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Research Papers: Heat and Mass Transfer

Simultaneous Effects of Nonlinear Mixed Convection and Radiative Flow Due to Riga-Plate With Double Stratification

[+] Author and Article Information
Tasawar Hayat

Department of Mathematics,
Quaid-I-Azam University,
45320,
Islamabad 44000, Pakistan;
Nonlinear Analysis and Applied Mathematics
(NAAM) Research Group,
Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
P. O. Box 80203,
Jeddah 21589, Saudi Arabia

Ikram Ullah

Department of Mathematics,
Quaid-I-Azam University,
45320,
Islamabad 44000, Pakistan
e-mail: ikramullah@math.qau.edu.pk

Ahmed Alsaedi, Bashir Ahamad

Nonlinear Analysis and Applied Mathematics
(NAAM) Research Group,
Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
P. O. Box 80203,
Jeddah 21589, Saudi Arabia

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 11, 2017; final manuscript received April 6, 2018; published online June 11, 2018. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 140(10), 102008 (Jun 11, 2018) (8 pages) Paper No: HT-17-1676; doi: 10.1115/1.4039994 History: Received November 11, 2017; Revised April 06, 2018

This paper addresses nonlinear mixed convection flow due to Riga plate with double stratification. Heat transfer analysis is reported for heat generation/absorption and nonlinear thermal radiation. Physical problem is mathematically modeled and nonlinear system of partial differential equations is achieved. Transformations are then utilized to obtain nonlinear system of ordinary differential equations. Homotopic technique is utilized for the solution procedure. Graphical descriptions for velocity, temperature, and concentration distributions are captured and argued for several set of physical variables. Features of skin friction and Nusselt and Sherwood numbers are also illustrated. Our computed results indicate that the attributes of radiation and temperature ratio variables enhance the temperature distribution. Moreover, the influence of buoyancy ratio and modified Hartmann number has revers effects on rate of heat transfer.

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References

Gupta, P. S. , and Gupta, A. S. , 1974, “ Radiation Effect on Hydromagnetic Convection in a Vertical Channel,” Int. J. Heat Mass Transfer, 17(12), pp. 1437–1442. [CrossRef]
Hossain, M. A. , and Takhar, H. S. , 1996, “ Radiative Effect on Mixed Convection Along a Vertical Plate With Uniform Surface Temperature,” Int. J. Heat Mass Transfer, 31(4), pp. 243–248. [CrossRef]
Hossain, M. A. , Alim, M. A. , and Rees, D. A. , 1999, “ Effect of Radiation on Free Convection From a Porous Vertical Plate,” Int. J. Heat Mass Transfer, 42(1), pp. 181–191. [CrossRef]
Rashidi, M. M. , Ali, M. , Freidoonimehr, N. , Rostami, B. , and Hossain, M. A. , 2014, “ Mixed Convection Heat Transfer for MHD Viscoelastic Fluid Flow Over a Porous Wedge With Thermal Radiation,” Adv. Mech. Eng., 6, p. 735939. [CrossRef]
Hayat, T. , Ullah, I. , Ahmed, B. , and Alsaedi, A. , 2017, “ MHD Mixed Convection Flow of Third Grade Liquid Subject to Non-Linear Thermal Radiation and Convective Condition,” Results Phys., 7, pp. 2804–2811. [CrossRef]
Gireesha, B. J. , Mahanthesh, B. , Gorla, R. S. R. , and Krupalakshmi, K. L. , 2016, “ Mixed Convection Two-Phase Flow of Maxwell Fluid Under the Influence of Non-Linear Thermal Radiation, NonUniform Heat Source/Sink and Fluid-Particle Suspension,” Ain Shams Eng. J., in press.
Hayat, T. , Qayyum, S. , Alsaedi, A. , and Ahmad, B. , 2017, “ Magnetohydrodynamic (MHD) Nonlinear Convective Flow of Walter-B Nanofluid Over a Nonlinear Stretching Sheet With Variable Thickness,” Int. J. Heat Mass Transfer, 110, pp. 506–514. [CrossRef]
Hayat, T. , Qayyum, S. , Shehzad, S. A. , and Alsaedi, A. , 2017, “ Magnetohydrodynamic Three-Dimensional Nonlinear Convection Flow of Oldroyd-B Nanoliquid With Heat Generation/Absorption,” J. Mol. Liq., 230, pp. 641–651. [CrossRef]
Lee, L. L. , 2014, “Boundary Layer Over a Thin Needle,” Phys. Fluids, 10, p. 820.
Fang, T. , Zhang, J. , and Zhong, Y. , 2012, “ Boundary Layer Flow Over a Stretching Sheet With Variable Thickness,” Appl. Math. Comput., 218(13), pp. 7241–7252.
Abdel-Wahed, M. S. , Elbashbeshy, E. M. A. , and Emam, T. G. , 2015, “ Flow and Heat Transfer Over a Moving Surface With Non-Linear Velocity and Variable Thickness in a Nanofluids in the Presence of Brownian Motion,” Appl. Math. Comput., 254, pp. 49–62.
Hayat, T. , Farooq, M. , Alsaedi, A. , and Al-Solamy, F. , 2015, “ Impact of Cattaneo-Christov Heat Flux in the Flow Over a Stretching Sheet With Variable Thickness,” AIP Adv., 5(8), p. 087159. [CrossRef]
Zhang, X. , Zhang, H. , and Wang, Z. , 2016, “ Bending Collapse of Square Tubes With Variable Thickness,” Int. J. Mech. Sci., 106, pp. 107–116. [CrossRef]
Hayat, T. , Ullah, I. , Alsaedi, A. , and Farooq, M. , 2017, “ MHD Flow of Powell-Eyring Nanofluid Over a Non-Linear Stretching Sheet With Variable Thickness,” Res. Phys., 7, pp. 189–196.
Gailitis, A. , and Lielausis, O. , 1961, “ On a Possibility to Reduce the Hydrodynamic Resistance of a Plate in an Electrolyte,” Appl. Magneto-Hydrodyn. Rep. Phys. Inst. Riga, 12, pp. 143–146.
Grinberg, E. , 1961, “ On Determination of Properties of Some Potential Fields,” Appl. Magnetohydrodyn. Rep. Phys. Inst. Riga, 12, pp. 147–154.
Pang, J. , and Choi, K. S. , 2004, “ Turbulent Drag Reduction by Lorentz Force Oscillation,” Phys. Fluids, 16(5), pp. 35–38. [CrossRef]
Hayat, T. , Abbas, T. , Ayub, M. , Farooq, M. , and Alsaedi, A. , 2016, “ Flow of Nanofluid Due to Convectively Heated Riga Plate With Variable Thickness,” J. Mol. Liq., 222, pp. 854–862. [CrossRef]
Ahmad, R. , Mustafa, M. , and Turkyilmazoglu, M. , 2017, “ Buoyancy Effects on Nanofluid Flow Past a Convectively Heated Vertical Riga-Plate: A Numerical Study,” Int. J. Heat Mass Transfer, 111, pp. 827–835. [CrossRef]
Farooq, M. , Anjum, A. , Hayat, T. , and Alsaedi, A. , 2016, “ Melting Heat Transfer in the Flow Over a Variable Thicked Riga Plate With Homogeneous-Heterogeneous Reactions,” J. Mol. Liq., 224(Pt. B), pp. 1341–1347. [CrossRef]
Liao, S. J. , 2004, “ On the Homotopy Analysis Method for Nonlinear Problems,” Appl. Math. Comput., 147(2), pp. 499–513.
Dehghan, M. , Manafian, J. , and Saadatmandi, A. , 2010, “ Solving Nonlinear Fractional Partial Differential Equations Using the Homotopy Analysis Method,” Numer. Meth. Partial Differ. Equations, 26, pp. 448–479.
Bansod, V. , and Jadhav, R. , 2010, “ Effect of Double Stratification on Mixed Convection Heat and Mass Transfer From a Vertical Surface in a Fluid-Saturated Porous Medium,” Heat Transfer Asian Res., 39, pp. 378–395.
Hayat, T. , Ullah, I. , Muhammad, T. , Alsaedi, A. , and Shehzad, S. A. , 2016, “ Three-Dimensional Flow of Powell-Eyring Nanofluid With Heat and Mass Flux Boundary Conditions,” Chin. Phys. B, 25(7), p. 074701. [CrossRef]
Hayat, T. , Ullah, I. , Alsaedi, A. , and Ahmad, B. , 2017, “ Radiative Flow of Carreau Liquid in Presence of Newtonian Heating and Chemical Reaction,” Results Phys., 7, pp. 715–722. [CrossRef]
Abbasbandy, S. , Hayat, T. , Alsaedi, A. , and Rashidi, M. M. , 2014, “ Numerical and Analytical Solutions for Falkner-Skan Flow of MHD Oldroyd-B Fluid,” Int. J. Numer. Methods Heat Fluid Flow, 24(2), pp. 390–401. [CrossRef]
Hayat, T. , Ullah, I. , Alsaedi, A. , and Ahmad, B. , 2017, “ Modeling Tangent Hyperbolic Nanoliquid Flow With Heat and Mass Flux Conditions,” Eur. Phys. J. Plus, 132(3), p. 112. [CrossRef]
Hayat, T. , Ullah, I. , Muhammad, T. , and Alsaedi, A. , 2016, “ Magnetohydrodynamic (MHD) Three-Dimensional Flow of Second Grade Nanofluid by a Convectively Heated Exponentially Stretching Surface,” J. Mol. Liq., 220, pp. 1004–1012. [CrossRef]
Ellahi, R. , Hassan, M. , and Zeeshan, A. , 2015, “ Shape Effects of Nanosize Particles in Cu-H2O Nanofluid on Entropy Generation,” Int. J. Heat Mass Transfer, 81, pp. 449–456. [CrossRef]
Hayat, T. , Ullah, I. , Muhammad, T. , and Alsaedi, A. , 2017, “ Radiative Three-Dimensional Flow With Soret and Dufour Effects,” Int. J. Mech. Sci., 133, pp. 829–837. [CrossRef]
Turkyilmazoglu, M. , 2016, “ An Effective Approach for Evaluation of the Optimal Convergence Control Parameter in the Homotopy Analysis Method,” Filomat, 30(6), pp. 1633–1650. [CrossRef]
Hayat, T. , Ullah, I. , Muhammad, T. , and Alsaedi, A. , 2017, “ A Revised Model for Stretched Flow of Third Grade Fluid Subject to Magneto Nanoparticles and Convective Condition,” J. Mol. Liq., 230, pp. 608–615. [CrossRef]
Ahmad, T. , Javed, T. , Hayat, M. , and Sajid , 2011, “ Series Solutions for the Radiation-Conduction Interaction on Unsteady MHD Flow,” J. Porous Media, 14(10), pp. 927–941. [CrossRef]
Hayat, T. , Ullah, I. , Muhammad, T. , and Alsaedi, A. , 2017, “ Thermal and Solutal Stratification in Mixed Convection Three-Dimensional Flow of an Oldroyd-B Nanofluid,” Results Phys., 7, pp. 3797–3805. [CrossRef]
Hayat, T. , Ullah, I. , Alsaedi, A. , Waqas, M. , and Ahmad, B. , 2017, “ Three-Dimensional Mixed Convection Flow of Sisko Nanoliquid,” Int. J. Mech. Sci., 133, pp. 273–282. [CrossRef]
Turkyilmazoglu, M. , 2017, “ Parametrized Adomian Decomposition Method With Optimum Convergence,” Trans. Model. Comput. Simul., 27(4), p. 22.
Hayat, T. , Ullah, I. , Alsaedi, A. , and Ahmad, B. , 2018, “ Numerical Simulation for Homogeneous–Heterogeneous Reactions in Flow of Sisko Fluid,” J. Braz. Soc. Mech. Sci. Eng., 40(2), p. 73. [CrossRef]
Zaigham Zia, Q. M. , Ullah, I. , Waqas, M. , Alsaedi, A. , and Hayat, T. , 2018, “ Cross Diffusion and Exponential Space Dependent Heat Source Impacts in Radiated Three-Dimensional (3D) Flow of Casson Fluid by Heated Surface,” Results Phys., 8, pp. 1275–1282. [CrossRef]
Farooq, M. , Javed, M. , Ijaz Khan, M. , Anjum, A. , and Hayat, T. , 2017, “ Melting Heat Transfer and Double Stratification in Stagnation Flow of Viscous Nanofluid,” Results Phys., 7, pp. 2296–2301. [CrossRef]
Ramzan, M. , Bilal, M. , and Chung, J. D. , 2017, “ Radiative Williamson Nanofluid Flow Over a Convectively Heated Riga Plate With Chemical Reaction-a Numerical Approach,” Chin. J. Phys., 55(4), pp. 1663–1673. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Physical configuration of problem

Grahic Jump Location
Fig. 2

ℏ-Curve for f(ξ)

Grahic Jump Location
Fig. 3

ℏ-Curves for θ(ξ) and ϕ(ξ)

Grahic Jump Location
Fig. 4

(a) Residual error in f(ξ), (b) residual error in θ(ξ), and (c) residual error in ϕ(ξ)

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Fig. 5

Variation of f′(ξ) via Q

Grahic Jump Location
Fig. 6

Variation of f′(ξ) via λ

Grahic Jump Location
Fig. 7

Variation of f′(ξ) via α

Grahic Jump Location
Fig. 8

Variation of f′(ξ) via Nr

Grahic Jump Location
Fig. 9

Variation of f′(ξ) via β1

Grahic Jump Location
Fig. 10

Variation of θ(ξ) via Rd

Grahic Jump Location
Fig. 11

Variation of θ(ξ) via θw

Grahic Jump Location
Fig. 12

Variation of θ(ξ) via γ1

Grahic Jump Location
Fig. 13

Variation of θ(ξ) via S1

Grahic Jump Location
Fig. 14

Variation of θ(ξ) via Q

Grahic Jump Location
Fig. 15

Variation of ϕ(ξ) via S2

Grahic Jump Location
Fig. 16

Variation of λ via Nr on CfxRex−0.5

Grahic Jump Location
Fig. 17

Behavior of Q via Nr on NuxRex−0.5

Grahic Jump Location
Fig. 18

Behavior of Q via Le on ShxRex−0.5

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