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Marangoni convection flow along a wavy surface with non-linear radiation. (English) Zbl 07168300

Summary: A boundary-layer analysis is presented for steady, two-dimensional, Marangoni convection along an irregular surface. Thick radiation limit is considered to express the radiative heat flux. A coordinate transformation is adopted to convert the physical domain into computational domain. Implicit finite difference method is then used to obtain the solutions of the problem. The main purpose of this study is to demonstrate the radiation effects on the dissipative layers. Numerical solutions are presented in the form of skin friction coefficient, heat transfer coefficient, velocity and temperature profiles, streamlines and isotherms. It is observed that thermal radiation has a pronounced effect on the flow field and amplitude of the harmonic oscillations also decay with \(R_d\). The momentum and thermal boundary-layer thickness increases as \(R_d\) gets augmented.

MSC:

76Rxx Diffusion and convection
35Kxx Parabolic equations and parabolic systems
76Dxx Incompressible viscous fluids
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[1] L. G. Napolitano, Microgravity fluid dynamics, in: 2nd Levitch conference, Washington, 1978.; Napolitano, L. G.; , in, Microgravity fluid dynamics (1978)
[2] L. G. Napolitano, Marangoni boundary layers, in: Proceedings of the 3rd European symposium on material science in space, Grenoble, 1979.; Napolitano, L. G., Marangoni boundary layers, in: Proceedings of the 3rd European symposium on material science in space, Grenoble (1979) · Zbl 0485.76032
[3] L. G. Napolitano and C. Golia, Similar plane Marangoni boundary layers, 3rd Levitch Conf., Madrid, 1980.; Napolitano, L. G.; Golia, C., Similar plane Marangoni boundary layers, 3rd Levitch Conf., Madrid (1980) · Zbl 0485.76032
[4] L. G. Napolitano and C. Golia, Coupled Marangoni boundary layers, Acta Astronaut. 8 (1981), 417-434.; Napolitano, L. G.; C. Golia, Coupled Marangoni boundary layers Acta Astronaut, 8, 417-434 (1981) · Zbl 0485.76032
[5] L. G. Napolitano, Surface and buoyancy driven free convection, Acta Astronaut. 9 (1982), 199-215.; Napolitano, L. G., Surface and buoyancy driven free convection, Acta Astronaut, 9, 199-215 (1982) · Zbl 0495.76082
[6] L. G. Napolitano and S. Russo, Similar axially symmetric Marangoni boundary layers, Acta Astronaut. 11 (1984), 189-198.; Napolitano, L. G.; Russo, S., Similar axially symmetric Marangoni boundary layers, Acta Astronaut, 11, 189-198 (1984) · Zbl 0559.76037
[7] C. Golia and A. Viviani, Non isobaric boundary layers related to Marangoni flows, Meccanica. 21 (1986), 200-204.; Golia, C.; Viviani, A., Non isobaric boundary layers related to Marangoni flows Meccanica, 21, 200-204 (1986) · Zbl 0609.76109
[8] L. G. Napolitano, A. Viviani and R. Savino, Double-diffusive boundary layers along vertical free surfaces, Int. J. Heat Mass Transfer. 35 (1992), 1003-1025.; Napolitano, L. G.; Viviani, A.; Savino, R., Double-diffusive boundary layers along vertical free surfaces, Int. J. Heat Mass Transfer, 35, 1003-1025 (1992) · Zbl 0825.76849
[9] A. Oron and P. Rosenau, On a nonlinear thermocapillary effect in thin liquid layers, J. Fluid Mech. 273 (1994), 361-374.; Oron, A.; Rosenau, P.; Fluid Mech, J., On a nonlinear thermocapillary effect in thin liquid layers, 273, 361-374 (1994) · Zbl 0825.76240
[10] Z. Zeng, H. Mizuseki, K. Higashino and Y. Kawazoe, Direct numerical simulation of oscillatory Marangoni convection in cylindrical liquid bridges, J. Crystal Growth. 204 (1999), 395-404.; Zeng, Z.; Mizuseki, H.; Higashino, K.; Kawazoe, Y.; Crystal Growth, J., Direct numerical simulation of oscillatory Marangoni convection in cylindrical liquid bridges, 204, 395-404 (1999) · Zbl 1015.76073
[11] D. M. Christopher and B. Wang, Prandtl number effects for Marangoni convection over a flat surface, Int. J. Therm. Sci. 40 (2001), 564-570.; Christopher, D. M.; Wang, B., Prandtl number effects for Marangoni convection over a flat surface, Int. J. Therm. Sci, 40, 564-570 (2001)
[12] Z. Zeng, H. Mizuseki, K. Shimamura, K. Higashino, T. Fukuda and Y. Kawazoe, Marangoni convection in model of floating zone under microgravity, J. Crystal Growth. 229 (2001), 601-604.; Zeng, Z.; Mizuseki, H.; Shimamura, K.; Higashino, K.; Fukuda, T.; Kawazoe, Y.; Crystal Growth, J., Marangoni convection in model of floating zone under microgravity, 229, 601-604 (2001) · Zbl 1015.76073
[13] Z. Zeng, H. Mizuseki, K. Simamura, T. Fukuda, K. Higashino and Y. Kawazoe, Three dimensional oscillatory thermocapillary convection in liquid bridge under microgravity, Int. J. Heat Mass Transfer. 44 (2001), 3765-3774.; Zeng, Z.; Mizuseki, H.; Simamura, K.; Fukuda, T.; Higashino, K.; Kawazoe, Y.; ; Heat Mass, Int. J., dimensional oscillatory thermocapillary convection in liquid bridge under microgravity, Transfer, 44, 3765-3774 (2001) · Zbl 1015.76073
[14] Z. Zeng, H. Mizuseki, K. Shimamura, T. Fukuda, Y. Kawazoe and K. Higashino, Usefulness of experiments with model fluid for thermocapillary convection-effect of Prandtl number on two-dimensional thermocapillary, J. Crystal Growth. 234 (2001), 272-278.; Zeng, Z.; Mizuseki, H.; Shimamura, K.; Fukuda, T.; Kawazoe, Y.; Higashino, K., Usefulness of experiments with model fluid for thermocapillary convection-effect of Prandtl number on two-dimensional thermocapillary, J. Crystal Growth, 234, 272-278 (2001) · Zbl 1015.76073
[15] I. Pop, A. Postelnicu and T. Grosan, Thermosolutal Marangoni forced convection boundary layers, Meccanica. 36 (2001), 555-571.; Pop, I.; Postelnicu, A.; Grosan, T., Thermosolutal Marangoni forced convection boundary layers, Meccanica, 36, 555-571 (2001) · Zbl 1060.76109
[16] A. Al-Mudhaf and A.J. Chamkha, Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects, Heat Mass Transfer. 42 (2005), 112-121.; Al-Mudhaf, A.; Chamkha, A. J.; Transfer, Heat Mass, Similarity solutions for MHD thermosolutal Marangoni convection over a flat surface in the presence of heat generation or absorption effects, 42, 112-121 (2005)
[17] J. Zueco and O. A. Bèg, Network numerical simulation of hydromagnetic Marangoni mixed convection boundary layers, Chem. Eng. Commun. 198 (2011), 552-571.; Zueco, J.; Bèg, O. A.; , Network numerical simulation of hydromagnetic Marangoni mixed convection boundary layers, 198, 552-571 (2011)
[18] Y. Lin, L. Zheng and X. Zhang, Magnetohydrodynamics thermocapillary marangoni convection heat transfer of power-law fluids driven by temperature gradient, J. Heat Transfer. 135 (2013), 051702-051702-6.; Lin, Y.; Zheng, L.; Zhang, X., Magnetohydrodynamics thermocapillary marangoni convection heat transfer of power-law fluids driven by temperature gradient, J. Heat Transfer, 135 (2013)
[19] Y. Lin, L. Zheng and X. Zhang, Radiation effects on Marangoni convection flow and heat transfer in pseudo-plastic non-Newtonian nanofluids with variable thermal conductivity, Int. J. Heat Mass Transfer. 77 (2014), 708-716.; Lin, Y.; Zheng, L.; Zhang, X.; Heat Mass, Int. J.; , Radiation effects on Marangoni convection flow and heat transfer in pseudo-plastic non-Newtonian nanofluids with variable thermal conductivity, 77, 708-716 (2014)
[20] Y. Lin and L. Zheng, Marangoni boundary layer flow and heat transfer of copper-water nanofluid over a porous medium disk, AIP Adv. 5 (2015), 107225-1-15.; Lin, Y.; Zheng, L., Marangoni boundary layer flow and heat transfer of copper-water nanofluid over a porous medium disk, AIP Adv, 5 (2015)
[21] L. S. Yao, Natural convection along a vertical wavy surface. ASME J. Heat Transfer. 105 (1983), 465-468.; Yao, L. S.; , Natural convection along a vertical wavy surface. ASME J. Heat, 105, 465-468 (1983)
[22] S. G. Moulic and L. S. Yao, Natural convection along a wavy surface with uniform heat flux, ASME J. Heat Tranfer. 111 (1989), 1106-1108.; Moulic, S. G.; Yao, L. S., Natural convection along a wavy surface with uniform heat flux, ASME J. Heat Tranfer, 111, 1106-1108 (1989)
[23] S. G. Moulic and L. S. Yao, Mixed convection along a wavy surface, ASME J. Heat Transfer. 111 (1989), 974-979.; Moulic, S. G.; Yao, L. S., Mixed convection along a wavy surface, ASME J. Heat Transfer, 111, 974-979 (1989)
[24] D. A. S. Rees and I. Pop, Boundary layer flow and heat transfer on a continuous wavy surface, Acta Mech. 12 (1995), 149-158.; Rees, D. A. S.; Pop, I.; , Boundary layer flow and heat transfer on a continuous wavy surface, 12, 149-158 (1995) · Zbl 0856.76017
[25] D. A. S. Rees and I. Pop, Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium, ASME J. Heat Transfer, 117 (1995), 545-550.; Rees, D. A. S.; Pop, I.; Heat Transfer, ASME J., Free convection induced by a vertical wavy surface with uniform heat flux in a porous medium, 117, 545-550 (1995)
[26] D. A. S. Rees and I. Pop, The effect of longitudinal surface waves on free convection from vertical surfaces in porous media, Int. Commun. Heat Mass. 24 (1997), 419-425.; Rees, D. A. S.; Pop, I.; Mass, Heat, The effect of longitudinal surface waves on free convection from vertical surfaces in porous media, Int. Commun, 24, 419-425 (1997)
[27] M. A. Hossain and D. A. S. Rees, Radiation-conduction interaction on mixed convection flow along a slender vertical cylinder, J. Thermophys. Heat Transfer. 12 (1998), 611-614.; Hossain, M. A.; Rees, D. A. S.; , Radiation-conduction interaction on mixed convection flow along a slender vertical, 12, 611-614 (1998)
[28] S. Siddiqa, M. A. Hossain and S.C. Saha, The effect of thermal radiation on the natural convection boundary layer flow over a wavy horizontal surface, Int. J. Therm. Sci. 84 (2014), 143-150.; Siddiqa, S.; Hossain, M. A.; Saha, S. C.; , The effect of thermal radiation on the natural convection boundary layer flow over a, 84, 143-150 (2014)
[29] E. M. Sparrow and R. D. Cess, Radiation heat transfer, augmented edition, hemisphere media, Int. J. Heat Mass Transfer. 5 (1962), 179-806.; Sparrow, E. M.; Cess, R. D.; , Radiation heat transfer, augmented edition hemisphere media, 5, 179-806 (1962)
[30] V. S. Arpaci, Effect of thermal radiation on the laminar free convection from a heated vertical plate, Int. J. Heat Mass Transfer. 11 (1968), 871-881.; Arpaci, V. S., Effect of thermal radiation on the laminar free convection from a heated vertical plate, Int. J. Heat Mass Transfer, 11, 871-881 (1968) · Zbl 0159.57902
[31] M. A. Hossain, M. Kutubuddin and I. Pop, Effect of conduction-radiation interaction on the mixed convection flow from a horizontal cylinder, Int. J. Heat Mass Transfer. 35 (1999), 307-314.; Hossain, M. A.; Kutubuddin, M.; Pop, I.; , Effect of conduction-radiation interaction on the mixed convection flow from a horizontal cylinder, 35, 307-314 (1999)
[32] M. M. Molla and M. A. Hossain, Radiation effect on mixed convection laminar flow along a vertical wavy surface, Int. J. Therm. Sci. 46 (2007), 926-935.; Molla, M. M.; Hossain, M. A., Radiation effect on mixed convection laminar flow along a vertical wavy surface, IntJ. Therm. Sci, 46, 926-935 (2007)
[33] S. Siddiqa, N. Begum and M. A. Hossain, Radiation effects from an isothermal vertical wavy cone with variable fluid properties, Appl. Math. Comput. 289 (2016), 149-158.; Siddiqa, S.; Begum, N.; Hossain, M. A., Radiation effects from an isothermal vertical wavy cone with variable fluid properties, Appl. Math. Comput, 289, 149-158 (2016) · Zbl 1410.76425
[34] S. Siddiqa, N. Begum, M. A. Hossain and N. Massarotti, Influence of thermal radiation on contaminated air and water flow past a vertical wavy frustum of a cone, Int. Commun. Heat Mass. 76 (2016), 63-68.; Siddiqa, S.; Begum, N.; Hossain, M. A.; Massarotti, N., Influence of thermal radiation on contaminated air and water flow past a vertical wavy frustum of a cone, Int. Commun. Heat Mass, 76, 63-68 (2016) · Zbl 1410.76425
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