Natural Convection Flow and Heat Transfer Enhancement of a Nanofluid past a Truncated Cone with Magnetic Field Effect

ABSTRACT

A nonsimilarity analysis is performed to investigate the laminar, free convection boundary layer flow over a permeable isothermal truncated cone in the presence of a transverse magnetic field effect. A suitable set of dimensionless variables is used and non-similar equations governing the problem are obtained. Fourth order Runge-Kutta with shooting technique is employed for the numerical solution of the obtained equations. Different water-based nanofluids containing Cu, Ag, CuO, Al_{2}O_{3}, and TiO_{2} are taken into consideration. The effects of pertinent parameters such as the solid volume fraction of nanoparticles, and magnetic field parameter have been investigated. Furthermore, different models of nanofluid based on different formulas for thermal conductivity and dynamic viscosity on the flow and heat transfer characteristics are discussed. Various comparisons with previously published work for the case of a vertical plate are performed and the results are found to be in excellent agreement.

A nonsimilarity analysis is performed to investigate the laminar, free convection boundary layer flow over a permeable isothermal truncated cone in the presence of a transverse magnetic field effect. A suitable set of dimensionless variables is used and non-similar equations governing the problem are obtained. Fourth order Runge-Kutta with shooting technique is employed for the numerical solution of the obtained equations. Different water-based nanofluids containing Cu, Ag, CuO, Al

Cite this paper

nullS. Ahmed and A. Mahdy, "Natural Convection Flow and Heat Transfer Enhancement of a Nanofluid past a Truncated Cone with Magnetic Field Effect,"*World Journal of Mechanics*, Vol. 2 No. 5, 2012, pp. 272-279. doi: 10.4236/wjm.2012.25033.

nullS. Ahmed and A. Mahdy, "Natural Convection Flow and Heat Transfer Enhancement of a Nanofluid past a Truncated Cone with Magnetic Field Effect,"

References

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[2] T. Y. Na and J. P. Chiou, “Laminar Natural Convection over a Slender Vertical Frustum of a Cone,” Heat and Mass Transfer, Vol. 12, No. 2, 1979, pp. 83-87. doi:10.1007/BF01002323

[3] T. Y. Na and J. P. Chiou, “Laminar Natural Convection over a Frustum of a Cone,” Applied Scientific Research, Vol. 35, No. 5-6, 1979, pp. 409-421. doi:10.1007/BF00420389

[4] A. J. Chamkha, “Coupled Heat and Mass Transfer by Natural Convection about a Truncated Cone in the Presence of Magnetic Field and Radiation Effects,” Numerical Heat Transfer, Part A, Vol. 39, No. 5, 2001, pp. 511-530.

[5] A. Raptis and A. K. Singh, “MHD Free Convection Flow Past an Accelerated Vertical Plate,” International Communications in Heat and Mass Transfer, Vol. 10, No. 4, 1983, pp. 313-321. doi:10.1016/0735-1933(83)90016-7

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[9] R. G. Hering and R. J. Grosh, “Laminar Free Convection from a Non-Isothermal Cone at Low Prandtl Number,” International Journal of Heat and Mass Transfer, Vol. 8, No. 10, 1965, pp. 1333-1337. doi:10.1016/0017-9310(65)90059-1

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[11] H. S. Takhar and P. C. Ram, “Magnetohydrodynamics Free Convection Flow of Water at 4?C, through a Porous Medium,” International Communications in Heat and Mass Transfer, Vol. 21, No. 3, 1994, pp. 371-376. doi:10.1016/0735-1933(94)90005-1

[12] Y. Xuan and O. Li, “Heat Transfer Enhancement of Nanofluids,” International Journal of Heat and Fluid Flow, Vol. 21, No. 1, 2000, pp. 58-64. doi:10.1016/S0142-727X(99)00067-3

[13] Q. Li and Y. Xuan, “Experimental Investigation of Transport Properties of Nanofluids,” In: B. X. Wang, Ed., Heat transfer science & technology, Higher Education Press, Beijing, 2000, pp. 757-784.

[14] D. Wen and Y. Ding, “Experimental Investigation into Convective Heat Transfer of Nanofluids at the Entrance Region under Laminar Flow Conditions, International Journal Heat and Mass Transfer, Vol. 47, No. 24, 2004, pp. 5181-5188. doi:10.1016/j.ijheatmasstransfer.2004.07.012

[15] P. Bhattacharya, S. Saha, A. Yadav, P. Phelan and R. Prasher, “Brownian Dynamics Simulation to Determine the Effect Thermal Conductivity of Nanofluids,” Journal of Applied Physics, Vol. 95, No. 11, 2004, pp. 6492-6494. doi:10.1063/1.1736319

[16] A. Mokmeli and M. Saffar-Avval, “Prediction of Nanofluid Convective Heat Transfer Using the Dispersion Model,” International Journal of Thermal Sciences, Vol. 49, No. 3, 2010, pp. 471-478. doi:10.1016/j.ijthermalsci.2009.09.005

[17] M. Mansour, R. Mohamed, M. Abd-Elaziz and S. Ahmed, “Numerical Simulation of Mixed Convection Flows in a Square Lid-Driven Cavity Partially Heated from Below Using Nanofluid, International Communications in Heat and Mass Transfer, Vol. 37, No. 10, 2010, pp. 1504-1512. doi:10.1016/j.icheatmasstransfer.2010.09.004

[18] R. Lotfi, Y. Saboohi and A. Rashidi, “Numerical Study of Forced Convective Heat Transfer of Nanofluids: Comparison of Different Approaches, International Communications in Heat and Mass Transfer, Vol. 37, No. 1, 2010, pp. 74-78. doi:10.1016/j.icheatmasstransfer.2009.07.013

[19] S. Choi, Z. Zhang, W. Yu, F. Lockwood and E. Grulke, “Anomalously Thermal Conductivity Enhancement in Nanotube Suspensions, Applied Physics Letter, Vol. 79, No. 14, 2001, pp. 2252-2254. doi:10.1063/1.1408272

[20] A. Mahdy and S. E .Ahmed, “Laminar Free Convection over a Vertical Wavy Surface Embedded in a Porous Medium Saturated with a Nanofluid,” Transport in Porous Media, Vol. 91, No. 2, 2012, pp. 423-435. doi:10.1007/s11242-011-9852-4

[21] W. Khan and I. Pop, “Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet,” International Journal of Heat and Mass Transfer, Vol. 53, No. 11-12, 2010, pp. 2477-2483. doi:10.1016/j.ijheatmasstransfer.2010.01.032

[22] M. Hojjat, S. Etemad and R. Bagheri, “Laminar Heat Transfer of Non-Newtonian Nanofluids in a Circular Tube,” Korean Journal of Chemical Engineering, Vol. 27, No. 5, 2010, pp. 1391-1396. doi:10.1007/s11814-010-0250-3

[23] H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” International Journal of Heat Fluid Flow, Vol. 29, No. 5, 2008, pp. 1326-1336. doi:10.1016/j.ijheatfluidflow.2008.04.009

[24] Z. Alloui, P. Vasseur and M. Reggio, “Natural Convection of Nanofluids in a Shallow Cavity Heated from Below,” International Journal of Thermal Sciences, Vol. 50, No. 3, 2011, pp. 385-393. doi:10.1016/j.ijthermalsci.2010.04.006

[25] K. A. Yih, “Effect of Radiation on Natural Convection about a Truncated Cone,” International Journal of Heat Mass Transfer, Vol. 42, No. 23, 1999, pp. 4299-4305. doi:10.1016/S0017-9310(99)00092-7

[26] T. Cebeci and P. Bradshaw, “Physical and Computational Aspects of Convective Heat Transfer,” Springer, New York, 1984, p. 270.

[27] P. Rana and R. Bhargava, “Numerical Study of Heat Transfer Enhancement in Mixed Convection Flow along a Vertical Plate with Heat Source/Sink Utilizing Nanofluids, Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 11, 2011, pp. 43184334. doi:10.1016/j.cnsns.2011.03.014

[1] H. T. Lin and C. C. Chen, “Mixed Convection on Vertical Plate for Fluids of Any Prandtl Number,” Heat and Mass Transfer, Vol. 22, No. 3-4, 1988, pp. 159-168. doi:10.1007/BF01052981

[2] T. Y. Na and J. P. Chiou, “Laminar Natural Convection over a Slender Vertical Frustum of a Cone,” Heat and Mass Transfer, Vol. 12, No. 2, 1979, pp. 83-87. doi:10.1007/BF01002323

[3] T. Y. Na and J. P. Chiou, “Laminar Natural Convection over a Frustum of a Cone,” Applied Scientific Research, Vol. 35, No. 5-6, 1979, pp. 409-421. doi:10.1007/BF00420389

[4] A. J. Chamkha, “Coupled Heat and Mass Transfer by Natural Convection about a Truncated Cone in the Presence of Magnetic Field and Radiation Effects,” Numerical Heat Transfer, Part A, Vol. 39, No. 5, 2001, pp. 511-530.

[5] A. Raptis and A. K. Singh, “MHD Free Convection Flow Past an Accelerated Vertical Plate,” International Communications in Heat and Mass Transfer, Vol. 10, No. 4, 1983, pp. 313-321. doi:10.1016/0735-1933(83)90016-7

[6] T. T. Kao, “Local Nonsimilar Solution for Laminar Free Convection Adjacent to a Vertical Wall,” Transactions of ASME Journal of Heat Transfer, Vol. 98, No. 2, 1976, pp. 321-322. doi:10.1115/1.3450544

[7] T. Y. Na, “Numerical Solution of Natural Convection Flow Past a Non-Isothermal Vertical Flat Plate,” Applied Scientific Research, Vol. 33, No. 5-6, 1978, pp. 519-543.

[8] S. Roy, “Free Convection from a Vertical Cone at High Prandtl Numbers,” Transactions of ASME Journal of Heat Transfer, Vol. 96, No. 1, 1974, pp. 115-117. doi:10.1115/1.3450128

[9] R. G. Hering and R. J. Grosh, “Laminar Free Convection from a Non-Isothermal Cone at Low Prandtl Number,” International Journal of Heat and Mass Transfer, Vol. 8, No. 10, 1965, pp. 1333-1337. doi:10.1016/0017-9310(65)90059-1

[10] M. Alamgir, “Over-All Heat Transfer from Vertical Cones in Laminar Free Convection: An Approximate Method,” Transactions of ASME Journal of Heat Transfer, Vol. 101, No. 1, 1979, pp. 174-176. doi:10.1115/1.3450912

[11] H. S. Takhar and P. C. Ram, “Magnetohydrodynamics Free Convection Flow of Water at 4?C, through a Porous Medium,” International Communications in Heat and Mass Transfer, Vol. 21, No. 3, 1994, pp. 371-376. doi:10.1016/0735-1933(94)90005-1

[12] Y. Xuan and O. Li, “Heat Transfer Enhancement of Nanofluids,” International Journal of Heat and Fluid Flow, Vol. 21, No. 1, 2000, pp. 58-64. doi:10.1016/S0142-727X(99)00067-3

[13] Q. Li and Y. Xuan, “Experimental Investigation of Transport Properties of Nanofluids,” In: B. X. Wang, Ed., Heat transfer science & technology, Higher Education Press, Beijing, 2000, pp. 757-784.

[14] D. Wen and Y. Ding, “Experimental Investigation into Convective Heat Transfer of Nanofluids at the Entrance Region under Laminar Flow Conditions, International Journal Heat and Mass Transfer, Vol. 47, No. 24, 2004, pp. 5181-5188. doi:10.1016/j.ijheatmasstransfer.2004.07.012

[15] P. Bhattacharya, S. Saha, A. Yadav, P. Phelan and R. Prasher, “Brownian Dynamics Simulation to Determine the Effect Thermal Conductivity of Nanofluids,” Journal of Applied Physics, Vol. 95, No. 11, 2004, pp. 6492-6494. doi:10.1063/1.1736319

[16] A. Mokmeli and M. Saffar-Avval, “Prediction of Nanofluid Convective Heat Transfer Using the Dispersion Model,” International Journal of Thermal Sciences, Vol. 49, No. 3, 2010, pp. 471-478. doi:10.1016/j.ijthermalsci.2009.09.005

[17] M. Mansour, R. Mohamed, M. Abd-Elaziz and S. Ahmed, “Numerical Simulation of Mixed Convection Flows in a Square Lid-Driven Cavity Partially Heated from Below Using Nanofluid, International Communications in Heat and Mass Transfer, Vol. 37, No. 10, 2010, pp. 1504-1512. doi:10.1016/j.icheatmasstransfer.2010.09.004

[18] R. Lotfi, Y. Saboohi and A. Rashidi, “Numerical Study of Forced Convective Heat Transfer of Nanofluids: Comparison of Different Approaches, International Communications in Heat and Mass Transfer, Vol. 37, No. 1, 2010, pp. 74-78. doi:10.1016/j.icheatmasstransfer.2009.07.013

[19] S. Choi, Z. Zhang, W. Yu, F. Lockwood and E. Grulke, “Anomalously Thermal Conductivity Enhancement in Nanotube Suspensions, Applied Physics Letter, Vol. 79, No. 14, 2001, pp. 2252-2254. doi:10.1063/1.1408272

[20] A. Mahdy and S. E .Ahmed, “Laminar Free Convection over a Vertical Wavy Surface Embedded in a Porous Medium Saturated with a Nanofluid,” Transport in Porous Media, Vol. 91, No. 2, 2012, pp. 423-435. doi:10.1007/s11242-011-9852-4

[21] W. Khan and I. Pop, “Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet,” International Journal of Heat and Mass Transfer, Vol. 53, No. 11-12, 2010, pp. 2477-2483. doi:10.1016/j.ijheatmasstransfer.2010.01.032

[22] M. Hojjat, S. Etemad and R. Bagheri, “Laminar Heat Transfer of Non-Newtonian Nanofluids in a Circular Tube,” Korean Journal of Chemical Engineering, Vol. 27, No. 5, 2010, pp. 1391-1396. doi:10.1007/s11814-010-0250-3

[23] H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” International Journal of Heat Fluid Flow, Vol. 29, No. 5, 2008, pp. 1326-1336. doi:10.1016/j.ijheatfluidflow.2008.04.009

[24] Z. Alloui, P. Vasseur and M. Reggio, “Natural Convection of Nanofluids in a Shallow Cavity Heated from Below,” International Journal of Thermal Sciences, Vol. 50, No. 3, 2011, pp. 385-393. doi:10.1016/j.ijthermalsci.2010.04.006

[25] K. A. Yih, “Effect of Radiation on Natural Convection about a Truncated Cone,” International Journal of Heat Mass Transfer, Vol. 42, No. 23, 1999, pp. 4299-4305. doi:10.1016/S0017-9310(99)00092-7

[26] T. Cebeci and P. Bradshaw, “Physical and Computational Aspects of Convective Heat Transfer,” Springer, New York, 1984, p. 270.

[27] P. Rana and R. Bhargava, “Numerical Study of Heat Transfer Enhancement in Mixed Convection Flow along a Vertical Plate with Heat Source/Sink Utilizing Nanofluids, Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 11, 2011, pp. 43184334. doi:10.1016/j.cnsns.2011.03.014