Numerical simulation of laminar flow and free convection heat transfer from an isothermal vertical flat plate

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, University of Sciences and the Technology of Oran, L.P 1505 El-MNAOUER, USTO 31000 Oran, Algeria.

2 Department of Motor Vehicles and Motors, Faculty of Engineering, University of Kragujevac, 6 SestreJanjić STR., 34000 Kragujevac, Serbia.

3 Department of System Technologies and Mechanical Design Methodology, Hamburg University of Technology, Hamburg, Germany.

Abstract

In this modest work, we present a numerical study of the phenomenon of laminar natural convection in a vertical plate, whose wall was maintained at a constant temperature. It was assumed that the boundary layer problem was initially given in a two-dimensional flow even though the physical properties of the fluid were considered to be constant except for the density change with the temperature. The governing equations of the model have been transformed and simplified into a non-linear system of Ordinary Differential Equations (ODE) through the use of similarity variables which we were able to solve numerically using the Runge-Kutta method. This method has better opted for the numerical resolution of this system which was developed in FORTRAN code on the computer. The numerical results of the model were presented in tabular form and the velocity and temperature profiles for various Prandtl numbers were analyzed and depicted graphically. Also, the expressions of the mean heat transfer rate and the average Nusselt number for the whole plate were obtained in the analysis. The results were compared at the end with the numerical results obtained in the literature, showing that they were in good agreement.

Keywords

Main Subjects

References

References:
1.Nouri-Borujerdi, A. and Sepahi, F. “Effect of severalheated interior bodies on turbulent naturalconvection in enclosures”, Scientia Iranica, 26(3),pp. 1335-1349 (2019).https://doi.org/10.24200/sci.2018.20588.
2.Bhuvaneswari, M., Eswaramoorthi, S., Sivasankaran,S., et al. “Effects of viscous dissipation and convectiveheating on convection flow of a second-grade liquidover a stretching surface: An analytical and numericalstudy”, Scientia Iranica, 26(3), pp. 1350-1357 (2019).https://doi.org/10.24200/sci.2018.20414.
3.Sepahi-Younsi, J., Soltani, M.R., Abedi, M., et al.“Experimental investigation into the effects of Machnumber and boundary-layer bleed on flow stabilityof a supersonic air intake”, Scientia Iranica, 27(3),pp. 1197-1205 (2020).https://doi.org/10.24200/sci.2019.21683.
4.Saeidinezhad, A., Dehghan, A.A., and DehghanManshadi, M. “Boundary layer and surface pressuredistribution behavior over a submarine nose model withtwo different nose shapes”, Scientia Iranica, 27(3), pp.1277-1289. (2020).https://doi.org/10.24200/sci.2019.50454.1703.
5.Golkar, S.H., Khayat, M., and Zareh, M. “Experimentalstudy of heat transfer characteristics of nanofluidnucleate and film boiling on horizontal flat plate”,Scientia Iranica, 28(6), pp. 3216-3231 (2021).https://doi.org/10.24200/sci.2021.56967.4997.
6.Shakiba, A. and Rahimi, A.B. “Role of movement ofwalls with time-dependent velocity on flow andmixed convection in vertical cylindrical annuluswith suction/injection”, Scientia Iranica, 28(3), pp.1306-1317 (2021).https://doi.org/10.24200/sci.2020.54784.3917.
7.Lakshmi Devi, G., Niranjan, H., and Sivasankaran,S. “Effects of chemical reactions, radiation, andactivation energy on MHD buoyancy inducednanofluid flow past a vertical surface”, ScientiaIranica, 29(1), pp. 90-100 (2022).https://doi.org/10.24200/sci.2021.56835.4934.
8.Mokaddes Ali, M., Rushd, S., Akhter, R., et al.“Magneto-hydrodynamic mixed convective heattransfer in a nanofluid filled wavy conduit with rotatingcylinders”, Scientia Iranica, 29(2), pp. 486-501 (2022). https://doi.org/10.24200/sci.2021.56422.4717.
9.Ibitoye, S.E., Adegun, I.K., Olayemi, O.A., et al.“Experimental and numerical investigation of flowbehaviors of some selected food supplements in modeled intestine”, Scientia Iranica, 30(1), pp. 39-51 (2023). https://doi.org/10.24200/sci.2022.60130.6613.
10.Khader, M.M., Inc, M., and Akgul, A. “Numericalappraisal of the unsteady Casson fluid flow throughFinite Element Method (FEM)”, Scientia Iranica,30(2), pp. 454-463 (2023).https://doi.org/10.24200/sci.2022.60176.6644.
11.Alomar, O.R., Basher, N.M, and Yousif, A.A.“Natural convection heat transfer from a bank oforthogonal heated plates embedded in a porousmedium using LTNE model: A comparison betweenin-line and staggered arrangements”, InternationalJournal of Thermal Sciences, 160, 106692 (2021).https://doi.org/10.1016/j.ijthermalsci.2020.106692.
12.Shah, N.A., Awan, A.U., Khan, R., et al. “Freeconvection Hartmann flow of a viscous fluid withdamped thermal transport through cylindrical tube”,Chinese Journal of Physics, 80, pp. 19-33 (2022). https://doi.org/10.1016/j.cjph.2021.09.019.
13.Awan, A.U., Ali, Q., Riaz, S., et al. “A thermaloptimization through an innovative mechanism of freeconvection flow of Jeffrey fluid using non-local kernel”, Case Studies in Thermal Engineering, 24, 100851(2021). https://doi.org/10.1016/j.csite.2021.100851.
14.Awan, A.U., Riaz, S., Sattar, S., et al. “Fractionalmodeling and synchronization of ferrofluid on freeconvection flow with magnetolysis”, The EuropeanPhysical Journal Plus, 135, 841 (2020). https://doi.org/10.1140/epjp/s13360-020-00852-4.
15.Qasim, A., Riaz, S., and Awan, A.U. “Freeconvection MHD flow of viscous fluid by means ofdamped shear and thermal flux in a vertical circulartube”, Physica Scripta, 95(9), 095212 (2020).http://dx.doi.org/10.1088/1402-4896/abab39.
16.Awan, A.U., Shah, N.A., Ahmed, N., et al. “Analysis offree convection flow of viscous fluid with dampedthermal and mass fluxes”, Chinese Journal of Physics,60, pp. 98–106 (2019).https://doi.org/10.1016/j.cjph.2019.05.006.
17.Kim, K.M., Lim, S.T., Kim, S.H., et al. “Transitionphenomena of natural convection of the air in anasymmetrically heated vertical channel with a damper”,International Journal of Heat and Mass Transfer, 183,Part C, 122196 (2022).https://doi.org/10.1016/j.ijheatmasstransfer.2021.122196.
18.Kandaswamy, P., Abdul Hakeem, A.K., Saravanan,S. “Internal natural convection driven by anorthogonal pair of differentially heated plates”,Computers and Fluids, 111, pp. 179-186 (2015). https://doi.org/10.1016/j.compfluid.2015.01.015.
19.Ismaeel, A.M., Mansour, M.A., Ibrahim, F.S., et al.“Numerical simulation for nanofluid extravasationfrom a vertical segment of a cylindrical vessel intothe surrounding tissue at the microscale”, AppliedMathematics and Computation, 417, 126758 (2022). https://doi.org/10.1016/j.amc.2021.126758.
20.Hady, F., Ibrahim, F., El-Hawary, H., et al. “Effect ofsuction/injection on natural convective boundary-layer flow of A nanofluid past a vertical porous platethrough a porous medium”, International Journal ofHeat and Fluid Flow, 3(1), pp. 53-63(2012).http://dx.doi.org/10.20454/jmmnm.2012.169.
21.Talluru, K.M., Pan, H.F., Patterson, J.C., et al.“Convection velocity of temperature fluctuations in anatural convection boundary layer”, InternationalJournal of Heat and Fluid Flow, 84, 108590 (2020).https://doi.org/10.1016/j.ijheatfluidflow.2020.108590.
22.Belhocine, A. and Wan Omar, W.Z. “An analyticalmethod for solving exact solutions of the convectiveheat transfer in fully developed laminar flow through a circular tube”, Heat Transfer Asian Research,46(8), pp. 1342-1353 (2017).https://doi.org/10.1002/htj.21277.
23.Belhocine, A. and Wan Omar, W.Z. “Numericalstudy of heat convective mass transfer in a fullydeveloped laminar flow with constant walltemperature”, Case Studies in Thermal Engineering,6, pp. 43-60 (2015).https://doi.org/10.1016/j.csite.2015.08.003.
24.Belhocine, A. and Abdullah, O.I. “Numericalsimulation of thermally developing turbulent flowthrough a cylindrical tube”, The InternationalJournal of Advanced Manufacturing Technology,102(5-8), pp. 2001–2012 (2019).https://doi.org/10.1007/s00170-019-03315-y.
25.Belhocine, A. and Wan Omar, W.Z. “Analyticalsolution and numerical simulation of the generalizedLevèque equation to predict the thermal boundarylayer”, Mathematics and Computers in Simulation,180, pp. 43–60 (2021).https://doi.org/10.1016/j.matcom.2020.08.007.
26.Belhocine, A., Stojanovic, N., and Abdullah, O.I.“Numerical simulation of laminar boundary layer flowover a horizontal flat plate in external incompressibleviscous fluid”, European Journal of ComputationalMechanics, 30(4-6), pp. 337-386 (2021). http://dx.doi.org/10.13052/ejcm2642-2085.30463.
27.Jena, S.K. and Mathur, M.N. “Similarity solutionsfor laminar free convection flow of athermomicropolar fluid past a non-isothermalvertical flat plate”, International Journal ofEngineering Science, 19(2), pp. 1431-1439 (1981).https://doi.org/10.1016/0020-7225(81)90040-9.
28.Ostrach, S. “An analysis of laminar free convectionflow and heat transfer about a flat plate parallel tothe direction of the generating body force”, NationalAdvisory Committee for Aeronautics, Report 1111,(1953).
29.Yıldız, S. “Investigation of natural convection heattransfer at constant heat flux along a vertical andinclined plate”, Journal of Thermal Engineering,4(6), pp. 2432-2444 (2018).https://doi.org/10.18186/thermal.465654.
30.LeFevre, E.J. “Laminar free convection from avertical plane surface”. International Journal ofHeat and Mass Transfer, Brussels, 4, p. 168 (1956). http://dx.doi.org/10.1016/0017-9310(84)90008-5.
Scientia Iranica
Volume 32, Issue 6
Transactions on Mechanical Engineering
March and April 2025 Article ID:7139

Files

History

  • Receive Date: 10 September 2022
  • Revise Date: 13 January 2023
  • Accept Date: 30 August 2023

Share

How to cite

Statistics