Abstract.
The present model is devoted to investigate the streamwise and cross flow of a viscous fluid over a heated moving surface. Viscous dissipation effects are also considered with heat and mass transfer effects and these effects with cross flow have not been explored yet in the literature. Governing boundary layer equations consist in the form of nonlinear partial differential equations (PDEs). Compatible transformations are applied to change such equations into ordinary differential equations which are further solved using the Runge-Kutta technique and shooting method. Linear stability analysis is also performed over the obtained solutions to validate the results and to determine the smallest eigenvalues. Three different kinds of fluids namely: acetone, water and ethaline glycol are investigated to analyse the heat transfer rate. The problem contains important physical parameters namely: Prandtl number, Eckert numbers and Lewis number. The obtained solutions are discussed in detail against each physical parameter using graphs and tables.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Robert T. Jones, Effects of sweepback on boundary layer and separation, Report no. 884 (National Advisory Committee for Aeronautics, 1947)
Artur Mager, J. Aeronaut. Sci. 21, 835 (1954)
Henk G. Loos, J. Aeronaut. Sci. 22, 35 (1955)
Tsung Yen Na, Arthur G. Hansen, Int. J. Non-Linear Mech. 2, 373 (1967)
Halit Karabulut, O. Ercan Ataer, Int. J. Heat Mass Transfer 41, 2677 (1998)
Tiegang Fang, Chia-fon F. Lee, Acta Mech. 204, 235 (2009)
A. Uranga, P.-O. Persson, M. Drela, J. Peraire, Preliminary investigation into the effects of cross-flow on low Reynolds number transition, in 20th AIAA Computational Fluid Dynamics Conference, Hawaii (2011), June 27-30 (2011)
Krishnendu Bhattacharayya, Ion Pop, Chin. Phys. B 23, 024701 (2014)
Rizwan Ul Haq, Z.H. Khan, W.A. Khan, Inayat Ali Shah, Int. J. Chem. React. Eng. (2016) DOI:10.1515/ijcre-2016-0059
N.A. Cumpsty, Crossflow in turbulent boundary layers, Ministry of Technology Aeronautical Research Council Current Papers (1970)
P.D. Weidman, Z. Angew. Math. Phys. 48, 341 (1997)
R. Mittal, P. Rampunggoon, H.S. Udaykumar, Interaction of a synthetic jet with a flat plate boundary layer (American Institute of Aeronautics and Astronautics, 2001)
Lars-Uve Schrader, Luca Bradt, Dan S. Henningson, J. Fluid Mech. 618, 209 (2009)
S.J. Garrett, Z. Hussain, S.O. Stephen, J. Fluid Mech. 622, 209 (2009)
Francesca De Santi, Stefania Scarsoglio, William O. Criminale, Daniela Tordella, Perturbed cross-flow boundary layer: nontrivial effects of the obliquity angle at small and high Reynolds numbers, in 14th European Turbulence Conference, France (2013)
Sertac Cadirci, Hasan Gunes, Ulrich Rist, Eur. J. Mech. B/Fluids 44, 42 (2014)
Francesca De Santi, Stefania Scarsoglio, William O. Criminale, Daniela Tordella, Int. J. Heat Fluid Flow 52, 64 (2015)
J.H. Merkin, J. Eng. Math. 20, 171 (1986)
P.D. Weidman, D.G. Kubitschek, A.M.J. Davis, Int. J. Eng. Sci. 44, 730 (2006)
A. Postelnicu, I. Pop, Appl. Math. Comput. 217, 4359 (2011)
Z. Hussain, S.J. Garrett, S.O. Stephen, J. Fluid Mech. 755, 274 (2014)
Z. Hussain, S.J. Garrett, S.O. Stephen, P.T. Griffiths, J. Fluid Mech. 788, 70 (2016)
P.D. Towers, Z. Hussain, P.T. Griffiths, S.J. Garrett, IMA J. Appl. Math. 81, 940 (2016)
T.Y. Na, Computational Methods in Engineering Boundary Value Problem (Academic Press, New York, 1979)
T. Cebeci, P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer (Springer-Verlag, New York, 1984)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rizwan-ul-Haq, Soomro, F.A., Khan, Z.H. et al. Numerical study of streamwise and cross flow in the presence of heat and mass transfer. Eur. Phys. J. Plus 132, 214 (2017). https://doi.org/10.1140/epjp/i2017-11473-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11473-1