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Impact of moving walls on combined convection flow and thermal performance in a wavy chamber

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Abstract

The impact of wall movements in different directions on mixed convection flow and thermal performance in a wavy chamber is reported. The wavy wall of the chamber is heated non-uniformly, and the upper wall is kept at a constant cold temperature, while the vertical walls of the chamber are adiabatic. Four different cases, namely Case-1, Case-2, Case-3 and Case-4, are considered on the basis of multi-directional movements of the walls of the chamber. Mathematical model of the flow physics consists of the Navier–Stokes (N-S) equations in streamfunction (\(\psi\)) —vorticity (\(\zeta\)) formulation including the energy transport equations which are solved by higher-order compact (HOC) scheme on curvilinear grids Pandit SK, Chattopadhyay A.(Comput Math Appl 74(6):1414–34 2017) [45]. It is found that the fluid flow and thermal performance are both influenced by the direction of moving lids and the undulations of the wavy bottom surface of the chamber. Optimum thermal performance is noticed when the wavy bottom surface of the chamber is employed with one undulation at low Richardson number (Ri). Moreover, for \(Ri=0.01\), Case-2, in which the upper lid is moving in left direction and the left lid is moving in upward direction, gives better heat transfer rate with maximum value of average Nusselt number for one undulation. Furthermore, it is noticed that among all the cases, the cases (Case-2 and Case-4) in which upper lid is moving in left direction produce minimum entropy generation for every undulations of the wavy surface with each of the Ri values. So, on the basis of better heat transfer rate and the minimum entropy generation, Case-2 and Case-4 may be recommended as optimum configurations.

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Abbreviations

Be :

Bejan number

Gr :

Grashof number \((g{\beta _\text{T}}'L^3(T'_\text{h}-T'_\text{c})/\nu ^2)\)

g :

Gravitational acceleration (\(\hbox {ms}^{-2}\))

k :

Thermal conductivity (Wm−1 K−1)

L :

Side length of a square chamber (m)

Nu :

Local Nusselt number

\({\overline{Nu}}\) :

Average Nusselt number

p :

Non-dimensional pressure

\(U_0\) :

Non-dimensional velocity of the horizontal moving walls (ms−1)

Pr :

Prandtl number \((\nu /\alpha )\)

P :

Dimensionless pressure \((p/\rho U^2_0)\)

Re :

Reynolds number \((U_0 L/\nu )\)

\(S_T\) :

Total entropy generation number

t :

Non-dimensional time

\(T'\) :

Dimensional temperature (K)

T :

Non-dimensional temperature \((T'-T'_\text{c})\)/\((T'_\text{h}-T'_\text{c})\)

\(T_0\) :

Bulk temperature (K)

\(T'_h\) :

Temperature on hot surface (K)

\(T'_c\) :

Temperature on cold vertical wall (K)

u, v :

Dimensional velocity components (ms−1)

U, V :

Non-dimensional velocity components in x, y directions (\(u/U_{0}\), \(v/U_{0}\))

x, y :

Dimensional Cartesian coordinates (m)

X, Y :

Non-dimensional Cartesian coordinates (xL−1, yL−1)

\(\alpha\) :

Thermal diffusivity (\(({\text{m}}^{{\text{2}}}\,{\text{s}}^{{ - 1}})\))

\({\beta _T}'\) :

Thermal expansion coefficient (K−1)

\(\nu\) :

Kinematic viscosity (\({\text{m}}^{{\text{2}}}\,{\text{s}}^{{ - 1}}\))

\(\lambda\) :

Wave amplitude of the wavy wall

\(\mu\) :

Dynamic viscosity (kgm−1 s−1)

\(\tau\) :

Irreversibility distribution ratio

\(\rho\) :

Density (\({\text{kgm}}^{{\text{3}}}\))

\(\psi\) :

Stream function

\(\zeta\) :

Vorticity

\(\xi\) :

Non-dimensional horizontal coordinate in computational plane

\(\eta\) :

Non-dimensional vertical coordinate in computational plane

i, j :

Cell faces

c :

Cold wall

h :

Hot wall

d :

Wave undulation of the wavy surface

References

  1. Oztop HF, Al-Salem KA. A review on entropy generation in natural and mixed convection heat transfer for energy systems. Renew Sustain Energy Rev. 2012;16:911–20.

    Article  CAS  Google Scholar 

  2. Arefmanesh A, Aghaei A, Ehteram H. Mixed convection heat transfer in a CuO-water filled trapezoidal enclosure, effects of various constant and variable properties of the nanofluid. Appl Math Model. 2016;40(2):815–31.

    Article  Google Scholar 

  3. Shankar PN, Meleshko, Nikiforovich EI. Slow mixed convection in rectangular containers. J Fluid Mech. 2002;471:203-217.

  4. Basak T, Roy S, Sharma PK, Pop I. Analysis of mixed convection flows within a square cavity with uniform and non-uniform heating of bottom wall. Int J Therm Sci. 2009;48:891–912.

    Article  Google Scholar 

  5. Oztop HF, Dagtekin I. Mixed convection in two-sided lid-driven differentially heated square cavity. Int J Heat and Mass Transf. 2007;47:1761–9.

    Article  Google Scholar 

  6. Ismael MA, Pop I, Chamkha AJ. Mixed convection in a lid-driven square cavity with partial slip. Int J Therm Sci. 2014;82:47–61.

    Article  Google Scholar 

  7. Pandit SK, Chattopadhyay A, Oztop HF. A fourth order compact scheme for heat transfer problem in porous media. Comput Math Appl. 2016;71:805–32.

    Article  Google Scholar 

  8. Roy M, Roy S, Basak T. Role of various moving walls on energy transfer rates via heat flow visualization during mixed convection in square cavities. Energy. 2015;82:1–22.

    Article  Google Scholar 

  9. Ovando G, Juarez H, Huelsz G, Ramos E. Vortex formation in a cavity with oscillating walls. Phys Fluids. 2009;21:024101-1-024101-13.

  10. Alsabery AI, Ismael MA, Chamkha AJ, Hashim I. Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater. J Therm Anal Calorim. 2019;135(1):729–50.

    Article  CAS  Google Scholar 

  11. Rashad AM, Ismael MA, Chamkha AJ, Mansour MA. MHD mixed convection of localized heat source/sink in a nanofluid-filled lid-driven square with partial slip. J Tai Inst Chem Eng. 2016;68:173–86.

    Article  CAS  Google Scholar 

  12. Ismael MA, Armaghani T, Chamkha AJ. Mixed convection and entropy generation in a lid-driven cavity filled with a hybrid nanofluid and heated by a triangular solid. Heat Transf Res. 2018;49(17):1645–65.

    Article  Google Scholar 

  13. Selimefendigil F, Oztop HF, Chamkha AJ. MHD mixed convection in a nanofluid filled vertical lid-driven cavity having a flexible fin attached to its upper wall. J Therm Anal Calorim. 2019;135(1):325–40.

    Article  CAS  Google Scholar 

  14. Ismael MA, Mansour MA, Chamkha AJ, Rashad AM. Mixed convection in a nanofluid filled-cavity with partial slip subjected to constant heat flux and inclined magnetic field. J Magn Magn Mater. 2016;416:25–36.

    Article  CAS  Google Scholar 

  15. Ismael MA, Chamkha AJ. Mixed convection in lid-driven trapezoidal cavities with an aiding or opposing side wall. Numer Heat Transf Part A Appl. 2015;68(3):312–35.

    Article  CAS  Google Scholar 

  16. Das PK, Mahmud S. Numerical investigation of natural convection inside a wavy enclosure. Int J Therm Sci. 2003;42(4):397–406.

    Article  Google Scholar 

  17. Morsli S, Sabeur-Bendehina A. Entropy generation and natural convection in square cavities with wavy walls. J Appl Mech Tech Phys. 2013;54(6):913–20.

    Article  CAS  Google Scholar 

  18. Dalal A, Das MK. Laminar natural convection in an inclined complicated cavity with spatially variable upper wall temperature. Int J Heat Mass Transf. 2005;48(18):3833–54.

    Article  CAS  Google Scholar 

  19. Al-Amiri A, Khanafer K, Bull J, Pop I. Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity. Int J Heat Mass Transf. 2006;50(9–10):1771–80.

    Google Scholar 

  20. Bhardwaj S, Dalal A, Pati S. Influence of wavy wall and non-uniform heating on natural convection heat transfer and entropy generation inside porous complex enclosure. Energy. 2015;79:467–81.

    Article  Google Scholar 

  21. Gibanov NS, Sheremet MA, Oztop HF, Hamdeh NA. Mixed convection with entropy generation of nanofluid in a lid-driven cavity under the effects of a heat-conducting solid wall and vertical temperature gradient. Euro J Mech B/Fluids. 2018;70:148–59.

    Article  Google Scholar 

  22. Hassan M, Marin M, Alsharif A, Ellahi R. Convective heat transfer flow of nanofluid in a porous medium over wavy surface. Phys Lett A. 2018;382(38):2749–53.

    Article  CAS  Google Scholar 

  23. Alsabery AI, Ismael M, Chamkha AJ, Hashim I. Numerical investigation of mixed convection and entropy generation in a wavy-walled cavity filled with nanofluid and involving a rotating cylinder. Entropy. 2018;20(9):664.

    Article  PubMed Central  Google Scholar 

  24. Alsabery AI, Selimefendigil F, Hashim I, Chamkha AJ, Ghalambaz M. Fluid-structure interaction analysis of entropy generation and mixed convection inside a cavity with flexible right wall and heated rotating cylinder. Int J Heat Mass Transf. 2019;140:331–45.

    Article  Google Scholar 

  25. Izadi S, Armaghani T, Ghasemiasl R, Chamkha AJ, Molana M. A comprehensive review on mixed convection of nanofluids in various shapes of enclosures. Pow tech. 2018;343:880–907.

    Article  Google Scholar 

  26. Biswal P, Basak T. Investigation on thermal efficiency via entropy generation analysis within cavities with curved walls subjected to differential/Rayleigh-Benard heating. Mat Today: Proc. 2018;5(11):23107–18.

    Google Scholar 

  27. Pal SK, Bhattacharyya S, Pop I. A numerical study on non-homogeneous model for the conjugate-mixed convection of a Cu-water nanofluid in an enclosure with thick wavy wall. Appl Math Comput. 2019;356:219–34.

    Google Scholar 

  28. Ismael MA. Numerical solution of mixed convection in a lid-driven cavity with arc-shaped moving wall. Eng Comput. 2017;34:1–32.

    Article  Google Scholar 

  29. Selimefendigil F, Oztop HF. Numerical study of forced convection of nanofluid flow over a backward facing step with a corrugated bottom wall in the presence of different shaped obstacles. Heat Transf Eng. 2016;37(15):1280–92.

    Article  CAS  Google Scholar 

  30. Selimefendigil F, Chamkha AJ. Magnetohydrodynamics mixed convection in a lid-driven cavity having a corrugated bottom wall and filled with a non-Newtonian power-law fluid under the influence of an inclined magnetic field. J Therm Sci Eng Appl. 2016;8(2):021023-1-021023-8.

  31. Selimefendigil F, Oztop HF. Numerical analysis and ANFIS modeling for mixed convection of CNT-water nanofluid filled branching channel with an annulus and a rotating inner surface at the junction. J Heat Mass Transf. 2018;127:583–99.

    Article  CAS  Google Scholar 

  32. Hajjar A, Mehryan SA, Ghalambaz M. Time periodic natural convection heat transfer in a nano-encapsulated phase-change suspension. Int J Mech Sci. 2020;166:105243.

    Article  Google Scholar 

  33. Mehryan SA, Ghalambaz M, Gargari LS, Hajjar A, Sheremet M. Natural convection flow of a suspension containing nano-encapsulated phase change particles in an eccentric annulus. J Energy Stora. 2020;28:101236.

    Article  Google Scholar 

  34. Selimefendigil F, Oztop HF. Corrugated conductive partition effects on MHD free convection of CNT-water nanofluid in a cavity. Int J Heat Mass Transf. 2019;129:265–77.

    Article  CAS  Google Scholar 

  35. Mehryan SA, Alsabery A, Modir A, Izadpanahi E, Ghalambaz M. Fluid-structure interaction of a hot flexible thin plate inside an enclosure. Int J Therm Sci. 2020;153:106340.

    Article  Google Scholar 

  36. Selimefendigil F, Oztop HF. Fluid-solid interaction of elastic-step type corrugation effects on the mixed convection of nanofluid in a vented cavity with magnetic field. Int J Mech Sci. 2019;152:185–97.

    Article  Google Scholar 

  37. Alsabery AI, Hashim I, Hajjar A, Ghalambaz M, Nadeem S, Saffari Pour M. Entropy generation and natural convection flow of hybrid nanofluids in a partially divided wavy cavity including solid blocks. Energies. 2020;13(11):2942.

    Article  CAS  Google Scholar 

  38. Alsabery AI, Ismael MA, Chamkha AJ, Hashim I. Impact of finite wavy wall thickness on entropy generation and natural convection of nanofluid in cavity partially filled with non-Darcy porous layer. Neural Comput Appl. 2020;17:1–21.

    Google Scholar 

  39. Hussain S, Oztop HF, Mehmood K. Mixed convection and entropy production in a nanofluid-filled closed space with inclined magnetic field. J Therm Anal Calorim. 2019;137: 1735–1755.

  40. Rashidi S, Eskandarian M, Mahian O, Poncet S. Combination of nanofluid and inserts for heat transfer enhancement. J Therm Anal Calorim. 2019;135(1):437–60.

    Article  CAS  Google Scholar 

  41. Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131:2027–39.

  42. Armaghani T, Chamkha AJ, Rashad AM. Inclined magneto: convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media. J Therm Anal Calorim. 2020;1-13

  43. Izadi M, Hashemi Pour SMR, Karimdoost Yasuri A, Chamkha AJ. Mixed convection of a nanofluid in a three-dimensional channel, effect of opposed buoyancy force on hydrodynamic parameters, thermal parameters and entropy generation. J Therm Anal Calorim. 2019;136:2461–75.

  44. Cho Chang C. Heat transfer and entropy generation of mixed convection flow in Cu-water nanofluid-filled lid-driven cavity with wavy surface. Int J Heat Mass Transf. 2018;119:163–74.

    Article  CAS  Google Scholar 

  45. Pandit SK, Chattopadhyay A. A robust higher order compact scheme for solving general second order partial differential equation with derivative source terms on nonuniform curvilinear meshes. Comput Math Appl. 2017;74(6):1414–34.

    Article  Google Scholar 

  46. Pandit SK, Kalita JC, Dalal DC. A fourth-order accurate compact scheme for the solution of steady Navier-Stokes equations on non-uniform grids. Comput Fluids. 2008;37:121–34.

    Article  CAS  Google Scholar 

  47. Sharif MA. Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom. Appl Therm Eng. 2007;27:1036–42.

    Article  CAS  Google Scholar 

  48. Bejan A. Entropy Generation Minimization. Boca Raton: CRC Press; 1996.

    Google Scholar 

  49. Kaluri RS, Basak T. Analysis of entropy generation for distributed heating in processing of materials by thermal convection. Int J Heat Mass Transf. 2011;42:2578–94.

    Article  Google Scholar 

  50. Ilis GG, Mobedi M, Sunden B. Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls. Int Com Heat Mass Transf. 2008;35:696–703.

    Article  CAS  Google Scholar 

  51. Basak T, Kaluri RS, Balakrishnan AR. Effects of thermal boundary conditions on entropy generation during natural convection. Numer Heat Transf Part A. 2011;59:372–402.

    Article  Google Scholar 

  52. Kelley CT Iterative methods for linear and nonlinear equations, SIAM Publications, Philadelphia,1995.

  53. Van Der Vorst H. BiCGSTAB: A fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems. SIAM J Sci Comput. 1992;13:631–44.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Government General Degree College Ranibandh, Bankura, West Bengal, 722 135, India

    Anirban Chattopadhyay

  2. Integrated Science Education and Research Centre (ISERC) Visva-Bharati, Santiniketan, West Bengal, 731 235, India

    Hemanta Karmakar & Swapan K. Pandit

  3. Faculty of Engineering, Kuwait College of Science and Technology, Doha District, Kuwait

    Ali J. Chamkha

  4. Center of Excellence in Desalination Technology, King Abdulaziz University, P.O. Box 80200, Jeddah, 21589, Saudi Arabia

    Ali J. Chamkha

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  1. Anirban Chattopadhyay
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  2. Hemanta Karmakar
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  3. Swapan K. Pandit
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  4. Ali J. Chamkha
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Correspondence to Anirban Chattopadhyay.

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Chattopadhyay, A., Karmakar, H., Pandit, S.K. et al. Impact of moving walls on combined convection flow and thermal performance in a wavy chamber. J Therm Anal Calorim 147, 3731–3752 (2022). https://doi.org/10.1007/s10973-021-10663-z

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