Abstract
Technologically, multi-layer fluid models are important in understanding fluid-fluid or fluid-nanoparticle interactions and their effects on flow and heat transfer characteristics. However, to the best of the authors’ knowledge, little attention has been paid to the study of three-layer fluid models with nanofluids. Therefore, a three-layer fluid flow model with nanofluids is formulated in this paper. The governing coupled nonlinear differential equations of the problem are non-dimensionalized by using appropriate fundamental quantities. The resulting multi-point boundary value problem is solved numerically by quasi-linearization and Richardson’s extrapolation with modified boundary conditions. The effects of the model parameters on the flow and heat transfer are obtained and analyzed. The results show that an increase in the nanoparticle concentration in the base fluid can modify the fluid-velocity at the interface of the two fluids and reduce the shear not only at the surface of the clear fluid but also at the interface between them. That is, nanofluids play a vital role in modifying the flow phenomena. Therefore, one can use nanofluids to obtain the desired qualities for the multi-fluid flow and heat transfer characteristics.
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References
Lavine, A. S. Analysis of fully developed opposing mixed convection between inclined parallel plates. Warme-und Stoffübetragung, 23, 249–257 (1988)
Barletta, A. Analysis of combined forced and free flow in a vertical channel with viscous dissipation and isothermal-isoflux boundary conditions. Journal of Heat Transfer, 121, 349–356 (1999)
Cheng, P. Heat transfer in geothermal systems. Advances in Heat Transfer (eds. Hartnett, J. P. and Irvine, J. F.), Academic Press, New York (1978)
Aung, W. Mixed convection in internal flow. Handbook of Single Phase Convective Heat Transfer (eds. Kakac, S., Shah, R. K., and Aung, W.), Wiley, New York (1987)
Rohsenow, W. M., Hartnett, J. P., and Cho, Y. I. Handbook of Heat Transfer, McGraw-Hill, New York (1998)
Tao, L. N. On combined free and forced convection in channels. Journal of Heat Transfer, 82, 233–238 (1960)
Habchi, S. and Acharya, S. Laminar mixed convection in a symmetrically or asymmetrically heated vertical channel. Numerical Heat Transfer, 9, 605–618 (1986)
Aung, W. and Worku, G. Developing flow and flow reversal in a vertical channel with asymmetric wall temperature. Journal of Heat Transfer, 108, 299–304 (1986)
Cheng, C. H., Kou, H. S., and Huang, W. H. Flow reversal and heat transfer of fully developed mixed convection in vertical channels. Journal of Thermophysics and Heat Transfer, 4, 375–383 (1990)
Vajravelu, K. and Sastri, K. S. Fully developed laminar free convection flow between two parallel vertical walls—I. International Journal of Heat and Mass Transfer, 20, 655–660 (1977)
Umavathi, J. C. and Malashetty, M. S. Magnetohydrodynamic mixed convection in a vertical channel. International Journal of Non-Linear Mechanics, 40, 91–101 (2005)
Ostrach, S. Low-gravity fluid flows. Annual Review of Fluid Mechanics, 14, 313–345 (1985)
Langlois, W. E. Buoyancy-driven flows in crystal-growth melts. Annual Review of Fluid Mechanics, 17, 191–215 (1985)
Schwabe, D. Surface-tension-driven flow in crystal growth metals. Crystals, 11, 848–852 (1986)
Kimura, T., Heya, N., Takeuchi, M., and Isomi, H. Natural convection heat transfer phenomena in an enclosure filled with two stratified fluids. Japan Society of Mechanical Engineering (B), 52, 617–625 (1986)
Malashetty, M. S., Umavathi, J. C., and Prathap-Kumar, J. Two-fluid magnetoconvection flow in an inclined channel. International Journal of Transport Phenomena, 3, 73–84 (2001)
Malashetty, M. S., Umavathi, J. C., and Prathap-Kumar, J. Magnetoconvection of two-immiscible fluids in a vertical enclosure. Heat and Mass Transfer, 42, 977–993 (2006)
Choi, S. U. S. Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exhibition, No.CONF-951135-29, OSTI, San Francisco (1995)
Choi, S. U. S., Zhang, Z. G., Yu, W., Lockwood, F. E., and Grulke, E. A. Anomalouly thermal conductivity enhancement in nanotube suspension. Applied Physics Letters, 79, 2252–2254 (2001)
Buongiorno, J. and Hu, W. Nanofluid coolants for advanced nuclear power plants. Proceedings of International Congress on Advances in Nuclear Power Plants, No. 5705, Carran Associate lnc., Seoul (2005)
Kaka, S. and Pramuanjaroenkij, A. Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer, 52, 3187–3196 (2009)
Buongiorno, J. Convective transport in nanofluids. Journal of Heat Transfer, 128, 240–250 (2006)
Kuznetsov, A. V. and Nield, D. A. Natural convective boundary-layer flow of a nanofluid past a vertical plate. International Journal of Thermal Sciences, 49, 243–247 (2010)
Aminossadati, S. M. and Ghasemi, B. Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure. European Journal of Mechanics B/Fluids, 28, 630–640 (2009)
Khanafer, K., Vafai, K., and Lightstone, M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International Journal of Heat and Mass Transfer, 46, 3639–3653 (2003)
Oztop, H. F. and Abu-Nada, E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow, 29, 1326–1336 (2008)
Yu, M. Z., Lin, J. Z., and Chen, L. H. Nanoparticle coagulation in a planar jet via moment method. Applied Mathematics and Mechanics (English Edition), 28(11), 1445–1453 (2007) DOI 10.1007/s10483-007-1104-8
Yin, Z. Q., Lin, J. Z., and Zhou, K. Research on nucleation and coagulation of nanoparticles in parallel twin jets. Applied Mathematics and Mechanics (English Edition), 29(2), 153–162 (2008) DOI 10.1007/s10483-008-0203-y
Lin, P. F. and Lin, J. Z. Prediction of nanoparticle transport and deposition in bends. Applied Mathematics and Mechanics (English Edition), 30(8), 957–968 (2009) DOI 10.1007/s10483-009-0802-z
Vajravelu, K., Prasad, K. V., Jinho, L., Changhoon, L., Pop, I., and Robert, A. V. G. Convective heat transfer in the flow of viscous Ag-water and Cu-water nanofluids over a stretching surface. International Journal of Thermal Sciences, 50, 843–851 (2011)
Das, S. K., Choi, S. U. S., Yu, W. Y., and Pradeep, T. Nanofluid: Science and Technology, Wiley InterScience, New Jersey (2007)
Na, T. Y. Computational Methods in Engineering Boundary Value Problems, Academic Press, New York (1979)
Bulirsch, R. and Stoer, J. Fehlerabschtzungen und extrapolation mit rationalen funktionen bei verfahren vom Richardson-typus. Numerische Mathematik, 6, 413–427 (1964)
Umavathi, J. C., Liu, I. C., Prathap-Kumar, J., and Shaik-Meera, D. Unsteady flow and heat transfer of porous media sandwiched between viscous fluids. Applied Mathematics and Mechanics (English Edition), 31(12), 1497–1516 (2010) DOI 10.1007/s10483-010-1379-6
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Project supported by the Imam Khomeini International University of Iran (No. 751166-91)
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Vajravelu, K., Prasad, K.V. & Abbasbandy, S. Convective transport of nanoparticles in multi-layer fluid flow. Appl. Math. Mech.-Engl. Ed. 34, 177–188 (2013). https://doi.org/10.1007/s10483-013-1662-6
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DOI: https://doi.org/10.1007/s10483-013-1662-6