Abstract
This paper deals with the boundary layer flow and heat transfer of nanofluids over a stretching wedge with velocity-slip boundary conditions. In this analysis, Hall effect and Joule heating are taken into consideration. Four different types of water-base nanofluids containing copper (Cu), silver (Ag), alumina (Al2O3), and titania (TiO2) nanoparticles are analyzed. The partial differential equations governing the flow and temperature fields are converted into a system of nonlinear ordinary differential equations using a similarity transformation. The resulting similarity equations are then solved by using the shooting technique along with the fourth order Runge-Kutta method. The effects of types of nanoparticles, the volume fraction of nanoparticles, the magnetic parameter, the Hall parameter, the wedge angle parameter, and the velocityslip parameter on the velocity and temperature fields are discussed and presented graphically, respectively.
[1] X. Yimin, L. Qiang, Int. J. Heat Fluid Fl. 21, 58 (2000) http://dx.doi.org/10.1016/S0142-727X(99)00067-310.1016/S0142-727X(99)00067-3Search in Google Scholar
[2] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Netsu Bussei 7, 227 (1993) http://dx.doi.org/10.2963/jjtp.7.22710.2963/jjtp.7.227Search in Google Scholar
[3] S. K. Das, U. S. Stephen, Y. Wenhua, T. Pradeep, Nanofluids: Science and Technology, (Wiley- Interscience, Hoboken, 2007) http://dx.doi.org/10.1002/978047018069310.1002/9780470180693Search in Google Scholar
[4] S. Kakac, A. Pramuanjaroenkij, Int. J. Heat Mass Tran. 52, 3187 (2009) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2009.02.00610.1016/j.ijheatmasstransfer.2009.02.006Search in Google Scholar
[5] S. Witharana, H. Chen, Y. Ding, Nanoscale Res. Lett. 6, 231 (2011) http://dx.doi.org/10.1186/1556-276X-6-23110.1186/1556-276X-6-231Search in Google Scholar PubMed PubMed Central
[6] R. Nazar, M. Jaradat, N. M. Arifin, I. Pop, Cent. Eur. J. Phys. 9, 1195 (2011) http://dx.doi.org/10.2478/s11534-011-0024-510.2478/s11534-011-0024-5Search in Google Scholar
[7] A. A. Minea, R. S. Luciu, Microfluid Nanofluid 13, 977 (2012) http://dx.doi.org/10.1007/s10404-012-1017-410.1007/s10404-012-1017-4Search in Google Scholar
[8] J. H. Lee et al., Int. J. Micro-Nano Scale Transport 1, 269 (2010) http://dx.doi.org/10.1260/1759-3093.1.4.26910.1260/1759-3093.1.4.269Search in Google Scholar
[9] J. Eagen, R. Rusconi, R. Piazza, S. Yip, ASME J. Heat Transfer 132, 102402 (2010) http://dx.doi.org/10.1115/1.400130410.1115/1.4001304Search in Google Scholar
[10] K. F. V. Wong, O. D. Leon, Adv. Mech. Eng. 2010, 519659 (2010) 10.1155/2010/519659Search in Google Scholar
[11] J. Fan, L. Wang, ASME J. Heat Transfer 133, 040801 (2011) http://dx.doi.org/10.1115/1.400263310.1115/1.4002633Search in Google Scholar
[12] M. Sheikholeslami, M. Gorji-Bandpay, D. D. Ganji, Int. Commun. Heat Mass 39, 978 (2012) http://dx.doi.org/10.1016/j.icheatmasstransfer.2012.05.02010.1016/j.icheatmasstransfer.2012.05.020Search in Google Scholar
[13] S. Soleimani, M. Sheikholeslami, D. D. Ganji, M. Gorji-Bandpay, Int. Commun. Heat Mass 39, 565 (2012) http://dx.doi.org/10.1016/j.icheatmasstransfer.2012.01.01610.1016/j.icheatmasstransfer.2012.01.016Search in Google Scholar
[14] T. Grosan, I. Pop, ASME J. Heat Transfer 134, 082501 (2012) http://dx.doi.org/10.1115/1.400615910.1115/1.4006159Search in Google Scholar
[15] O. Mahian, A. Kianifar, S. A. Kalogirou, I. Pop, S. Wongwises, Int. J. Heat Mass Tran. 57, 582 (2013) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.10.03710.1016/j.ijheatmasstransfer.2012.10.037Search in Google Scholar
[16] M. Mustafa, T. Hayat, I. Pop, Int. J. Heat Mass Tran. 54, 5588 (2011) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.07.02110.1016/j.ijheatmasstransfer.2011.07.021Search in Google Scholar
[17] M. A. A. Hamad, M. Ferdows, Commun. Nonlinear Sci. Numer. Simulat. 17, 132 (2012) http://dx.doi.org/10.1016/j.cnsns.2011.02.02410.1016/j.cnsns.2011.02.024Search in Google Scholar
[18] N. Bachok, A. Ishak, I. Pop, Int. J. Heat Mass Tran. 55, 642 (2012) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.10.04710.1016/j.ijheatmasstransfer.2011.10.047Search in Google Scholar
[19] M. A. A. Hamad, M. Ferdows, Appl. Math. Mech. Engl. Ed. 33, 923 (2012) http://dx.doi.org/10.1007/s10483-012-1595-710.1007/s10483-012-1595-7Search in Google Scholar
[20] K. Vajravelu, et al., Int. J. Therm. Sci. 50, 843 (2011) http://dx.doi.org/10.1016/j.ijthermalsci.2011.01.00810.1016/j.ijthermalsci.2011.01.008Search in Google Scholar
[21] N. A. Yacob, A. Ishak, R. Nazar, I. Pop, Int. Commun. Heat mass 38, 149 (2011) http://dx.doi.org/10.1016/j.icheatmasstransfer.2010.12.00310.1016/j.icheatmasstransfer.2010.12.003Search in Google Scholar
[22] M. S. Abel, N. Mahesha, Appl. Math. Model. 32, 1965 (2008) http://dx.doi.org/10.1016/j.apm.2007.06.03810.1016/j.apm.2007.06.038Search in Google Scholar
[23] M. S. Abel, M. M. Nandeppanavar, Commun. Nonlinear Sci. Numer. Simul. 14, 2120 (2009) http://dx.doi.org/10.1016/j.cnsns.2008.06.00410.1016/j.cnsns.2008.06.004Search in Google Scholar
[24] T. R. Mahapatra, S. K. Nandy, A. S. Gupta, Int. J. Nonlinear Mech. 44, 124 (2009) http://dx.doi.org/10.1016/j.ijnonlinmec.2008.09.00510.1016/j.ijnonlinmec.2008.09.005Search in Google Scholar
[25] S. Dinarvand, Cent. Eur. J. Phys. 7, 114 (2009) http://dx.doi.org/10.2478/s11534-008-0145-710.2478/s11534-008-0145-7Search in Google Scholar
[26] T. Hayat, R. Ellahi, S. Asghar, Chem. Eng. Commun. 194, 37 (2007) http://dx.doi.org/10.1080/0098644060064286810.1080/00986440600642868Search in Google Scholar
[27] R. Ellahi, M. Hameed, Int. J. Numer. Meth. Heat Fluid Flow. 22, 24 (2012) http://dx.doi.org/10.1108/0961553121118877510.1108/09615531211188775Search in Google Scholar
[28] R. Ellahi, Appl. Math. Model. 37, 1451 (2013) http://dx.doi.org/10.1016/j.apm.2012.04.00410.1016/j.apm.2012.04.004Search in Google Scholar
[29] M. A. A. Hamad, I. Pop, A. I. Md. Ismail, Nonlinear Anal. Real World Appl. 12, 1338 (2011) http://dx.doi.org/10.1016/j.nonrwa.2010.09.01410.1016/j.nonrwa.2010.09.014Search in Google Scholar
[30] M. S. Khan, I. Karim, L. E. Ali, A. Islam, Int. Nano Lett. 2, 24 (2012) http://dx.doi.org/10.1186/2228-5326-2-2410.1186/2228-5326-2-24Search in Google Scholar
[31] G. W. Sutton, A. Sherman, Engineering Magnetohydrodynamics, 1rd edition (McGraw-Hill, New York, 1965) Search in Google Scholar
[32] T. Hayat, R. Ellahi, S. Asghar, Chem. Eng. Commun. 195, 958 (2008) http://dx.doi.org/10.1080/0098644080190657510.1080/00986440801906575Search in Google Scholar
[33] T. Hayat, S. Nadeem, R. Ellahi, S. Asghar, Nonlinear Anal. Real World Appl. 11, 184 (2010) http://dx.doi.org/10.1016/j.nonrwa.2008.10.04610.1016/j.nonrwa.2008.10.046Search in Google Scholar
[34] E. M. Abo-Eldahab, A. M. Salem, Int. Commun. Heat Mass 31, 343 (2004) http://dx.doi.org/10.1016/j.icheatmasstransfer.2004.02.00510.1016/j.icheatmasstransfer.2004.02.005Search in Google Scholar
[35] A. M. Salem, M. A. El-Aziz, Appl. Math. Model. 32, 1236 (2008) http://dx.doi.org/10.1016/j.apm.2007.03.00810.1016/j.apm.2007.03.008Search in Google Scholar
[36] M. A. El-Aziz, Meccanica 45, 97 (2010) http://dx.doi.org/10.1007/s11012-009-9227-x10.1007/s11012-009-9227-xSearch in Google Scholar
[37] X. H. Su, L. C. Zheng, X. X. Zhang, Appl. Math. Mech. Engl. Ed. 33, 1555 (2012) http://dx.doi.org/10.1007/s10483-012-1643-910.1007/s10483-012-1643-9Search in Google Scholar
[38] J. Zhu, L. C. Zheng, Z. G. Zhang, Appl. Math. Mech. Engl. Ed. 31, 439 (2010) http://dx.doi.org/10.1007/s10483-010-0404-z10.1007/s10483-010-0404-zSearch in Google Scholar
[39] T. Fang, J. Zhang, S. Yao, Commun. Nonlinear Sci. Numer. Simul. 14, 3731 (2009) http://dx.doi.org/10.1016/j.cnsns.2009.02.01210.1016/j.cnsns.2009.02.012Search in Google Scholar
[40] C. Y. Wang, Nonlinear Anal. Real World Appl. 10, 375 (2009) http://dx.doi.org/10.1016/j.nonrwa.2007.09.01310.1016/j.nonrwa.2007.09.013Search in Google Scholar
[41] B. Sahoo,Cent. Eur. J. Phys. 8, 498 (2010) Search in Google Scholar
[42] S. Mukhopadhyay, Ain Shams Eng. J. 4, 485 (2013) http://dx.doi.org/10.1016/j.asej.2012.10.00710.1016/j.asej.2012.10.007Search in Google Scholar
[43] J. J. Niu, L. C. Zheng, X. X. Zhang, Adv. Materials Res. 354, 45 (2011) http://dx.doi.org/10.4028/www.scientific.net/AMR.354-355.4510.4028/www.scientific.net/AMR.354-355.45Search in Google Scholar
[44] L. C. Zheng, C. L. Zhang, X. X. Zhang, J. H. Zhang, J. Franklin. Inst. 350, 990 (2013) http://dx.doi.org/10.1016/j.jfranklin.2013.01.02210.1016/j.jfranklin.2013.01.022Search in Google Scholar
[45] W. Ibrahim, B. Shankar, Comput. Fluids 75, 1 (2013) http://dx.doi.org/10.1016/j.compfluid.2013.01.01410.1016/j.compfluid.2013.01.014Search in Google Scholar
[46] L. G. Grubka, K. M. Bobba, ASME J Heat Transfer 107, 248 (1985) http://dx.doi.org/10.1115/1.324738710.1115/1.3247387Search in Google Scholar
[47] C. H. Chen, Heat Mass Transfer 33, 471 (1998) http://dx.doi.org/10.1007/s00231005021710.1007/s002310050217Search in Google Scholar
© 2013 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.