Heat transfer for boundary layers with cross flow

doi:10.1088/1674-1056/23/2/024701

Abstract An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.

Keywords: heat transfer boundary layer cross flow viscous dissipation dual solutions

Received: 21 March 2013
Revised: 03 May 2013
Accepted manuscript online:

PACS:	47.15.Cb	(Laminar boundary layers)
	44.20.+b	(Boundary layer heat flow)
	44.27.+g	(Forced convection)

Corresponding Authors: Krishnendu Bhattacharyya, Ioan Pop
E-mail: krish.math@yahoo.com;popm.ioan@yahoo.co.uk

About author: 47.15.Cb; 44.20.+b; 44.27.+g

Cite this article:

Krishnendu Bhattacharyya, Ioan Pop Heat transfer for boundary layers with cross flow 2014 Chin. Phys. B 23 024701

[1]	Bejan A 2004 Convective Heat Transfer, 3rd edn. (New York: Wiley)
[2]	Schlichting H and Gersten K 2000 Boundary-Layer Theory (New York: Springer)
[3]	Pop I and Ingham D B 2001 Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media (Oxford: Pergamon)
[4]	Kubitschek J P and Weidman P D 2003 Int. J. Heat Mass Transfer 46 3697
[5]	Aziz A 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1064
[6]	Magyari E 2011 Commun. Nonlinear Sci. Numer. Simul. 16 599
[7]	Sowerby L 1954 Rep. Aero. Res. Coun. Lond., No. 16832
[8]	Loos H G 1955 J. Acro. Sci. 22 35
[9]	Klemp J B and Acrivos A A 1972 J. Fluid Mech. 53 177
[10]	Klemp J B and Acrivos A A 1976 J. Fluid Mech. 76 363
[11]	Hussaini M Y, Lakin W D and Nachman A 1987 SIAM J. Appl. Math. 47 699
[12]	Weidman P D 1997 J. Appl. Math. Phys. (ZAMP) 48 341
[13]	Weidman P D, Kubitschek D G and Davis A M J 2006 Int. J. Eng. Sci. 44 730
[14]	Fang T 2003 Acta Mech. 163 161
[15]	Fang T 2003 Acta Mech. 163 183
[16]	Pop I, Ishak A and Nazar R 2007 Chin. Phys. Lett. 24 2274
[17]	Pop I, Nazar R and Ishak A 2007 Chin. Phys. Lett. 24 2895
[18]	Fang T and Lee C F 2009 Acta Mech. 204 235
[19]	Ishak A 2009 Chin. Phys. Lett. 26 034701
[20]	Zhang J, Fang T and Yao S S 2009 Chin. Phys. Lett. 26 014703
[21]	Fang T, Zhang J and Yao S S 2010 Chin. Phys. Lett. 27 124702
[22]	Ishak A, Lok Y Y and Pop I 2010 Chem. Eng. Commun. 197 1417
[23]	Bhattacharyya K and Layek G C 2011 Int. J. Heat Mass Transfer 54 302
[24]	Bhattacharyya K, Mukhopadhyay S and Layek G C 2011 Int. J. Heat Mass Transfer 54 308
[25]	Lok Y Y, Ishak A and Pop I 2011 Int. J. Numer. Meth. Heat Fluid Flow 21 61
[26]	Yacob N A, Ishak A and Pop I 2011 Comput. Fluids 47 16
[27]	Mahapatra T R, Nandy S K and Gupta A S 2011 ASME J. Appl. Mech. 78 021015
[28]	Bhattacharyya K 2011 Chin. Phys. Lett. 28 084702
[29]	Bhattacharyya K 2011 Int. Commun. Heat Mass Transfer 38 917
[30]	Rosali H, Ishak A and Pop I 2011 Int. Commun. Heat Mass Transfer 38 1029
[31]	Bhattacharyya K and Vajravelu K 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2728
[32]	Mukhopadhyay S, Bhattacharyya K and Layek G C 2011 Int. J. Heat Mass Transfer 54 2751
[33]	Bhattacharyya K 2012 Int. J. Heat Mass Transfer 55 3482
[34]	Bhattacharyya K, Layek G C and Gorla R S R 2012 Int. J. Fluid Mech. Res. 39 438
[35]	Bhattacharyya K 2013 Ain Shams Eng. J. 4 259
[36]	Bhattacharyya K 2013 Chin. Phys. B 22 074705
[37]	Bhattacharyya K, Hayat T and Alsaedi A 2013 Chin. Phys. B 22 024702
[38]	Bhattacharyya K, Mukhopadhyay S and Layek G C 2011 Chin. Phys. Lett. 28 024701
[39]	Bhattacharyya K 2011 Chin. Phys. Lett. 28 074701
[40]	Bhattacharyya K and Layek G C 2011 Chem. Eng. Commun. 198 1354
[41]	Bhattacharyya K and Layek G C 2011 Chin. Phys. Lett. 28 084705
[42]	Bhattacharyya K, Mukhopadhyay S and Layek G C 2011 Chin. Phys. Lett. 28 094702
[43]	Bhattacharyya K and Pop I 2011 Magnetohydrodynamics 47 337
[44]	Bhattacharyya K, Mukhopadhyay S, Layek G C and Pop I 2012 Int. J. Heat Mass Transfer 55 2945
[45]	Weidman P D, Davis A M J and Kubitschek D G 2008 J. Appl. Math. Phys. (ZAMP) 59 313
[46]	Paullet J and Weidman P 2007 Int. J. Nonlinear Mech. 42 1084
[47]	Postelnicu A and Pop I 2011 Appl. Math. Comput. 217 4359

[1]	Effect of bio-tissue deformation behavior due to intratumoral injection on magnetic hyperthermia Yundong Tang(汤云东), Jian Zou(邹建), Rodolfo C.C. Flesch, and Tao Jin(金涛). Chin. Phys. B, 2023, 32(3): 034304.
[2]	Heat transport properties within living biological tissues with temperature-dependent thermal properties Ying-Ze Wang(王颖泽), Xiao-Yu Lu(陆晓宇), and Dong Liu(刘栋). Chin. Phys. B, 2023, 32(1): 014401.
[3]	Effects of single synthetic jet on turbulent boundary layer Jin-Hao Zhang(张津浩), Biao-Hui Li(李彪辉), Yu-Fei Wang(王宇飞), and Nan Jiang(姜楠). Chin. Phys. B, 2022, 31(7): 074702.
[4]	Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface Noor Wali Khan, Arshad Khan, Muhammad Usman, Taza Gul, Abir Mouldi, and Ameni Brahmia. Chin. Phys. B, 2022, 31(6): 064403.
[5]	Accurate prediction of the critical heat flux for pool boiling on the heater substrate Fengxun Hai(海丰勋), Wei Zhu(祝薇), Xiaoyi Yang(杨晓奕), and Yuan Deng(邓元). Chin. Phys. B, 2022, 31(6): 064401.
[6]	Influence of various shapes of nanoparticles on unsteady stagnation-point flow of Cu-H₂O nanofluid on a flat surface in a porous medium: A stability analysis Astick Banerjee, Krishnendu Bhattacharyya, Sanat Kumar Mahato, and Ali J. Chamkha. Chin. Phys. B, 2022, 31(4): 044701.
[7]	Experimental investigation on drag reduction in a turbulent boundary layer with a submerged synthetic jet Biao-Hui Li(李彪辉), Kang-Jun Wang(王康俊), Yu-Fei Wang(王宇飞), and Nan Jiang(姜楠). Chin. Phys. B, 2022, 31(2): 024702.
[8]	Numerical simulation of anode heat transfer of nitrogen arc utilizing two-temperature chemical non-equilibrium model Chong Niu(牛冲), Surong Sun(孙素蓉), Jianghong Sun(孙江宏), and Haixing Wang(王海兴). Chin. Phys. B, 2021, 30(9): 095206.
[9]	Improved nonlinear parabolized stability equations approach for hypersonic boundary layers Shaoxian Ma(马绍贤), Yi Duan(段毅), Zhangfeng Huang(黄章峰), and Shiyong Yao(姚世勇). Chin. Phys. B, 2021, 30(5): 054701.
[10]	Continuous droplet rebound on heated surfaces and its effects on heat transfer property: A lattice Boltzmann study Qing-Yu Zhang(张庆宇), Qi-Peng Dong(董其鹏), Shan-Lin Wang(王山林), Zhi-Jun Wang(王志军), and Jian Zhou(周健). Chin. Phys. B, 2021, 30(4): 044703.
[11]	Model predictive inverse method for recovering boundary conditions of two-dimensional ablation Guang-Jun Wang(王广军), Ze-Hong Chen(陈泽弘), Guang-Xiang Zhang(章广祥), and Hong Chen(陈红). Chin. Phys. B, 2021, 30(3): 030203.
[12]	Anti-parity-time symmetric phase transition in diffusive systems Pei-Chao Cao(曹培超) and Xue-Feng Zhu(祝雪丰). Chin. Phys. B, 2021, 30(3): 030505.
[13]	Influence of uniform momentum zones on frictional drag within the turbulent boundary layer Kangjun Wang(王康俊) and Nan Jiang(姜楠). Chin. Phys. B, 2021, 30(3): 034703.
[14]	Effects of heat transfer in a growing particle layer on microstructural evolution during solidification of colloidal suspensions Jia-Xue You(游家学), Yun-Han Zhang(张运涵), Zhi-Jun Wang(王志军), Jin-Cheng Wang(王锦程), and Sheng-Zhong Liu(刘生忠). Chin. Phys. B, 2021, 30(2): 028103.
[15]	Lattice Boltzmann simulation on thermal performance of composite phase change material based on Voronoi models Meng-Yue Guo(郭孟月), Qun Han(韩群), Xiang-Dong Liu(刘向东), and Bo Zhou(周博). Chin. Phys. B, 2021, 30(10): 104401.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Heat transfer for boundary layers with cross flow

Cite this article:

Online attention