A mathematical model describing the homogeneous–heterogeneous reactions in the vicinity of the forward stagnation point of a cylinder immerged in a nanofluid is established. We assume that the homogeneous reaction is given by isothermal cubic autocatalator kinetics, while the heterogeneous reaction is chosen as first-order kinetics. The existence of multiple solutions through hysteresis bifurcations is discussed in detail for the various diffusion coefficients of reactant and autocatalyst.
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References
1.
Chaudhary
, M. A.
, and Merkin
, J. H.
, 1994
, “Free-Convection Stagnation-Point Boundary Layers Driven by Catalytic Surface Reactions—I: The Steady States
,” J. Eng. Math.
, 28
(2
), pp. 145
–171
.2.
Chaudhary
, M. A.
, and Merkin
, J. H.
, 1995
, “A Simple Isothermal Model for Homogeneous–Heterogeneous Reactions in Boundary-Layer Flow—I: Equal Diffusivities
,” Fluid Dyn. Res.
, 16
(6
), pp. 311
–333
.3.
Chaudhary
, M. A.
, and Merkin
, J. H.
, 1995
, “A Simple Isothermal Model for Homogeneous–Heterogeneous Reactions in Boundary-Layer Flow—II: Different Diffusivities for Reactant and Autocatalyst
,” Fluid Dyn. Res.
, 16
(6
), pp. 335
–359
.4.
Song
, X.
, Williams
, W. R.
, Schmidt
, L. D.
, and Aris
, R.
, 1991
, “Bifurcation Behavior in Homogeneous–Heterogeneous Combustion—II: Computations for Stagnation-Point Flow
,” Combust. Flame
, 84
(3–4
), pp. 292
–311
.5.
Song
, X.
, Schmidt
, L. D.
, and Aris
, R.
, 1991
, “Steady States and Oscillations in Homogeneous–Heterogeneous Reaction Systems
,” Chem. Eng. Sci.
, 46
(5
), pp. 1203
–1215
.6.
Ikeda
, H.
, Libby
, P. A.
, Williams
, F. A.
, and Sato
, J. I.
, 1993
, “Catalytic Combustion of Hydrogen-Air Mixtures in Stagnation Flows
,” Combust. Flame
, 93
(1
), pp. 138
–148
.7.
Williams
, W. R.
, Stenzel
, M. T.
, Song
, X.
, and Schmidt
, L. D.
, 1991
, “Bifurcation Behavior in Homogeneous–Heterogeneous Combustion—I: Experimental Results Over Platinum
,” Combust. Flame
, 84
(3–4
), pp. 277
–291
.8.
Williams
, W. R.
, Zhao
, J.
, and Schmidt
, L. D.
, 1991
, “Ignition and Extinction of Surface and Homogeneous Oxidation of NH3 and CH4
,” AIChE J.
, 37
(5
), pp. 641
–649
.9.
Ogren
, P. J.
, 1975
, “Analytical Results for First-Order Kinetics in Flow Tube Reactors With Wall Reactions
,” J. Phys. Chem.
, 79
(17
), pp. 1749
–1752
.10.
Dang
, V. D.
, and Steinberg
, M.
, 1980
, “Convective Diffusion With Homogeneous and Heterogeneous Reactions in a Tube
,” J. Phys. Chem.
, 84
(2
), pp. 214
–219
.11.
Nigam
, K. M.
, Srivastava
, V. K.
, and Nigam
, K. D. P.
, 1982
, “Homogeneous–Heterogeneous Reactions in a Tubular Reactor: An Analytical Solution
,” J. Phys. Chem.
, 25
(2
), pp. 147
–150
.12.
Ching-Yuan
, C.
, Yueh-Jiun
, Y.
, and Ching-Feng
, L.
, 1985
, “Mixed Convection and Diffusion of Reactants, Products, and Heat With Arbitrary-Order Heterogeneous and Homogeneous Reactions in a Rectangular Duct
,” Int. J. Heat Transfer
, 28
(10
), pp. 1813
–1821
.13.
Choi
, S. U. S.
, 1995
, “Enhancing Thermal Conductivity of Fluids With Nanoparticles
,” ASME International Mechanical Engineering Congress and Exposition FED 231/MD66
, ASME, San Francisco, CA, 1995
, pp. 99
–106
.14.
Xuan
, Y.
, and Roetzel
, W.
, 2000
, “Conceptions for Heat Transfer Correlation of Nanofluids
,” Int. J. Heat Transfer
, 43
(19
), pp. 3701
–3707
.15.
Buongiorno
, J.
, 2006
, “Convective Transport in Nanofluids
,” ASME J. Heat Transfer
, 128
(3
), pp. 240
–250
.16.
Kameswaran
, P. K.
, Shaw
, S.
, Sibanda
, P.
, and Murthy
, P. V. S. N.
, 2013
, “Homogeneous–Heterogeneous Reactions in a Nanofluid Flow Due to a Porous Stretching Sheet
,” Int. J. Heat Mass Transfer
, 57
(2
), pp. 465
–472
.17.
Magyari
, E.
, 2011
, “Comment on the Homogeneous Nanofluid Models Applied to Convective Heat Transfer Problems
,” Acta Mech.
, 222
(3–4
), pp. 381
–385
.18.
Merkin
, J. H.
, 1996
, “A Model for Isothermal Homogeneous–Heterogeneous Reactions in Boundary-Layer Flow
,” Math. Comput. Model.
, 24
(8
), pp. 125
–136
.19.
Bachok
, N.
, Ishak
, A.
, and Pop
, I.
, 2011
, “On the Stagnation-Point Flow Towards a Stretching Sheet With Homogeneous–Heterogeneous Reactions Effects
,” Commun. Nonlinear Sci. Numer. Simul.
, 16
(11
), pp. 4296
–4302
.20.
Mustafa
, M.
, Hayat
, T.
, Pop
, I.
, Asghar
, S.
, and Obaidat
, S.
, 2011
, “Stagnation-Point Flow of a Nanofluid Towards a Stretching Sheet
,” Int. J. Heat Mass Transfer
, 54
(25
), pp. 5588
–5594
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