int. J. Thermophys. 33, 1055 (2012). https://doi.org/10.1007/s10765-012-1210-4

    Article  ADS  Google Scholar 

  6. H.K. Aasi, M. Mishra, Transient behavior of three-fluid cross-flow heat exchanger under the influence of temperature nonuniformity. J. Therm. Sci. Eng. Appl. 10, 061012 (2018). https://doi.org/10.1115/1.4040987

    Article  Google Scholar 

  7. S. Han, C. Zhang, Y. Wu, Y. Lu, J. Niu, Study on flow and heat transfer performance of molten salt based nanofluids in shell and twisted tube heat exchanger with shutter baffle. Int. J. Thermophys. 44, 30 (2023). https://doi.org/10.1007/s10765-022-03134-6

    Article  ADS  Google Scholar 

  8. H. Bayat, A.M. Lavasani, T. Maarefdoost, Experimental study of thermal-hydraulic performance of cam-shaped tube bundle with staggered arrangement. Energ. Convers. Manag. 85, 470 (2014). https://doi.org/10.1016/j.enconman.2014.06.009

    Article  Google Scholar 

  9. X. Li, C.T. Wilson, L. Zhang, B. Bhatia, L. Zhao, A. Leroy, O. Brandt, R. Orta-Guerra, J.P. Youngblood, R.W. Trice, Design and modeling of a multiscale porous ceramic heat exchanger for high temperature applications with ultrahigh power density. Int. J. Heat Mass Transf. 194, 122996 (2022). https://doi.org/10.1016/j.ijheatmasstransfer.2022.122996

    Article  Google Scholar 

  10. https://www.gab-neumann.com/block-heat-exchangers

  11. Y. Jiang, E. Liese, S.E. Zitney, D. Bhattacharyya, Design and dynamic modeling of printed circuit heat exchangers for supercritical carbon dioxide Brayton power cycles. Appl. Energy 231, 1019–1032 (2018). https://doi.org/10.1016/j.apenergy.2018.09.193

    Article  Google Scholar 

  12. M.M. Rathore, P.R.A. Kapuno, Engineering Heat Transfer, 2nd edn. (Sudbury, Jones & Bartlett Learning, 2011), p.988

    Google Scholar 

  13. T. Gao, J. Greer, B. Sammakia, Review and analysis of cross flow heat exchanger transient modeling for flow rate and temperature variations. J. Therm. Sci. Eng. Appl. 7, 041017 (2015)

    Article  Google Scholar 

  14. A.C. Mueller, Heat exchangers, in Handbook of Heat Transfer. ed. by W.M. Rohsenow, J.P. Hartnett (McGraw-Hill, New York, 1973)

    Google Scholar 

  15. R. Deeb, New correlations for predicting convective heat transfer of single and multi-row heat exchangers employing staggered drop-shaped tubes. Int. J. Heat Mass Transf. 202, 123689 (2023). https://doi.org/10.1016/j.ijheatmasstransfer.2022.123689

    Article  Google Scholar 

  16. P. Liu, M.R. Nasr, G. Ge, M.J. Alonso, H.M. Mathisen, F. Fathieh, C. Simonson, A theoretical model to predict frosting limits in cross-flow air-to-air flat plat heat/energy exchangers. Energy Build. 110, 404–414 (2016). https://doi.org/10.1016/j.enbuild.2015.11.007

    Article  Google Scholar 

  17. D.G. Shepherd, Elements of Fluid Mechanics (Harcourt, Brace & World Inc., New York, 1965)

    Google Scholar 

  18. R.E. Bolz, G.L. Tuve (eds.), Handbook of Tables for Applied Engineering Science, 2nd edn. (CRC Press, Cleveland, 1973)

    Google Scholar 

  19. Materials Selection Considerations for Thermal Process Equipment, U.S. Dept. of Energy, DOE/GO-102004-1974, Nov. (2004)

  20. D.R. Lide (ed.), CRC Handbook of Chemistry and Physics, 74th edn. (CRC Press, Boca Raton, 1993)

    Google Scholar 

  21. A.P. Fraas, M.N. Ozisik, Heat Exchanger Design (Wiley, New York, 1965)

    Google Scholar 

  22. D.G. Zill, Differential Equations with Boundary Value Problems, 2nd edn. (PWS-Kent Publishing Co., Boston, 1989), pp.550–551

    MATH  Google Scholar 

  23. M.A. Pinsky, Introduction to Partial Differential Equations with Applications (McGraw-Hill Book Co., New York, 1984)

    Google Scholar 

Download references

Funding

The authors’ have no funding sources to acknowledge.

Author information

Authors and Affiliations

  1. Department of Physics, Woods Laboratories, The University of the South, Sewanee, TN, USA

    Douglas A. Barlow & Stephen S. Hancock

  2. School of Polytechnic, Purdue University Fort Wayne, Fort Wayne, IN, USA

    Jahan B. Bayat

Authors
  1. Douglas A. Barlow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jahan B. Bayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stephen S. Hancock
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

DAB: Supervision, methodology, investigation, writing original draft, formal analysis. JBB: Conceptualization, validation, writing review and editing. SSH: Formal analysis, validation, writing review and editing.

Corresponding author

Correspondence to Douglas A. Barlow.

Ethics declarations

Conflict of interest

The authors have no conflict of interests to report.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barlow, D.A., Bayat, J.B. & Hancock, S.S. Description and Analytical Modeling for a Solid Block Cross-flow High Temperature Heat Exchanger. Int J Thermophys 44, 107 (2023). https://doi.org/10.1007/s10765-023-03213-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10765-023-03213-2

Keywords

Search

Navigation