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Published in: Meccanica 3/2013

01-04-2013

Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition

Authors: M. M. Rahman, I. A. Eltayeb

Published in: Meccanica | Issue 3/2013

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Abstract

Heat transfer characteristics of a two-dimensional steady hydromagnetic natural convection flow of nanofluids over a non-linear stretching sheet taking into account the effects of radiation and convective boundary condition has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The local similarity solutions are obtained by using very robust computer algebra software Maple 13. The results corresponding to the dimensionless temperature profiles and the reduced Nusselt number, Sherwood number and skin friction coefficient are displayed graphically for various pertinent parameters. The results show that temperature within the boundary layer is enhanced with the increase of the Biot number, buoyancy due to nanoparticle concentration, strength of the applied magnetic field, Brownian motion parameter, and thermophoresis parameter. An opposite trend is observed for the increase of the buoyancy due to temperature, stretching index, and the radiation parameter. The results also show that the local rate of heat transfer strongly depends on the nonlinear stretching index, radiation parameter, Biot number, Brownian motion parameter, and thermophoresis parameter.

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Appendix
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Literature
1.
go back to reference Choi S (1995) Enhancing thermal conductivity of fluids with nanoparticle. In: Siginer DA, Wang HP (eds) Developments and applications of non-Newtonian flows, ASME FED, vol 231/MD, vol 66, pp 99–105 Choi S (1995) Enhancing thermal conductivity of fluids with nanoparticle. In: Siginer DA, Wang HP (eds) Developments and applications of non-Newtonian flows, ASME FED, vol 231/MD, vol 66, pp 99–105
2.
go back to reference Masuda H, Ebata A, Teramae K, Hishinuma N (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7:227–233 CrossRef Masuda H, Ebata A, Teramae K, Hishinuma N (1993) Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles. Netsu Bussei 7:227–233 CrossRef
3.
go back to reference Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240–250 CrossRef Buongiorno J (2006) Convective transport in nanofluids. ASME J Heat Transf 128:240–250 CrossRef
4.
go back to reference Kleinstreuer C, Li J, Koo J (2008) Microfluidics of nano-drug delivery. Int J Heat Mass Transf 51:5590–5597 MATHCrossRef Kleinstreuer C, Li J, Koo J (2008) Microfluidics of nano-drug delivery. Int J Heat Mass Transf 51:5590–5597 MATHCrossRef
5.
go back to reference Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018 MATHCrossRef Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transf 50:2002–2018 MATHCrossRef
6.
go back to reference Abu-Nada E (2008) Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int J Heat Fluid Flow 29:242–249 CrossRef Abu-Nada E (2008) Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int J Heat Fluid Flow 29:242–249 CrossRef
7.
go back to reference Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336 CrossRef Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336 CrossRef
8.
go back to reference Nield DA, Kuznetsov AV (2009) The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 52:5792–5795 MATHCrossRef Nield DA, Kuznetsov AV (2009) The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transf 52:5792–5795 MATHCrossRef
9.
go back to reference Abu-Nada E, Oztop HF (2009) Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid. Int J Heat Fluid Flow 30:669–678 CrossRef Abu-Nada E, Oztop HF (2009) Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid. Int J Heat Fluid Flow 30:669–678 CrossRef
10.
go back to reference Congedo PM, Collura S, Congedo PM (2009) Modeling and analysis of natural convection heat transfer in nanofluids. In: Proceedings of ASME summer heat transfer conference, vol 3, pp 569–579 Congedo PM, Collura S, Congedo PM (2009) Modeling and analysis of natural convection heat transfer in nanofluids. In: Proceedings of ASME summer heat transfer conference, vol 3, pp 569–579
11.
go back to reference Beg OA, Ghosh SK, Beg TA (2011) Applied magnetofluid dynamics: modelling and computation. Lambert Academic, Germany Beg OA, Ghosh SK, Beg TA (2011) Applied magnetofluid dynamics: modelling and computation. Lambert Academic, Germany
12.
go back to reference Rashidi MM, Bég OA, Asadi M, Rastegari MT (2011) DTM-Padé modeling of natural convective boundary layer flow of a nanofluid past a vertical surface. Int J Thermal Environ Eng 4(1):13–24 CrossRef Rashidi MM, Bég OA, Asadi M, Rastegari MT (2011) DTM-Padé modeling of natural convective boundary layer flow of a nanofluid past a vertical surface. Int J Thermal Environ Eng 4(1):13–24 CrossRef
13.
go back to reference Gorla RSR, El-Kabeir SMM, Rashad AM (2011) Heat transfer in the boundary layer on a stretching circular cylinder in a nanofluid. AIAA J Thermophys Heat Transf 25:183–186 CrossRef Gorla RSR, El-Kabeir SMM, Rashad AM (2011) Heat transfer in the boundary layer on a stretching circular cylinder in a nanofluid. AIAA J Thermophys Heat Transf 25:183–186 CrossRef
14.
go back to reference Gorla RSR, Chamkha A (2011) Natural convective boundary layer flow over a horizontal plate embedded in a porous medium saturated with a nanofluid. J Mod Phys 2:62–71 CrossRef Gorla RSR, Chamkha A (2011) Natural convective boundary layer flow over a horizontal plate embedded in a porous medium saturated with a nanofluid. J Mod Phys 2:62–71 CrossRef
15.
go back to reference Bég OA, Gorla RSR, Prasad VR, Vasu B, Prashad RD (2011) Computational study of mixed thermal convection nanofluid flow in a porous medium. In: 12th national heat transfer conference, Leeds University, UK, August 2011 Bég OA, Gorla RSR, Prasad VR, Vasu B, Prashad RD (2011) Computational study of mixed thermal convection nanofluid flow in a porous medium. In: 12th national heat transfer conference, Leeds University, UK, August 2011
16.
go back to reference Kuznetsov AV, Nield DA (2010) Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 49:243–247 CrossRef Kuznetsov AV, Nield DA (2010) Natural convective boundary-layer flow of a nanofluid past a vertical plate. Int J Therm Sci 49:243–247 CrossRef
17.
go back to reference Muthtamilselvan M, Kandaswamy P, Lee J (2010) Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure. Commun Nonlinear Sci Numer Simul 15:1501–1510 MathSciNetADSMATHCrossRef Muthtamilselvan M, Kandaswamy P, Lee J (2010) Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure. Commun Nonlinear Sci Numer Simul 15:1501–1510 MathSciNetADSMATHCrossRef
18.
go back to reference Bachok N, Ishak A, Pop I (2010) Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. Int J Therm Sci 49:1663–1668 CrossRef Bachok N, Ishak A, Pop I (2010) Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. Int J Therm Sci 49:1663–1668 CrossRef
19.
go back to reference Ahmad S, Pop I (2010) Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids. Int Commun Heat Mass Transf 37:987–991 CrossRef Ahmad S, Pop I (2010) Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids. Int Commun Heat Mass Transf 37:987–991 CrossRef
20.
go back to reference Das SK, Choi SUS, Yu W, Pradeep T (2007) Nanofluids: science and technology. Wiley, New Jersey CrossRef Das SK, Choi SUS, Yu W, Pradeep T (2007) Nanofluids: science and technology. Wiley, New Jersey CrossRef
21.
go back to reference Wang XQ, Mujumdar AS (2007) Heat transfer characteristics of nanofluids: a review. Int J Therm Sci 46:1–19 MATHCrossRef Wang XQ, Mujumdar AS (2007) Heat transfer characteristics of nanofluids: a review. Int J Therm Sci 46:1–19 MATHCrossRef
22.
go back to reference Wang XQ, Mujumdar AS (2008) A review on nanofluids—Part I: Theoretical and numerical investigations. Braz J Chem Eng 25:613–630 Wang XQ, Mujumdar AS (2008) A review on nanofluids—Part I: Theoretical and numerical investigations. Braz J Chem Eng 25:613–630
23.
go back to reference Wang XQ, Mujumdar AS (2008) A review on nanofluids—Part II: Experiments and applications. Braz J Chem Eng 25:631–648 CrossRef Wang XQ, Mujumdar AS (2008) A review on nanofluids—Part II: Experiments and applications. Braz J Chem Eng 25:631–648 CrossRef
24.
go back to reference Kakaç S, Pramuanjaroenkij A (2009) Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf 52:3187–3196 MATHCrossRef Kakaç S, Pramuanjaroenkij A (2009) Review of convective heat transfer enhancement with nanofluids. Int J Heat Mass Transf 52:3187–3196 MATHCrossRef
26.
go back to reference Crane LJ (1970) Flow past a stretching plate. J Appl Math Phys (ZAMP) 21:645–647 CrossRef Crane LJ (1970) Flow past a stretching plate. J Appl Math Phys (ZAMP) 21:645–647 CrossRef
27.
go back to reference Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483 MATHCrossRef Khan WA, Pop I (2010) Boundary-layer flow of a nanofluid past a stretching sheet. Int J Heat Mass Transf 53:2477–2483 MATHCrossRef
28.
go back to reference Hamad AAA, Pop I (2011) Scaling transformations for boundary layer flow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects. Transp Porous Media 87:25–39 MathSciNetCrossRef Hamad AAA, Pop I (2011) Scaling transformations for boundary layer flow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects. Transp Porous Media 87:25–39 MathSciNetCrossRef
29.
go back to reference Magyari E (2011) Note on the “Scaling transformations for boundary layer flow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects”. Transp Porous Media 87:41–48 MathSciNetCrossRef Magyari E (2011) Note on the “Scaling transformations for boundary layer flow near the stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects”. Transp Porous Media 87:41–48 MathSciNetCrossRef
30.
go back to reference Pop I (2011) Reply to the paper TIPM1512: note on the “Scaling transformations for boundary layer flow near the Stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects” by E. Magyari. Transp Porous Media 87:49–51 MathSciNetCrossRef Pop I (2011) Reply to the paper TIPM1512: note on the “Scaling transformations for boundary layer flow near the Stagnation-point on a heated permeable stretching surface in a porous medium saturated with a nanofluid and heat generation/absorption effects” by E. Magyari. Transp Porous Media 87:49–51 MathSciNetCrossRef
31.
go back to reference Travis KP, Todd BD, Evans DJ (1997) Poiseuille flow of molecular liquids. Physica A 240:315–327 ADSCrossRef Travis KP, Todd BD, Evans DJ (1997) Poiseuille flow of molecular liquids. Physica A 240:315–327 ADSCrossRef
33.
go back to reference Aziz A (2009) A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Commun Nonlinear Sci Numer Simul 14:1064–1068 MathSciNetADSCrossRef Aziz A (2009) A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Commun Nonlinear Sci Numer Simul 14:1064–1068 MathSciNetADSCrossRef
34.
go back to reference Bataller RC (2008) Radiation effects for the Blassius and Sakiadis flows with a convective surface boundary condition. Appl Math Comput 206:832–840 MathSciNetMATHCrossRef Bataller RC (2008) Radiation effects for the Blassius and Sakiadis flows with a convective surface boundary condition. Appl Math Comput 206:832–840 MathSciNetMATHCrossRef
35.
go back to reference Makinde OD, Aziz A (2010) MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int J Therm Sci 49:1813–1820 CrossRef Makinde OD, Aziz A (2010) MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int J Therm Sci 49:1813–1820 CrossRef
36.
go back to reference Ishak A (2010) Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl Math Comput 217:837–842 MathSciNetMATHCrossRef Ishak A (2010) Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl Math Comput 217:837–842 MathSciNetMATHCrossRef
37.
go back to reference Rahman MM (2010) Radiative heat transfer flow in a porous medium: effects of internal heat generation, mass flux and convective boundary condition. In: Proceedings of ICAMMM 2010, Sultan Qaboos University, Oman, 13–15 December 2010 Rahman MM (2010) Radiative heat transfer flow in a porous medium: effects of internal heat generation, mass flux and convective boundary condition. In: Proceedings of ICAMMM 2010, Sultan Qaboos University, Oman, 13–15 December 2010
38.
go back to reference Yao S, Fang T, Zhong Y (2011) Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun Nonlinear Sci Numer Simul 16:752–760 ADSMATHCrossRef Yao S, Fang T, Zhong Y (2011) Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun Nonlinear Sci Numer Simul 16:752–760 ADSMATHCrossRef
39.
go back to reference Rahman MM (2011) Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition. Meccanica 46:1127–1143 MathSciNetCrossRef Rahman MM (2011) Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition. Meccanica 46:1127–1143 MathSciNetCrossRef
40.
go back to reference Makinde OD, Zimba K, Beg OA (2012) Numerical study of chemically-reacting hydromagnetic boundary layer flow with Soret/Dufour effects and a convective surface boundary condition. Int J Thermal Environ Eng 4(1):89–98 CrossRef Makinde OD, Zimba K, Beg OA (2012) Numerical study of chemically-reacting hydromagnetic boundary layer flow with Soret/Dufour effects and a convective surface boundary condition. Int J Thermal Environ Eng 4(1):89–98 CrossRef
41.
go back to reference Cortell R (2008) Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys Lett A 372:631–636 ADSMATHCrossRef Cortell R (2008) Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys Lett A 372:631–636 ADSMATHCrossRef
42.
go back to reference Sparrow EM, Cess RD (1978) Radiation heat transfer. Hemisphere, Washington (Chaps. 7 & 10) Sparrow EM, Cess RD (1978) Radiation heat transfer. Hemisphere, Washington (Chaps. 7 & 10)
43.
go back to reference Kays WM, Crawford ME (1980) Convective heat and mass transfer. McGraw Hill, New York, pp 51–54 Kays WM, Crawford ME (1980) Convective heat and mass transfer. McGraw Hill, New York, pp 51–54
44.
go back to reference Chen CH (2008) Effects of magnetic field and suction/injection on convection heat transfer of non-Newtonian power-law fluids past a power-law stretched sheet with surface heat flux. Int J Therm Sci 47:954–961 CrossRef Chen CH (2008) Effects of magnetic field and suction/injection on convection heat transfer of non-Newtonian power-law fluids past a power-law stretched sheet with surface heat flux. Int J Therm Sci 47:954–961 CrossRef
Metadata
Title
Radiative heat transfer in a hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition
Authors
M. M. Rahman
I. A. Eltayeb
Publication date
01-04-2013
Publisher
Springer Netherlands
Published in
Meccanica / Issue 3/2013
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-012-9618-2

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