Skip to main content

Effect of double rotating cylinders on the MHD mixed convection and entropy generation of a 3D cubic enclosure filled by nano-PCM


In this manuscript, phase change material (PCM) including the nanoparticles is considered in a 3D cubic enclosure to investigate the mixed convection of heat transfer under the magnetic field effect. Double rotating cylinders also are located in the middle of the enclosure to study the effect of their angular velocity in different conditions. Governing equations are solved by Galerkin Finite Element Method (GFEM) and were confirmed by previous studies. As main outcomes, results with enhanced angular velocity, both the average temperature and cumulative energy were significantly decreased. Furthermore, unaltered fluidity (\(\hbox {Ha}=0\)) imposes greater entropy, but this tendency reverses when the Hartman number (Ha) rises, resulting in minimum entropy trends.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Data Availability

This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]



Radius of the cylinder, [m]


Dimensional length of the heated wall (m)


Static pressure \((\hbox {N/m}^{2})\)


Prandtl number


Dimensionless coordinate


Local temperature (\(^{^{\circ }}\hbox {K}\))


Velocity in the x-direction (m/s)


Velocity in the y-direction (m/s)


Dimensionless velocity

\(C_{ps}\) :

solid PCM-specific heat (kJ/kgK)

\(C_{pl}\) :

liquid PCM-specific heat (kJ/kgK)


latent heat of fusion of the PCM (kJ/kg)

\(\hbox {T}_{\mathrm{m}}\) :

PCM melting temperature (K)

\(\upalpha \) :

Thermal diffusivity (\(\hbox {m}^{2}/\hbox {s}\))

\(\beta \) :

Coefficient of thermal expansion (\(1/^{{\circ }}\hbox {K}\))

\(\theta \) :

Dimensionless temperature

\(k_{ls}\) :

solid  PCM  thermal  conductivity \((\hbox {W/m}\cdot \hbox {K})\)

\(k_{l}\) :

liquid  PCM  thermal  conductivity \((\hbox {W/m}\cdot \hbox {K})\)

\(\rho _{l}\) :

liquid  PCM  density \(\left( \mathrm {kg/}\mathrm {m}^{\mathrm {3}} \right) \)

\(\rho _{s}\) :

solid  PCM  density \(\left( \mathrm {kg/}\mathrm {m}^{\mathrm {3}} \right) \)

\(\upnu \) :

Kinematic viscosity (\(\hbox {m}^{2\, }/\hbox {s}\))

\(\upmu \) :

Dynamic viscosity (kg/ms)

\(\Omega \) :

angular rotational speed of the cylinder, [rad/s]


  1. F.S. Javadi, H.S.C. Metselaar, P. Ganesan, Performance improvement of solar thermal systems integrated with phase change materials (PCM), a review. Sol. Energy 206, 330–352 (2020)

    ADS  Article  Google Scholar 

  2. N. Abdollahi, M. Rahimi, Heat transfer enhancement in a hybrid PV/PCM based cooling tower using Boehmite nanofluid, Heat Mass Transf. und Stoffuebertragung, pp. 859–869, 2019

  3. A. E. Kabeel, M. M. Khairat Dawood, T. Nabil, B. E. Alonafal, Improving the performance of stepped solar still using a graphite and PCM as hybrid store materials with internal reflectors coupled with evacuated tube solar collector, Heat Mass Transf. und Stoffuebertragung, pp. 891–899, 2019

  4. K. Du, J. Calautit, P. Eames, Y. Wu, A state-of-the-art review of the application of phase change materials (PCM) in Mobilized-Thermal Energy Storage (M-TES) for recovering low-temperature industrial waste heat (IWH) for distributed heat supply. Renew. Energy 168, 1040–1057 (2021)

    Article  Google Scholar 

  5. L. Kalapala, J.K. Devanuri, Influence of operational and design parameters on the performance of a PCM based heat exchanger for thermal energy storage - A review. J. Energy Storage 20, 497–519 (2018)

    Article  Google Scholar 

  6. D. Lee, C. Kang, Evaluation of heat storage and release in a double shell and tube heat exchanger with a PCM layer. J. Mech. Sci. Technol. 34(8), 3471–3480 (2020)

    Article  Google Scholar 

  7. J. Park, D.H. Shin, Y. Shin, S.W. Karng, Analysis of heat transfer in latent heat thermal energy storage using a flexible PCM container. Heat Mass Transf. und Stoffuebertragung 55(6), 1571–1581 (2019)

    ADS  Article  Google Scholar 

  8. M. S. Mahdi, H. B. Mahood, A. N. Campbell, A. A. Khadom, Natural convection improvement of PCM melting in partition latent heat energy storage: Numerical study with experimental validation, Int. Commun. Heat Mass Transf., vol. 126, 2021

  9. D. Lee, C. Kang, A study on development of the thermal storage type plate heat exchanger including PCM layer. J. Mech. Sci. Technol. 33(12), 6085–6093 (2019)

    Article  Google Scholar 

  10. W. Hua, L. Zhang, X. Zhang, Research on passive cooling of electronic chips based on PCM: A review. J. Mol. Liq. 340, 117183 (2021)

    Article  Google Scholar 

  11. G. Murali, G. S. N. Sravya, J. Jaya, V. Naga Vamsi, A review on hybrid thermal management of battery packs and it’s cooling performance by enhanced PCM, Renew. Sustain. Energy Rev., 150: 111513, 2021

  12. M. Joseph, V. Antony, and V. Sajith, Characterization of heat dissipation from PCM based heat sink using Mach–Zehnder Interferometry, Heat Mass Transf. und Stoffuebertragung, 2021

  13. S. Rukh, R.A. Pasha, M.A. Nasir, Heat transfer enhancement of round pin heat sinks using N-eicosane as PCM: an experimental study. Heat Mass Transf. und Stoffuebertragung 55(2), 309–325 (2019)

    ADS  Article  Google Scholar 

  14. M.H. Shojaeefard, G.R. Molaeimanesh, Y.S. Ranjbaran, Improving the performance of a passive battery thermal management system based on PCM using lateral fins. Heat Mass Transf. und Stoffuebertragung 55(6), 1753–1767 (2019)

    ADS  Article  Google Scholar 

  15. J.F. Sánchez-Pérez, C. Mascaraque-Ramírez, J.A. Moreno Nicolás, E. Castro, M. Cánovas, Study of the application of PCM to thermal insulation of UUV hulls using Network Simulation Method. Alexandria Eng. J. 60(5), 4627–4637 (2021)

    Article  Google Scholar 

  16. S. A. B. Al Omari, A. M. Ghazal, E. Elnajjar, A new approach using un-encapsulated discrete PCM chunks to augment the applicability of solid gallium as phase change material in thermal management applications, Energy Convers. Manag., vol. 158, no. December 2017, pp. 133–146, 2018

  17. H. Usman, H.M. Ali, A. Arshad, M.J. Ashraf, S. Khushnood, M.M. Janjua, S.N. Kazi, An experimental study of PCM based finned and un-finned heat sinks for passive cooling of electronics. Heat Mass Transf. und Stoffuebertragung 54(12), 3587–3598 (2018)

    ADS  Article  Google Scholar 

  18. A. Kasaeian, L. Bahrami, F. Pourfayaz, E. Khodabandeh, W.-M. Yan, Experimental studies on the applications of PCMs and nano-PCMs in buildings: A critical review. Energy Build. 154, 96–112 (2017)

    Article  Google Scholar 

  19. D. Zhou, C.Y. Zhao, Y. Tian, Review on thermal energy storage with phase change materials (PCMs) in building applications. Appl. Energy 92, 593–605 (2012)

    Article  Google Scholar 

  20. T. Yan, J. Li, J. Gao, X. Xu, J. Yu, Model validation and application of the coupled system of pipe-encapsulated PCM wall and nocturnal sky radiator. Appl. Therm. Eng. 194(December), 2021 (2020)

    Google Scholar 

  21. V. Vinayaka Ram, R. Singhal, R. Parameshwaran, Energy efficient pumpable cement concrete with nanomaterials embedded PCM for passive cooling application in buildings. Mater. Today Proc. 28, 1054–1063 (2019)

    Article  Google Scholar 

  22. J.H. Park, J. Jeon, J. Lee, S. Wi, B.Y. Yun, S. Kim, Comparative analysis of the PCM application according to the building type as retrofit system. Build. Environ. 151(January), 291–302 (2019)

    Article  Google Scholar 

  23. G. Evola, L. Marletta, F. Sicurella, Simulation of a ventilated cavity to enhance the effectiveness of PCM wallboards for summer thermal comfort in buildings. Energy Build. 70, 480–489 (2014)

    Article  Google Scholar 

  24. Z. Xiao, P. Mishra, A. Mahdavi Nejad, M. Tao, S. Granados-Focil, S. Van Dessel, Thermal optimization of a novel thermo-optically responsive SS-PCM coatings for building enclosures, Energy Build., vol. 247, 2021.

  25. H.-D. Yun, K.-L. Ahn, S.-J. Jang, B.-S. Khil, W.-S. Park, S.-W. Kim, Thermal and Mechanical Behaviors of Concrete with Incorporation of Strontium-Based Phase Change Material (PCM). Int. J. Concr. Struct. Mater. 13(1), 18 (2019)

    Article  Google Scholar 

  26. Y. Lin, Y. Jia, G. Alva, G. Fang, Review on thermal conductivity enhancement, thermal properties and applications of phase change materials in thermal energy storage. Renew. Sustain. Energy Rev. 82, 2730–2742 (2018)

    Article  Google Scholar 

  27. Z.A. Qureshi, H.M. Ali, S. Khushnood, Recent advances on thermal conductivity enhancement of phase change materials for energy storage system: A review. Int. J. Heat Mass Transf. 127, 838–856 (2018)

    Article  Google Scholar 

  28. S. Wu, T. Yan, Z. Kuai, W. Pan, Thermal conductivity enhancement on phase change materials for thermal energy storage: A review. Energy Storage Mater. 25, 251–295 (2020)

    Article  Google Scholar 

  29. N. Sharifi, T.L. Bergman, A. Faghri, Enhancement of PCM melting in enclosures with horizontally-finned internal surfaces. Int. J. Heat Mass Transf. 54(19–20), 4182–4192 (2011)

    MATH  Article  Google Scholar 

  30. C. Zhao, M. Opolot, M. Liu, F. Bruno, S. Mancin, K. Hooman, Numerical study of melting performance enhancement for PCM in an annular enclosure with internal-external fins and metal foams. Int. J. Heat Mass Transf. 150, 119348 (2020)

    Article  Google Scholar 

  31. C. Ji, Z. Qin, S. Dubey, F.H. Choo, F. Duan, Simulation on PCM melting enhancement with double-fin length arrangements in a rectangular enclosure induced by natural convection. Int. J. Heat Mass Transf. 127, 255–265 (2018)

    Article  Google Scholar 

  32. X. Zhou, Q. Yu, S. Zhang, C. Zhang, J. Feng, Porous silica matrices infiltrated with PCM for thermal protection purposes. Ceram. Int. 39(5), 5247–5253 (2013)

    Article  Google Scholar 

  33. Y. Li, J. Li, Y. Deng, W. Guan, X. Wang, T. Qian, Preparation of paraffin/porous TiO2 foams with enhanced thermal conductivity as PCM, by covering the TiO2 surface with a carbon layer. Appl. Energy 171, 37–45 (2016)

    Article  Google Scholar 

  34. W. Peng, O.K. Sadaghiani, Thermal function improvement of phase-change material (PCM) using alumina nanoparticles in a circular-rectangular cavity using Lattice Boltzmann method. J. Energy Storage 37(March), 102493 (2021)

    Article  Google Scholar 

  35. M. Bashar, K. Siddiqui, Experimental investigation of transient melting and heat transfer behavior of nanoparticle-enriched PCM in a rectangular enclosure. J. Energy Storage 18(June), 485–497 (2018)

    Article  Google Scholar 

  36. M.M. Rashidi, M. Sadri, M.A. Sheremet, Numerical Simulation of Hybrid Nanofluid Mixed Convection in a Lid-Driven Square Cavity with Magnetic Field Using High-Order Compact Scheme. Nanomaterials 11(9), 2250 (2021)

    Article  Google Scholar 

  37. M.M. Rashidi, F. Mohammadi, S. Abbasbandy, M.S. Alhuthali, Entropy Generation Analysis for Stagnation Point Flow in a Porous Medium over a Permeable Stretching Surface. J. Appl. Fluid Mech. 8(4), 753–765 (2015)

    Article  Google Scholar 

  38. M.V. Reddya, P. Lakshminarayana, Cross-diffusion and heat source effects on a three-dimensional MHD flow of Maxwell nanofluid over a stretching surface with chemical reaction. Eur. Phys. J. Spec. Top. 230, 1371–1379 (2021)

    Article  Google Scholar 

  39. M.V. Reddy, P. Lakshminarayana, influence of thermal radiation and viscous dissipation on MHD flow of UCM fluid over a porous stretching sheet with higher order chemical reaction. Spec. Top. Rev. Porous Media Int. J. 12(4), 33–49 (2021)

    Article  Google Scholar 

  40. M.V. Reddy, P. Lakshminarayana, K. Vajravelu, Magnetohydrodynamic radiative flow of a Maxwell fluid on an expanding surface with the effects of Dufour and Soret and chemical reaction. Comput. Therm. Sci. 12(4), 317–327 (2020)

    Article  Google Scholar 

  41. R. Meenakumari, P. Lakshminarayana, Radiation and Hall effects on a 3D flow of MHD Williamson fluid over a stretchable surface. Heat Transfer. 49, 4410–4426 (2020)

    Article  Google Scholar 

  42. M.V. Reddy, P. Lakshminarayana, K. Vajravelu, A comparative study of MHD non-Newtonian fluid flows with the effects of chemical reaction and radiation over a stretching sheet. Comput. Therm. Sci. 13(5), 17–29 (2021)

    Article  Google Scholar 

  43. G. Sucharitha, M.M. Rashidi, S. Sreenadh, P. Lakshminarayana, Effects of magnetic field and slip on convective peristaltic flow of a non-Newtonian fluid in an inclined non-uniform porous channel with flexible walls. J. Porous Media 21(10), 895–910 (2018)

    Article  Google Scholar 

  44. R. Meenakumari, P. Lakshminarayana, K. Vajravelu, Unsteady MHD flow of a Williamson nanofluid on a permeable stretching surface with radiation and chemical reaction effects. Euro. Phys. J. Spec. Top. 230, 1355–1370 (2021)

    ADS  Article  Google Scholar 

  45. M.M. Rashidi, S. Bagheri, E. Momoniat, N. Freidoonimehr, Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet. Ain Shams Eng. J. 8(1), 77–85 (2017)

    Article  Google Scholar 

  46. O. Fatla, G. Smaisim, A. Valera-Medina1, A. Rageb, N. Syred, Experimental and Numerical Investigation of Heat Transfer and Fluid Mechanics across a Rotating Circular Cylinder Dissipating Uniform Heat Flux by Crossflow. 10th Pacific Symposium on Flow Visualization and Image Processing Naples, Italy, 15-18 June, 2015

  47. Wael Al-Kouz, Abderrahmane Aissa, Aimad Koulali, Wasim Jamshed, Hazim Moria, Kottakkaran Sooppy Nisar, Abed Mourad, Abdel-Haleem Abdel-Aty, M. Motawi Khashan & I. S. Yahia, MHD darcy-forchheimer nanofluid flow and entropy optimization in an odd-shaped enclosure filled with a (MWCNT-Fe3O4/water) using galerkin finite element analysis. Sci Rep 11, 22635 (2021)

  48. Weal Al-Kouz, Aissa Abderrahmane, MD. Shamshuddin, Obai Younis, Sahnoun Mohammed, O. Anwar Beg and Davood Toghraie. Heat transfer and entropy generation analysis of water-Fe3O4/CNT hybrid magnetic nanofluid flow in a trapezoidal wavy enclosure containing porous media with the Galerkin finite element method. Eur. Phys. J. Plus 136, 1184 (2021)

  49. W. Al-Kouz, M.A. Medebber, Mohamed Abdelghany Elkotb, Aissa Abderrahmane, Koulali Aimad, Khaled Al-Farhany, Wasim Jamshed, Hazim Moria, Fayez Aldawi, C. Ahamed Saleel, Kottakkaran Sooppy Nisar, Galerkin finite element analysis of Darcy-Brinkman-Forchheimer natural convective flow in conical annular enclosure with discrete heat sources, Energy Reports 7, 6172–6181 (2021)

  50. A.J. Chamkha, F. Selimefendigil, MHD mixed convection of nanofluid due to an inner rotating cylinder in a 3D enclosure with a phase change material. Int. J. Numer. Methods Heat Fluid Flow 29(10), 3559–3583 (2019)

    Article  Google Scholar 

  51. K. Kant, A. Shukla, A. Sharma, P.H. Biwole, Heat transfer studies of photovoltaic panelcoupled with phase change material. Sol. Energy 140, 151–161 (2016)

    ADS  Article  Google Scholar 

  52. V. Alexiades, N. Hannoun, and T.Z. Mai, Tin Melting: Effect of Grid Size and Scheme on the Numerical Solution, In Proc. 5th Mississippi State Conf. Differential Equations and Computational Simulations, pp. 55–69, 2003

  53. A. Verma, S. Shashidhara, D. Rakshit, A comparative study on battery thermal management using phase change material (PCM). Therm. Sci. Eng. Prog. 11, 74–83 (2019)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Mohammad Hatami.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Abderrahmane, A., Hatami, M., Younis, O. et al. Effect of double rotating cylinders on the MHD mixed convection and entropy generation of a 3D cubic enclosure filled by nano-PCM. Eur. Phys. J. Spec. Top. (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: