## THERMAL SCIENCE

International Scientific Journal

### ENERGY AND MASS TRANSFER ANALYSIS OF 3-D BOUNDARY-LAYER FLOW OVER A ROTATING DISK WITH BROWNIAN MOTION AND THERMO-PHORETIC EFFECTS

**ABSTRACT**

The advancement of nanofluid technology has become an essential tool for investigating thermal conductivity enhancement, which is highly valuable for industrial and engineering applications in many fields including mathematics, physics, engineering, and materials science. This analysis focuses on 3-D boundary-layer flow on nanofluid over a rotating disk by incorporating chemical reaction and thermal radiations effects. One aim of this article is to analyze the energy and mass transport rates for nanofluids. In this study, the Brownian motion and thermophoretic impacts are considered. The governing flow equations are converted to ODE via suitable similarity transformations. The resulting equations were solved via well know technique Keller box method. This analysis revealed that the azimuthal and axial velocities show an inverse pattern against the various values of index factor, n, although the radial velocity has the highest value and decreases significantly. The behavior of the von Karman flow is also recovered for setting the index factor (n = 1). Moreover, it is found that the temperature of nano liquid increases by increasing the Brownian motion and thermophoretic factors.

**KEYWORDS**

PAPER SUBMITTED: 2022-08-15

PAPER REVISED: 2022-09-29

PAPER ACCEPTED: 2022-10-12

PUBLISHED ONLINE: 2023-01-21

- Von Kármán, T. Uber Laminare und Turbulente Reibung, Z. Angew. Math. Mech., 1 (1921), pp. 233-252
- Millsaps, K., Pohlhausen, K., Heat Transfer by Laminar Flow from a Rotating Plate, Journal of the Aeronautical Sciences, 19 (1952), 2, pp. 120-126
- Riley, N., The Heat Transfer from a Rotating Disk, The Quarterly Journal of Mechanics and Applied Mathematics, 17 (1964), 3, pp. 331-349
- Ramzan, M., et al., Von Karman Rotating Nanofluid flow with Modified Fourier Law and Variable Characteristics in Liquid and Gas Scenarios, Scientific Reports, 11 (2021), 1, pp. 1-17
- Chen, H., et al., Three‐Dimensional Boundary-Layer Flow Over a Rotating Disk with Power‐Law Stretching in a Nanofluid Containing Gyrotactic Microorganisms, Heat Transfer Asian Research, 47 (2018), 3, pp. 569-582
- Ramzan, M., et al., A Numerical Study of Chemical Reaction in a Nanofluid Flow Due to Rotating Disk in the Presence of Magnetic Field, Scientific Reports., 11 (2021),1, pp. 1-24
- Choi, S. U., Eastman, J. A., Enhancing Thermal Conductivity of Fluids with Nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29), Argonne National Lab., Argonne, Ill., USA, 1995
- Buongiorno, J., Convective Transport in Nanofluids, Journal of Heat Transfer, 128 (2006), 3, pp. 240-250
- Rafique, K., et al., Stratified Flow of Micropolar Nanofluid over Riga Plate: Numerical Analysis, Energies., 15 (2022), 1, 316
- Alotaibi, H., Rafique, K., Numerical Analysis of Micro-Rotation Effect on Nanofluid Flow for Vertical Riga Plate, Crystals., 11 (2021), 11, 1315
- Rafique, K., Alotaibi, H., Numerical Simulation of Williamson Nanofluid Flow over an Inclined Surface: Keller Box Analysis, Applied Sciences., 11 (2021), 23, 11523
- Rafique, K., et al., Energy and Mass Transport of Casson Nanofluid Flow Over a Slanted Permeable Inclined Surface, Journal of Thermal Analysis and Calorimetry, 144 (2021), 6, pp. 2031-2042
- Anwar, M. I., et al., Numerical Solution of Casson Nanofluid Flow Over a Non-Linear Inclined Surface with Soret and Dufour Effects by Keller-Box Method, Frontiers in Physics, 7 (2019), 139
- Hussain, A., Malik, M. Y., MHD Nanofluid Flow Over Stretching Cylinder with Convective Boundary Conditions and Nield Conditions in the Presence of Gyrotactic Swimming Microorganism: A Biomathematical Model, International Communications in Heat and Mass Transfer, 126 (2021), July, 105425
- Waini, I., et al., Nanofluid Flow on a Shrinking Cylinder with Al2O3 Nanoparticles, Mathematics, 9 (2021), 14, 1612
- Mastroberardino, A., Mahabaleswar, U. S., Mixed Convection in Viscoelastic Flow due to a Stretching Sheet in a Porous Medium, Journal of Porous Media, 16 (2013), 6
- Ghadikolaei, S. S., et al., Nonlinear Thermal Radiation Effect on Magneto Casson Nanofluid Flow with Joule Heating Effect Over an Inclined Porous Stretching Sheet, Case studies in Thermal Engineering, 12 (2018), Sept., pp. 176-187
- Sheikholeslami, M., et al., Effect of Thermal Radiation on Magnetohydrodynamics Nanofluid Flow and Heat Transfer by Means of Two Phase Model, Journal of Magnetism and Magnetic Materials, 374 (2015), Jan., pp. 36-43
- Bhandari, A., Radiation and Chemical Reaction Effects on Nanofluid Flow Over a Stretching Sheet, Fluid Dyn. Mater. Process, 15 (2019), 4, pp. 557-582.
- Khan, A., et al., Chemically Reactive Nanofluid Flow Past a Thin Moving Needle with Viscous Dissipation, Magnetic Effects and Hall Current. Plos one, 16 (2021),4, e0249264
- Panigrahi, L., et al., Heat and Mass Transfer of MHD Casson Nanofluid Flow Through a Porous Medium Past a Stretching Sheet with Newtonian Heating and Chemical Reaction, Karbala International Journal of Modern Science, 6 (2020), 3, 11
- Anjum, A., et al., Investigation of Binary Chemical Reaction in Magnetohydrodynamic Nanofluid Flow with Double Stratification, Advances in Mechanical Engineering, 13 (2021), 5, 16878140211016264
- Mondal, H., et al., Influence of an Inclined Stretching Cylinder Over MHD Mixed Convective Nanofluid Flow Due to Chemical Reaction and Viscous Dissipation, Heat Transfer, 49 (2020), 4, pp.2183-2193
- Reddy, S. R. R., et al., Activation Energy Impact on Chemically Reacting Eyring-Powell Nanofluid Flow Over a Stretching Cylinder, Arabian Journal for Science and Engineering, 45 (2020), Feb., pp. 1-16
- Bhatti, M. M., et al., A Mathematical Model of MHD Nanofluid Flow Having Gyrotactic Microorganisms with Thermal Radiation and Chemical Reaction Effects, Neural Computing and Applications, 30 (2018), 4, pp. 1237-1249
- Tlili, I., et al., Multiple Slips Effects on MHD SA-Al2O3 and SA-Cu Non-Newtonian Nanofluids Flow Over a Stretching Cylinder in Porous Medium with Radiation and Chemical Reaction, Results in physics, 8 (2018), Mar., pp. 213-222
- Rasheed, H. U., et al., An Analytical Study of Internal Heating and Chemical Reaction Effects on MHD Flow of Nanofluid with Convective Conditions, Crystals, 11 (2021), 12, 1523
- Rafique, K., et al., Keller-Box Study on Casson Nano Fluid Flow Over a Slanted Permeable Surface with Chemical Reaction, Asian Research Journal of Mathematics., 14 (2019), 4, pp. 1-17
- Alotaibi, H., Eid, M. R., Thermal Analysis of 3D Electromagnetic Radiative Nanofluid Flow with Suction/Blowing: Darcy-Forchheimer Scheme, Micromachines, 12 (2021), 11, 1395
- Saqib, M., et al., Generalized Magnetic Blood Flow in a Cylindrical Tube with Magnetite Dusty Particles, Journal of Magnetism and Magnetic Materials, 484 (2019), Aug., pp. 490-496
- Reddy, P. B. A., Magnetohydrodynamic Flow of a Casson Fluid Over an Exponentially Inclined Permeable Stretching Surface with Thermal Radiation and Chemical Reaction, Ain Shams Engineering Journal., 7 (2016), 2, pp. 593-602
- Saqib, M., et al., Heat Transfer in MHD Flow of Maxwell Fluid via Fractional Cattaneo-Friedrich Model: A Finite Difference Approach, Comput. Mater. Contin, 65 (2020), 3, pp. 1959-1973
- Ishak, A., MHD Boundary-Layer Flow Due to an Exponentially Stretching Sheet with Radiation Effect, Sains Malaysiana, 40 (2011), 4, pp. 391-395
- Turner, M. R., Weidman, P., The Boundary-Layer Flow Induced Above the Torsional Motion of a Disk. Physics of Fluids, 31 (2019), 4, 043604
- Anwar, M. I., et al., Numerical Study of Hydrodynamic Flow of a Casson Nanomaterial Past an Inclined Sheet Under Porous Medium, Heat Transfer Asian Research., 49 (2020), 1, pp. 307-334
- Shaheen, N., et al., Impact of Hall Current on a 3D Casson Nanofluid Flow Past a Rotating Deformable Disk with Variable Characteristics, Arabian Journal for Science and Engineering, 46 (2021), 12, pp. 12653-12666
- Salleh, S. N. A., et al., Numerical Analysis of Boundary-Layer Flow Adjacent to a Thin Needle in Nanofluid with the Presence of Heat Source and Chemical Reaction, Symmetry., 11 (2019), 4, 543
- Ulutas, E., et al., Exact Solutions of Stochastic Kdv Equation with Conformable Derivatives in White Noise Environment, Thermal Science, 25 (2021), Special Issue 2, pp. S143-S149
- Yildirim, E. N., et al., Reproducing Kernel Functions and Homogenizing Transforms, Thermal Science, 25 (2021), Special Issue 2, pp. S9-S18
- Abdelrahman, M. A. E., et al., Exact Solutions of the Cubic Boussinesq and the Coupled Higgs Systems, Thermal Science, 24 (2020), Suppl. 1, pp. S333-S342
- Menni, Y., et al., Heat and Mass Transfer of Oils in Baffled and Finned Ducts, Thermal Science, 24 (2021), Suppl. 1, pp. S267-276