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ORIGINAL PAPER
Effects of Pressure Gradient on Convective Heat Transfer in a Boundary Layer Flow of a Maxwell Fluid Past a Stretching Sheet
1
Department of Mathematical Sciences, Faculty of Science, Federal Urdu University of Arts Science & Technology, Karachi, Pakistan
2
Department of Mathematics, College of Science and Arts, King Abdul-Aziz University, 21911, Rabigh, Saudi Arabia
3
School of Applied Sciences and Mathematics, Universiti Teknologi Brunei, Jalan Tungku Link Gadong, BE1410, Brunei Darussalam
4
Faculty of Entrepreneurship and Business, Universiti Malaysia Kelantan, Pengkalan Chepa, 16100 Kota, Bharu, Kelantan, Malaysia
5
Ship & Offshore Extreme Technology Industry-Academy Cooperation Research Centre, Department of Naval Architecture & Ocean Engineering, Inha University, 100 Inha ro, Micheulol-gu, Incheon, Republic Of Korea, E-mail: visu20@yahoo.com
Online publication date: 2021-08-26
Publication date: 2021-09-01
International Journal of Applied Mechanics and Engineering 2021;26(3):104-118
KEYWORDS
Homotopy Perturbation Method (HPM)pressure gradient parameterconvective heat transferMaxwell fluidstretching sheet
ABSTRACT
The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (m), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of f '(η) and θ (η) which indicates the case of fluid cooling.
REFERENCES (40)
1.
Hayat T., Shehzad S.A. and Alsaedi A. (2012): Study on three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions.– International Journal of the Physical Sciences, vol.7, No.5, pp.761-768.
2.
Bhattacharyya K., Hayat T. and Gorla R. (2013): Heat transfer in the boundary layer flow of Maxwell fluid over a permeable shrinking sheet.– Thermal Energy and Power, vol.2, No.3, pp.72-78.
3.
Fathizadeh M. and Rashidi F. (2009): Boundary layer convective heat transfer with pressure gradient using homotopy perturbation method (HPM) over a flat plate.– Chaos, Solitons & Fractals, vol.42, No.4, pp.2413-2419.
4.
Aziz A. (2009): A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition.– Communications in Nonlinear Science and Numerical Simulation, vol.14, No.4, pp.1064-1068.
5.
Ishak A. (2010): Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition.– Applied Mathematics and Computation, vol.217, No.2, pp.837-842.
6.
Shagaiya Y. and Daniel S. (2015): Presence of pressure gradient on laminar boundary layer over a permeable surface with convective boundary condition.– American Journal of Heat and Mass Transfer, vol.2, No.1, pp.1-14.
7.
Surati H.C. and Timol M.G. (2010): Numerical study of forced convection wedge flow of some non-Newtonian fluids.– Int. J. of Appl. Math and Mech, vol.6, pp.50-65.
8.
Patel M. and Timol M.G. (2011): Numerical treatment of MHD Powell-Eyring fluid flow using the method of satisfaction of asymptotic boundary conditions.– International Journal of Mathematics and Scientific Computing, vol.1, No.2, pp.71-78.
9.
Hayat T., Iqbal Z., Qasim M. and Obaidat S. (2012): Steady flow of an Eyring-Powell fluid over a moving surface with convective boundary conditions.– International Journal of Heat and Mass Transfer, vol.55, No.7-8, pp.1817-1822.
10.
Malik R., Khan M., Munir A. and Khan W.A. (2014): Flow and heat transfer in Sisko fluid with convective boundary condition.– PLoS ONE, vol.9, No.10, pp.107-989.
11.
Singh V. and Agarwal S. (2014): MHD flow and heat transfer for Maxwell fluid over an exponentially stretching sheet with variable thermal conductivity in porous medium.– Thermal Science, vol.18, No.2, pp.599-615.
12.
Javed T., Ali N., Abbas Z. and Sajid M. (2013): Flow of Aneyring-Powell non-Newtonian fluid over a stretching sheet.– Chemical Engineering Communications, vol.200, No.3, pp.327-336.
13.
Shateyi S. (2013): A new numerical approach to MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction.– Boundary Value Problems, vol.196, pp.1-14.
14.
Mukhopadhyay S. (2013): MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium.– Alexandria Engineering Journal, vol.52, No.3, pp.259-265.
15.
Bhattacharyya K. (2011): Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet.– Int. Comm. in Heat and Mass Transfer, vol.38, No.7, pp.917-922.
16.
Ibrahim S.M. and Suneetha K. (2014): Radiation and heat generation effects on steady MHD flow near a stagnation point on a linear stretching sheet in porous medium in presence of variable thermal conductivity and mass transfer.– Int. J. Cur. Res. Acad. Rev, vol.2, No.7, pp.89-100.
17.
Rehman A. and Nadeem S. (2013): Heat transfer analysis of the boundary layer flow over a vertical exponentially stretching cylinder.– Global Journal of Science Frontier Research Mathematics and Decision Sciences, vol.13, No.11, pp.73-85.
18.
Saleh S., Arifin N., Nazar R., Ali F. and Pop I. (2014) : Mixed convection stagnation flow towards a vertical shrinking sheet.– International Journal of Heat and Mass Transfer, vol.73, pp.839-848.
19.
Ji-Huan H. (1999): Homotopy perturbation technique.– Computer Methods in Applied Mechanics and Engineering, vol.178, No.3, pp.257-262.
20.
Ji-Huan H. (2008): An elementary introduction to recently developed asymptotic methods and nano mechanics in textile engineering.– International Journal of Modern Physics B, vol.22, No.21, pp.3487-3578.
21.
Cveticanin L. (2006): Homotopy–perturbation method for pure nonlinear differential equation.– Chaos. Solitons & Fractals, vol.30, No.5, pp.1221-1230.
22.
El-Shahed M. (2005): Application of He’s homotopy perturbation method to Volterra’s integro-differential equation.– International Journal of Nonlinear Sciences and Numerical Simulation, vol.6, No.2, pp.163-168.
23.
Esmaeilpour M. and Ganji D. (2007): Application of He’s homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate.– Physics Letters A, vol.372, No.1, pp.33-38.
24.
Ghori Q., Ahmed M. and Siddiqui A. (2007) : Application of homotopy perturbation method to squeezing flow of a Newtonian fluid.– International Journal of Nonlinear Sciences and Numerical Simulation, vol.8, No.2, pp.179-184.
25.
Mahmood M., Hossain M., Asghar S. and Hayat T. (2008): Application of homotopy perturbation method to deformable channel with wall suction and injection in a porous medium.– International Journal of Nonlinear Sciences and Numerical Simulation, vol.9, No.2, pp.195-206.
26.
Siddiqui A., Ahmed M. and Ghori Q. (2006): Couette and Poiseuille flows for non-Newtonian fluids.– Int. J. of Nonlinear Sci. and Numerical Simul, vol.7, No.1, pp.15-26.
27.
Fan J., Shi J. and Xu X. (1999): Similarity solution of free convective boundary-layer behaviour at a stretching surface.– Heat and Mass Transfer, vol.35, pp.191-196.
28.
Ishak A. (2010): Unsteady MHD flow and heat transfer over a stretching plate.– Journal of Applied Sciences, vol.18, pp.2127-2131.
29.
Bhattacharyya K., Mukhopadhyay S. and Layek G. (2012): Effects of partial slip on boundary layer stagnation point flow and heat transfer towards a stretching sheet with temperature dependent fluid viscosity.– Acta Technica, vol.57, pp.183-195.
30.
Bhattacharyya K., Mukhopadhyay S. and Layek G.C. (2011): Slip effects on an unsteady boundary layer stagnation-point flow and heat transfer towards a stretching sheet.– Chin. Phys. Let, vol.28, No.9, pp.1-5.
31.
Motsa S.S. and Sibanda P. (2012): On the solution of MHD flow over a nonlinear stretching sheet by an efficient semi-analytical technique.– Int. J. Num. Meth. Fluids, vol.68, pp.1524-1537.
32.
Rahman M.M., Rahman M.A., Samad M.A. and Alam M.S. (2009): Heat transfer in a micropolar fluid along a non-linear stretching sheet with a temperature-dependent viscosity and variable surface temperature.– International Journal of Thermophysics, vol.30, No.5, pp.1649-1670.
33.
Hayat T., Shehzad S.A., Alsaedi A. and Alhothuali M.S. (2012): Mixed convection stagnation point flow of Casson fluid with convective boundary conditions.– Chinese Physics Letters, vol.29, No.11, pp.114-704.
34.
Kazem S., Shaban M. and Abbasbandy S. (2011): Improved analytical solutions to a stagnation-point flow past a porous stretching sheet with heat generation.– Journal of the Franklin Institute, vol.348, No.8, pp.2044-2058.
35.
Weisstein E.W. (2021): Adams method.– URL From Math World, A Wolfram Web Resource, http://mathworld.wolfram.com/A....
36.
Wolfgang C. (2007): Gear method.– The Journal of Gear Manufacturing, University of California, San Diego, http://renaissance.ucsd.edu/ch....
37.
Matthew B., Olyvia D., Viral P., Joel S., Van Eric B. (2007): Adams and gear methods for solving odes with mathematica.– URL https://controls.engin.umich.e... ODEs with Mathematica.
38.
Kaka C.S. and Yener Y. (1980): Convective Heat Transfer.– Middle East Technical University, p.432.
39.
Eosboee M., Pourmahmoud N., Mirzaie I., Khameneh P.M., Majidyfar S. and Ganji D. (2010): Analytical and numerical analysis of MHD boundary layer flow of an incompressible upper-convected Maxwell fluid.– International Journal of Engineering Science and Technology, vol.2, No.12, pp.6909-6917.
40.
Abbas Z., Wang Y., Hayat T. and Oberlack M. (2010): Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface.– Nonlinear Analysis: Real World Applications, vol.11, No.4, pp.3218-3228.
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