Analysis of Boundary Layer Thickness and Temperature Distribution in a Fluidic Stream across a Stretching Sheet with Thermal Nonequilibrium and Viscous Heating Effects

Yıl 2025, Cilt: 12 Sayı: 2, 134 - 152, 01.05.2025

Uchenna Uka , Edwin Esekhaigbe , Boniface Obi

https://doi.org/10.31202/ecjse.1513483

Cited By: 1

Öz

The analysis of boundary layer thickness and temperature distribution effects in a viscous fluid flow of varying Hartmann intensity and thermal nonequilibrium over an exponentially extending/attenuation sheet is discussed in the current work. The fundamental issue involves recovering the ordinary differential models from the leading Navier-Stokes equations of conservation of momentum, energy, and mass which appear in partial differential forms through the similarity estimation approach. The recovered coupled ordinary differential equations (CODEs) have been analytically resolved using the series technique and evaluated numerically by employing the MATHEMATICA scheme. Furthermore, graphics discussion of the velocity, temperature, and concentration profiles are provided. Notedly, it is observed that as the Hartmann parameter Ht, improves, the drag, as well as the fluid velocity decreases. Also, enhancement of the thermal nonequilibrium number begets a rise in the temperature. On the other hand, as the threshold thermal Grashof number values appreciate, the skin friction is improved. Equally, the local Nusselt number declines due to enhancing the Prandtl and thermal nonequilibrium parameters respectively. Correspondingly, when the numerical values for the local Nusselt number, and coefficient of skin friction are compared to the literature that is currently available, they are found to be in close and total agreement.

Anahtar Kelimeler

Heat Transfer , Thermal Gradient , Mass Diffusivity , Hydromagnetic , Drag

Kaynakça

• [1] B. C. Sakiadis, “Boundary layer behavior on continuous solid surfaces: I. Boundary layer equations for twodimensional and axisymmetric flow”, American Institute of Chemical Engineers (AIChE J.), vol. 7, pp. 26- 28, 1961. https://doi:10.1002/aic.690070108
• [2] V. Poply, P. Singh, and A. K. Yadav, “A study of Temperature-dependent fluid properties on MHD free stream flow and heat transfer over a non-linearly stretching sheet”, Proc Eng, vol. 127, pp. 391-397, 2015. https://doi:10.1016/j.proeng.2015.11.386
• [3] K. V. Prasad, K. Vajravelu, and P. S. Datti, “The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet”, International journal of thermal science, 49(3): 603- 610, (2010). https://doi:10.1016/j.ijthermalsci.2009.08.005
• [4] R. L. V. D. Renuka, T. Poornima, R. N. Bhaskar, and S. Venkataraman, “Radiation and mass transfer effects on MHD boundary layer flow due to an exponentially stretching sheet with a heat source”, International Journal of Engineering Innovative Technology, vol. 3, pp. 33-39, 2014.
• [5] S. Mukhopadhyay, “Slip effects on MHD boundary layer flow over an exponentially stretching sheet with suction/blowing and thermal radiation”, Ain Shams Engineering Journal, vol. 4, pp. 485-491, 2012. https://doi: 10.1016/jasej.2012.10.007
• [6] E. Mabood, W. A. Khan, and A. I. Md Ismail, “MHD flow over exponential radiating stretching sheet using Homotopy Analysis Method” Journal of King Saud University Engineering Science, vol. 29, pp. 68-74, 2017.
• [7] T. Poornima, and R. N. Bhask, “Radiation effects on MHD free convective boundary layer flow of nanofluids over a nonlinear stretching sheet”, Advances in Applied Science Research, vol. 4, pp. 190-202, 2013.
• [8] W. A. Khan, O. D. Makinde, and Z. H. Khan, “Non-aligned MHD stagnation point flow of variable viscosity nanofluids past a stretching sheet with radiative heat”, International Journal of Heat and Mass Transfer, vol. 96, pp. 525-534, 2016. https://doi: 10.1016/j..ijheatmasstransfer.2016.01.052.
• [9] N. Bachok, A. Ishak, and I. Pop, “Boundary layer stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet in a nanofluid”, International Journal of Heat and Mass Transfer, vol. 55, pp. 8122-8128, 2012. https://doi: 10.1016/j.ijheatmasstransfer.2012.08.051
• [10] M. Y. Malik, M. Naseer, S. Nadeem, and A. Rehman, “The boundary layer flow of Casson nanofluid over a vertical exponentially stretching cylinder”, Applied Nanoscience, vol. 4, pp. 869-873, 2014. https://doi: 10.1007/s13204-013-0267.0.
• [11] M. R. Eid, “Chemical reaction effect on MHD boundary-layer flow of two-phase nanofluid model over an exponentially stretching sheet with a heat generation”, Journal of Molecular Liquids, vol. 220, pp. 718-725, 2016. https://doi: 10.1016/j.molliq.2016.05.005.
• [12] T. Gangaiah, N. Saidulu, and L. A. Venkata, “Magnetohydrodynamic flow of nanofluid over an exponentially stretching sheet in the presence of viscous dissipation and chemical reaction”, Journal of Nanofluids, vol. 7, pp. 439-4448, 2018. https://doi: 10.1166/jon.2018.1465.
• [13] M. Abel, S. Mahantesh, M. Nandeppanavar, and V. Basanagouda, “Effects of variable viscosity, buoyancy, and variable thermal conductivity on mixed convection heat transfer due to an exponentially stretching surface with magnetic field”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, vol. 87, pp. 247-256, 2017. https://doi: 10.1007/s40010-016-0338-1.
• [14] M. A. Yousif, I. H. Farhan, T. Abbas, and R. Ellahi, “Numerical study of momentum and heat transfer of MHD Carreau nanofluid over an exponentially stretched plate with internal heat source/sink and radiation”, Heat Transfer Research, vol. 50(7), pp. 649-658, 2019. https://doi: 10.1615/HeatransRes.208025568
• [15] R. Ellahi, A. Zeeshan, F. Hussain, and T. Abbas, “Thermally charged MHD Bi-phase flow coatings with non- Newtonian nanofluid and Hafnium particles along slippery walls”, Coatings, vol. 9, No. 5, pp. 300, 2019. https://doi: 10.3390/coatings9050300.
• [16] Z. Ahmed, S. Nadeem, S. Saleem, and R. Ellahi, “Numerical study of unsteady flow and heat transfer CNTbased MHD nanofluid with variable viscosity over a permeable shrinking surface”, International Journal of Numerical Methods for heat and fluid flow, vol. 29(12), pp. 4607-4623, 2019. https://doi: 10.1108/HFF- 04-2019-0346.
• [17] M. Naseer, M. Y. Malik, S. Nadeem, and A. Rehman, “The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder”, Alexandra Engineering Journal, vol. 53, pp. 747-750, 2014.
• [18] R. R. Rangi, and N. Ahmad, “Boundary layer flow past over the stretching cylinder with variable thermal conductivity”, Applied Mathematics, vol. 3, p. 205-209, 2012.
• [19] M. S. Abel, and N. Mathesha, ”Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity and non-uniform heat source”, Applied Mathematical Modeling, vol. 32, pp. 1965-1983, 1997.
• [20] A. Öztürk, F. Sönme, and A. Kabakuş, “Determination of optimum parameters using different nanofluids in heat pipe heat exchangers with response surface method”, Chemical Engineering Communications, vol. 211, No. 5, pp. 725-735, 2023. https://doi.org/10.1080/00986445.2023.2289146
• [21] A. Öztürk, F. Sönme, and A. Kabakuş, “Optimization of Parameters Affecting the Thermal Efficiency in Heat Pipes Using Different Nanofluids with Taguchi Method”, Yüzüncü Yıl University Institute of Science and Technology Journal, vol. 28, No. 3, pp. 1081-1090, 2023. https://doi.org/10.10.53433/yyufbed.1242697
• [22] S. Mukhopadhyay, “Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at the boundary”, Alexandria Engineering Journal, vol. 52, pp. 563–569, 2013. http://dx.doi.org/10.1016/j.aej.2013.07.004
• [23] UI. H. Rizwan, Z. Zeeshan, S. S. Syed, " Existence of dual solution for MHD boundary layer flow over a stretching/shrinking surface in the presence of thermal radiation and porous media: KKL nanofluid model”, Heliyon, vol. 9(11), e20923, 2023.
• [24] B. Nagaraju, N. Kishan, J. V. Tawade, P. Meenapandi, B. Abdullaeva, M. Waqas, M. Gupta, N. Batool, and F. Ahmad, “Analysis of boundary layer flow of a Jeffrey fluid over a stretching or shrinking sheet immersed in a porous medium”, Partial Differential Equations in Applied Mathematics, vol. 12, 100951, 2024. https://doi.org/10.1016/j.padiff.2024.100951
• [25] R. S. Vidya, P. B. Mallikarjun, and A. J. Chamkha, “Analysis of MHD boundary layer flow of a viscous fluid past a stretching sheet employing the Legendre wavelet method”, International Journal of Ambient Energy, vol. 45(1). Article: 2310629, 2024. https://doi.org/10.1080/01430750.2024.2310629
• [26] M. K. Joseph, P. Ayuba , And A. S. Magaj, “Effect of Brinkman number and magnetic field on laminar convection in a vertical plate channel”, Science World Journal, vol. 12(4), pp. 58-62, 2017.
• [27] I. Buongiorno, ”Convective transport in nanofluids”, Journal of Heat Transfer, vol. 128, pp. 240-250, 2006.
• [28] A. R. Bestman, “The boundary layer flow past a semi-infinite heated porous plate for two-components plasma”, Astrophysics and Space Science, vol. 173, pp. 93-100, 1990.
• [29] F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th Edition., Wiley, 2017.
• [30] A. Bejan, Convection Heat Transfer, 4th edition, John Wiley & Sons, 2013.
• [31] B. R. Munson, A. T. Rothmayer, and T. H. Okiishi, Fundamentals of Fluid Mechanics, 7th Edition, John Wiley & Sons, 2013.
• [32] S. B. Pope, Turbulent Flows, Cambridge University Press, 2000.
• [33] T F. Laadhari, “Reynolds number effect on the dissipation function in wall-bounded flows”, Physics of Fluids, vol. 19(3), 038101, 2007. https://doi.org/10.1063/1.2711480
• [34] J. P. Monty, N. Hutchins, H. C. H. NG, I. Marusic and M. S. Chong, “A comparison of turbulent pipe, channel, and boundary layer flows”, Journal of Fluid Mechanics, vol. 632, pp 431-442, 2099. https://doi:10.1017/S0022112009007423
• [35] S. B. Pope, Turbulent Flows, Cambridge University Press, (Cornell University), 2000.
• [36] D. Modesti, and S. Pirozzoli, “Reynolds and Mach number effects in compressible turbulent channel flow”, International Journal of Heat and Fluid flows, vol. 39. Pp. 33-49, 2016.https://doi:10.1016/j.ijheatfluidflow.2016.01.007
• [37] H. Schlichting, and K. Gersten, Boundary-Layer Theory, 8th Revised and Enlarged edition, Springer, McGraw Hill, 2000. DOI 10.1007/978-3-642-85829-1
• [38] Y. A. Çengel, and A. J. Ghajar, Heat and Mass Transfer: Fundamentals and Applications, 5th Edition, McGraw- Hill, 2019.
• [39] F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, 7th edition, Wiley, 2017.
• [40] M. Ramzan, Z. Un Nisa, M. Ahmad, and M. Nazar, “Flow of Brinkman fluid with heat generation and chemical reaction”, Hindawi Complexity, vol. 2021, pp. 1-11, Article ID 5757991, 11 pages https://doi.org/10.1155/2021/5757991
• [41] N. S. Akhar, D. Tripathi, Z. H. Khan, and O. A. Beg, “A numerical study of magnetohydrodynamic transport of nanofluids over a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects, Chemical Physics Letters, 2016, https://doi.org/101016/j.cplett.2016.08.043
• [42] B. Bidin, and R. Nazar, “Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation”, European Journal of Scientific Research, vol 33(4), pp. 710-717, 2009.
• [43] A. Ishak, “MHD boundary layer flow due to an exponentially stretching sheet with radiation effect”, Sain Malaysiana, vol. 40, pp. 391-395, 2011.
• [44] S. R. Sherı, A. K. Suram1, and P. Modulgua, “Heat and Mass Transfer Effects On MHD Natural Convection Flow Past An Infinite Inclined Plate With Ramped Temperature”, J. KSIAM, Vol. 20(4), pp. 355–374, 2016. http://dx.doi.org/10.12941/jksiam.2016.20.355
• [45] Y. Dharmendar Reddy, B. Shankar Goud, Kottakkaran Sooppy Nisar, B. Alshahrani, M. Mahmoud, C. Park, “Heat absorption/generation effect on MHD heat transfer fluid flow along a stretching cylinder with a porous medium”, Alexandria Engineering Journal, Vol. 64, pp. 659-666, 2023. https://doi.org/10.1016/j.aej.2022.08.049
• [46] M. R. Krishnamurthy, B. C. Prasannakumara, B. J. Gireesha, and R. S. R. Gorla, R, “Effect of viscous dissipation on hydromagnetic fluid flow and heat transfer of nanofluid over an exponentially stretching sheet with fluidparticle suspension”, Cogent Mathematics, Vol. 2(1), pp. 1-18, 2015. https://doi.org/10.1080/23311835.2015.1050973
• [47] L. Shuguang, K. Raghunath, A. Alfaleh, A. et al. “Effects of activation energy and chemical reaction on unsteady MHD dissipative Darcy–Forchheimer squeezed flow of Casson fluid over horizontal channel”, Sci Rep, Vo. 13, 2666, 2023. https://doi.org/10.1038/s41598-023-29702-w