## THERMAL SCIENCE

International Scientific Journal

### UNSTEADY HOMOGENEOUS-HETEROGENEOUS REACTIONS IN MHD NANOFLUID MIXED CONVECTION FLOW PAST A STAGNATION POINT OF AN IMPULSIVELY ROTATING SPHERE

**ABSTRACT**

This paper establishes a mathematical analysis for describing the homogeneous and heterogeneous chemical reactions in the nearness of stagnation region of a sphere immersed in a single-phase nanofluid due to a Newtonian heating. The flow is resulted by an impulsively rotating sphere, and the nanofluid involves nanoparticles of Copper and Ferro. The available unsteady-states of the considered system are given in the case when the diffusion coefficients of both reactant and auto catalyst have the same size. The resulting non-linear dimensionless coupled partial differential equations in which governing the mixed convection flow have been tackled numerically via an implicit finite difference technique in combination with the quasi-linearization scheme. The similarities and differences in the behavior of physical pertinent fluid parameters have been elaborated and discussed graphically. It has been clarified that the nanofluid velocity and temperature profiles grow gradually by adding nanoparticles in the base fluid. Again it is noticed from present contribution that concentration of the nanofluid is decreases function by rising the strength of homogeneous and heterogeneous chemical reactions. Finally, numerical computations of the skin friction and heat transfer factors are presented.

**KEYWORDS**

PAPER SUBMITTED: 2019-07-12

PAPER REVISED: 2019-07-30

PAPER ACCEPTED: 2019-08-07

PUBLISHED ONLINE: 2019-10-06

**THERMAL SCIENCE** YEAR

**2021**, VOLUME

**25**, ISSUE

**Issue 1**, PAGES [243 - 256]

- Song X., Schmidt L.D., Aris R. Steady states and oscillations in homogeneous-heterogeneous reactions systems. Chem Eng Sci 46 (1991) 1203-1215.
- Song X., Schmidt L.D., Aris R. The ignition criteria for stagnation-point flow: SemenovFrank Kamenetskii or van't Hoff. Combust Sci and Tech 75 (1991) 311-31.
- Song X., Williams W.R., Schmidt L.D., Aris R. Bifurcation behaviour in homogeneous-heterogeneous combustion. II. Computations for stagnation-point flow. Combust Flame 84 (1991) 292-311.
- Williams W.R., Zhao J., Schmidt L.D. Ignition and extinction of surface and homogeneous oxidation of NH3 and CH4. AIChE J 37 (1991) 641-649.
- Williams W.R., Stenzel M.T., Song X., Schmidt L.D. Bifurcation behaviour in homogeneous-heterogeneous combustion. I. Experimental results over platinum. Combust Flame 84 (1991) 277-291.
- Chaudhary M.A., Merkin J.H. A simple isothermal model for homogeneous-heterogeneous reactions in boundary-layer flow. II unequal diffusivities. Fluid Dyn Res 16 (1995) 335-359.
- Chaudhary M.A., Merkin J.H. A simple isothermal model for homogeneous-heterogeneous reactions in boundary-layer flow. I equal diffusivities. Fluid Dyn Res 16 (1995) 311-333.
- Merkin J.H., A model for isothermal homogeneous-heterogeneous reactions in boundary layer flow, Math. Comput. Model. 24(8) (1996) 125-136.
- Hayat T., Khan M.I., Farooq M., Yasmeen T., Alsaedi A., Stagnation point flow with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions, J. Mol. Liq. 220 (2016) 49?55.
- Khan W.A., Pop I., Effects of homogeneous-heterogeneous reactions on the viscoelastic fluid towards a stretching sheet, ASME J. Heat Trans. 134 (2012) 1-5.
- Khan M.I., Hayat T., Waqas M., Khan M.I., Alsaedi A., Impact of heat generation/absorption and homogeneousheterogeneous reactions on flow of Maxwell fluid, J. Mol. Liq. 233 (2017) 465-470.
- Hayat T., Khan M.I., Imtiaz M., Alseadi A., Waqas M., Similarity transformation approach for ferromagnetic mixed convection flow in the presence of chemically reactive magnetic dipole, AIP Phys. Fluid. 28 (2016) 102003.
- Ashorynejad H.R., Sheikholeslami M., Pop I., Ganji D.D. Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field. Heat Mass Transf 2013;49:427-36.
- Abu-Nada E., Masoud Z., Hijazi A., Natural convection heat transfer enhancement in horizontal concentric annuli using nanofluids. Int Commun Heat Mass Transf 2008;35:657?65.
- Tiwari R.K., Das M.K., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transfer 50 (2007) 2002-2018.
- Buongiorno J. Convective transport in nanofluids. ASME J. Heat Transfer, 2006; 128: 240-250.
- Mahdy A., Unsteady mixed convection boundary layer ow and heat transfer of nanofluids due to stretching sheet, Nucl Eng Des 249 (2012) 248-255.
- Choi S.U.S. Enhancing thermal conductivity of fluids with nanoparticles. In Proceedings of the ASME Int. Mech. Eng. Congress and Exposition 1995; 66:99-105.
- Mahdy A., Sameh E. Ahmed, Laminar free convection over a vertical wavy surface embedded in a porous medium saturated with a nano uid, Transp Porous Med 91 (2012) 423-435.
- Mahdy A., Entropy generation of tangent hyperbolic nano fluid flow past a stretched permeable cylinder: Variable wall temperature, Proc IMechE Part E: J Process Mechanical Engineering, 233(3) (2019) 570-580
- Mahdy A., Chamkha A.J., Unsteady MHD boundary layer flow of tangent hyperbolic two-phase nanofluid of moving stretched porous wedge, International Journal of Numerical Methods for Heat and Fluid Flow 28(11) (2018) 2567-2580.
- Mahdy A., Aspects of homogeneous-heterogeneous reactions on natural convection flow of micropolar fluid past a permeable cone, Applied Mathematics and Computation, 352 (2019) 59-67.
- Oztop H.F. , Abu-Nada E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow 29 (2008) 1326-1336.
- Mahdy A., Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere, Appl. Math. Mech. -Engl. Ed. 39 (2018) 1327-1340
- Chaudhary M.A., Merkin J.H., A simple isothermal model for homogeneous-heterogeneous reactions in boundary layer flow: I. Equal diffusivities, Fluid Dynam. Res. 16 (1995) 311-333.
- Mahdy A., Ahmed S.E. Unsteady MHD convective ow of non-Newtonian Casson fluid in the stagnation region of an impulsively rotating sphere. J, Aer Engin 30(5) (2017) 04017036.
- Sameh E.A., Mahdy A., Unsteady MHD double diffusive convection in the stagnation region of an impulsively rotating sphere in the presence of thermal radiation effect. J Taiwan Institute Chem Engn 58 (2016) 173-180.
- Mahdy A., Chamkha A.J., Heat transfer and fluid flow of a non-Newtonian nanofluid over an unsteady contracting cylinder employing Buongiorno's model. International Journal of Numerical Methods and Heat Fluid Flow 25(4) (2015) 703-723.
- Chamkha A.J., Takhar H.S., Nath G., Unsteady MHD rotating flow over a rotating sphere near the equator. Acta Mechanica, 164(1/2) (2003)31-46.
- Takhar H.S., Slaouti A., Kumari M., Nath G., Unsteady free convection flow in the stagnation-point region of a rotating sphere. International Journal Non-Linear Mechanics, 33(5) (1998) 857-865.
- Takhar H.S., Chamkha A.J., Nath G. Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces. Heat and Mass Transfer, 37 (2001) 397-402.
- Ikeda H., Libby P.A., Williams F.A., Catalytic combustion of hydrogen-air mixtures in stagnation flows. Combust Flame 93 (1993) 138-48.
- Brinkman H.C., The viscosity of concentrated suspensions and solution, J. Chem. Phys. 20 (1952) 571-581.
- Jawad R., Azizah M.R., Zurni O., Numerical investigation of copper-water (Cu-water) nanofluid with different shapes of nanoparticles in a channel with stretching wall: slip effects, Math Comput. Appl. 21 (2016)43-58.
- Maxwell J., A Treatise on Electricity and Magnetism, second ed. Oxford University Press, Cambridge, UK, 1904.
- Nor A.M.Z., Ilyas K., Sharidan S., Ali S.A., Analysis of heat transfer for unsteady MHD free convection flow of rotating Jeffrey nanofluid saturated in a porous medium, Res. Phys. 7 (2017) 288-309.
- Abid H., Mohd Z.S., Ilyas K., Sharidan S., Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil, J. Mol. Liq. 229 (2017) 482-488.
- Jawad R., Fateh M., Chamkha A.J., Magnetohydrodynamic flow of molybdenum disulfide nanofluid in a channel with shape effects, Multidiscipline Modeling in Materials and Structures 15(4), (2019) 737-757.
- Liaquat A.L., Zurni O., Ilyas K., Jawad R., Mohsen B., Tlili I., Stability Analysis of Darcy-Forchheimer Flow of Casson Type Nanofluid Over an Exponential Sheet: Investigation of Critical Points, Symmetry 11 (2019) 412.