Magnetohydrodynamic and radiation effects on the heat transfer of a continuously stretching/shrinking sheet with mass transpiration of the horizontal boundary. (English) Zbl 07836280
Summary: The aim of this paper is the investigation of heat transfer regarding the cases of both stretching and shrinking sheets with a sponge-like horizontal wall that allows for mass transpiration. The effects of Prandtl number, radiation and external magnetic field are extensively examined. The Navier-Stokes equations are reduced to partial differential equations, which are eventually become ordinary differential equations and solved analytically. Furthermore, the power-law wall temperature and heat flux boundary conditions are imposed on the boundary layer energy equation for obtaining exact analytical solutions. The results revealed that in both the stretching and shrinking sheet scenarios the thickness of the thermal boundary layer decreases with either increasing of transpiration as well as the Chandrasekhar and Prandtl number numbers or decreasing radiation number. Additionally, the characteristics of the heat transfer regarding a shrinking sheet and those of a stretching sheet are found not to be similar. In fact, a new solution branch appeared which indicates that multiple solutions may emerge under certain circumstances. Finally, by using the present analytical relationships, theoretical guidelines can be given for regulating the procedure.
MSC:
| 76Dxx | Incompressible viscous fluids |
| 76Wxx | Magnetohydrodynamics and electrohydrodynamics |
| 76Mxx | Basic methods in fluid mechanics |
References:
| [1] | Weiss, P.; Fisher, E. G., Extrusion of plastics, 52-53, (1978), Halsted Press: Halsted Press New York, 3 (1976) 344 J. Polym. Sci. Polym. Lett. Ed. 16 |
| [2] | Polychronopoulos, N. D.; Papathanasiou, T. D., A study on the effect of drawing on extrudate swell in film casting, Appl. Rheol., 25, 1-7, (2015) |
| [3] | Polychronopoulos, N. D.; Sarris, I. E.; Papathanasiou, T. D., 3D features in the calendaring of thermoplastics: A computational investigation, Polym. Eng. Sci., 54, 1712-1722, (2014) |
| [4] | Benos, L. T.; Kakarantzas, S. C.; Sarris, I. E.; Grecos, A. P.; Vlachos, N. S., Analytical and numerical study of MHD natural convection in a horizontal shallow cavity with heat generation, Int. J. Heat Mass Transf., 75, 19-30, (2014) |
| [5] | Kakarantzas, S. C.; Benos, L. T.; Sarris, I. E.; Knaepen, B.; Grecos, A. P.; Vlachos, N. S., MHD liquid metal flow and heat transfer between vertical coaxial cylinders under horizontal magnetic field, Int. J. Heat Fluid Flow., 65, 342-351, (2017) |
| [6] | Karvelas, E.; Liosis, C.; Benos, L.; Karakasidis, T.; Sarris, I., Micromixing efficiency of particles in heavy metal removal processes under various inlet conditions, Water, 11, 6, 1135, (2019) |
| [7] | Benos, L.; Sarris, I. E., Analytical study of the Magnetohydrodynamic natural convection of a nanofluid filled horizontal shallow cavity with internal heat generation, Int. J. Heat Mass Transf., 130, 862-873, (2019) |
| [8] | Benos, L. T.; Karvelas, E. G.; Sarries, I. E., A theoretical model for the Magnetohydrodynamic natural convection of a CNT-water nanofluid incorporating a renovated Hamilton-Crosser model, Int. J. Heat Mass Transf., 135, 548-560, (2019) |
| [9] | Sakiadis, B. C., Boundary-layer behavior on continuous solid surface: I. boundary-layer equations for two-dimensional and axisymmetric flow, AIChE J, 7, 26-28, (1961) |
| [10] | Sakiadis, B. C., Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface, AIChE J, 7, 221-225, (1961) |
| [11] | Sakiadis, B. C., Boundary –layer behavior on continuous solid surfaces: III. The boundary layer on a continuous cylindrical surface, AIChE J, 7, 467-472, (1961) |
| [12] | Crane, L. J., Flow past a stretching plate, Zeitschrift Für Angew, Math. Und Phys. ZAMP., 21, 645-647, (1970) |
| [13] | Anderson, H. I.; Aarseth, J. B.; Dandapat, B. S., Heat transfer in a liquid film on an unsteady stretching surface, Int. J. Heat Mass Transf., 43, 69-74, (2000) · Zbl 1042.76507 |
| [14] | Liao, S. J., On the analytic solution of Magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, J. Fluid Mech., 189-212, (2003) · Zbl 1063.76671 |
| [15] | Mahabaleshwar, U. S.; Sarris, I. E.; Lorenzini, G., Effect of radiation and Navier slip boundary of Walter’s liquid B flow over a stretching sheet in a porous media, Int. J. Heat Mass Transf., 127, 1327-1337, (2018) |
| [16] | Mahabaleshwar, U. S.; Sarris, I. E.; Hill, A. A.; Lorenzini, G.; Pop, I., An MHD couple stress fluid due to a perforated sheet undergoing linear stretching with heat transfer, Int, J. Heat Mass Transf., 105, 157-167, (2017) |
| [17] | Benos, L. T.; Mahabaleshwar, U. S.; Sakanaka, P. H.; Sarris, I. E., Thermal analysis of the unsteady sheet stretching subject to slip and Magnetohydrodynamic effects, Therm. Sci. Eng. Prog., 13, (2019) |
| [18] | Gupta, P. S.; Gupta, A. S., Heat and mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. Eng., 55, 744-746, (1977) |
| [19] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Baleanu, D.; Lorenzini, G., An exact analytical solution of the unsteady magnetohydrodynamics nonlinear dynamics of laminar boundary layer due to an impulsively linear stretching sheet, Contin. Mech. Thermodyn., 29, 559-567, (2017) · Zbl 1365.76343 |
| [20] | Magyari, E.; Keller, B., Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface, J. Phys. D. Appl. Phys., 32, 577-585, (1999) |
| [21] | Liao, S., A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int. J. Heat Mass Transf., 48, 2529-2539, (2005) · Zbl 1189.76142 |
| [22] | Fang, T.; Liang, W.; Lee, C. F., A new solution branch for the Blasius equation-A shrinking sheet problem, Comput. Math. With Appl., 56, 12, 3088-3095, (2008) · Zbl 1165.76324 |
| [23] | Fang, T. G.; Zhang, J.; Yao, S. S., Viscous flow over an unsteady shrinking sheet with mass transfer, Chinese Phys. Lett., 26, (2009) |
| [24] | Fang, T., Boundary layer flow over a shrinking sheet with power-law velocity, Int. J. Heat Mass Transf., 51, 5838-5843, (2008) · Zbl 1157.76010 |
| [25] | Sajid, M.; Javed, T.; Hayat, T., MHD rotating flow of a viscous fluid over a shrinking surface, Nonlinear Dyn, 51, 259-265, (2008) · Zbl 1170.76366 |
| [26] | Hayat, T.; Abbas, Z.; Sajid, M., On the analytic solution of Magnetohydrodynamic flow of a second grade fluid over a shrinking sheet, J. Appl. Mech. Trans. ASME., 74, 1165-1171, (2007) |
| [27] | Fang, T.; Zhang, J., Thermal boundary layers over a shrinking sheet: An analytical solution, Acta Mech, 209, 325-343, (2010) · Zbl 1381.76056 |
| [28] | Mabood, F.; Ibrahim, S. M.; Khan, W. A., Effect of melting and heat generation/absorption on Sisko nanofluid over a stretching surface with nonlinear radiation, Phys. Scr., 94, Article 065701 pp., (2019) |
| [29] | Pelekasis, N.; Benos, L.; Gomes, R., Deflection of a liquid metal jet/drop in a tokamak environment, Fusion Eng. Des., 89, (2014) |
| [30] | Pelekasis, N.; Benos, L., Static arrangement of a capillary porous system (CPS): Modeling, Fusion Eng. Des., 117, (2017) |
| [31] | Liao, S. J., A new branch of solutions of boundary-layer flows over a permeable stretching plate, Int. J. Non. Linear. Mech., 42, 819-830, (2007) · Zbl 1200.76046 |
| [32] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Azese, M. N., Effect of radiation on thermosolutal Marangoni convection in a porous medium with chemical reaction and heat source/sink, Physics of Fluids, 32, 11, Article 113602 pp., (2020) |
| [33] | Siddheshwar, P. G.; Mahabaleshwar, U. S., Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet, Int. J. Nonlinear Mech., 40, 807-820, (2005) · Zbl 1349.76906 |
| [34] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Kelson, N. A., An MHD Navier’s Slip Flow Over Axisymmetric Linear Stretching Sheet Using Differential Transform Method, International Journal of Applied and Computational Mathematics, 4, 1, 30, (2017) · Zbl 1386.35347 |
| [35] | Mahabaleshwar, U. S.; Vinay Kumar, P. N.; Sheremet, M., Magnetohydrodynamics flow of a nanofluid driven by a stretching/shrinking sheet with suction, Springer Plus, 5, 1, 901, (2016) |
| [36] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Sheremet, M. A.; Baleanu, D.; Lorenzini, E., Mass transpiration on Newtonian flow over a porous stretching/shrinking sheet with slip, Chinese Journal of Physics, 63, 130-137, (2020) · Zbl 07829559 |
| [37] | Mahabaleshwar, U. S.; Vinay Kumar, P. N.; Nagaraju, K. R.; Bognár, G.; Nayakar, R. S.N., A new exact solution for the flow of a fluid through porous media for a variety of boundary conditions, Fluids, 4, 3, 125, (2019) |
| [38] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Nadagouda, M. N.; Bennacer, R.; Sheremet, M. A., Effects of Dufour and Sort mechanisms on MHD mixed convective-radiative non-Newtonian liquid flow and heat transfer over a porous sheet, Journal of Thermal Science and Engineering Progress, 16, Article 100459 pp., (2020) |
| [39] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Nadagouda, M. N.; Bennacer, R.; Baleanu, D., An MHD viscous liquid stagnation point flow and heat transfer with thermal radiation and transpiration, Journal of Thermal Science and Engineering Progress, 16, Article 100379 pp., (2020) |
| [40] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N.; Kelson, N. A., An MHD Navier’s Slip Flow Over Axisymmetric Linear Stretching Sheet Using Differential Transform Method, International Journal of Applied and Computational Mathematics, 4, 1, 30, (2017) · Zbl 1386.35347 |
| [41] | Mahabaleshwar, U. S.Vinay Kumar; P. N., Nagaraju; Gabriella Bognár, K. R.; Nayakar, R. S.N., A new exact solution for the flow of a fluid through porous media for a variety of boundary conditions, Fluids 2019, 4, 3, 125, (2019) |
| [42] | Yadav, D.; Mahabaleshwar, U. S.; Wakif, A.; Chand, R., Significance of the inconstant viscosity and internal heat generation on the occurrence of Darcy-Brinkman convective motion in a couple-stress fluid saturated porous medium: An exact analytical solution, International communications in heat and mass transfer, 122, Article 105165 pp., (2021) |
| [43] | Xenos, Michalis A.; Petropoulou, Eugenia N.; Siokis, Anastasios; Mahabaleshwar, U. S., Solving the nonlinear boundary layer flow equations with pressure gradient and radiation, Symmetry, 12, 5, 710, (2020) |
| [44] | Mahabaleshwar, U. S.; Nagaraju, K. R.; Vinay Kumar, P. N., Martin Ndi Azese, Effect of radiation on thermosolutal Marangoni convection in a porous medium with chemical reaction and heat source/sink, Physics of fluids, 32, 11, Article 113602 pp., (2020) |
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