THERMAL SCIENCE

International Scientific Journal

Muhammad Imran Asjad

,

Muhammad Danish Ikram

,

Rizwan Ali

,

Dumitru Baleanu

,

Ali Saleh Alshomrani

NEW ANALYTICAL SOLUTIONS OF HEAT TRANSFER FLOW OF CLAY-WATER BASE NANOPARTICLES WITH THE APPLICATION OF NOVEL HYBRID FRACTIONAL DERIVATIVE

ABSTRACT
Clay nanoparticles are hanging in three different based fluids (water, kerosene, and engine oil). The exact terminologies of Maxwell-Garnett and Brinkman for the current thermophysical properties of clay nanofluids are used, while the flow occurrence is directed by a set linear PDE with physical initial and boundary conditions. The classical governing equations are extended to non-integer order hybrid fractional derivative which is introduced in [33]. Analytical solutions for temperature and ve­locity fields are attained via Laplace transform technique. Some limiting solutions are also obtained from the existing literature and compared for different values of fractional parameter. To vision the impact of several flow parameters on the temperature and velocity some graphs are drawn using Mathcad software and designed in different figures. As a result, we found that hybrid fractional model is better in describing the decay behavior of temperature and velocity in comparison of classical derivatives. In comparison of nanofluid with different base fluids, it is concluded that water-based nanofluid has higher velocity than others.
KEYWORDS
hybrid fractional derivative, power law kernel, Clay-nanoparticles, analytical solutions
PAPER SUBMITTED: 2020-05-25
PAPER REVISED: 2020-06-30
PAPER ACCEPTED: 2020-07-15
PUBLISHED ONLINE: 2020-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI20S1343A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Supplement 1, PAGES [S343 - S350]
REFERENCES
  1. Choi, S. U. S., Enhancing Thermal Conductivity of Fluids with Nanoparticles Developments and Applications of Non-Newtonian Flows, ASME, 231 (1995), Jan., pp. 99-105
  2. Saqib, M., et al., Entropy Generation in Different Types of Fractionalized Nanofluids, Arabian Journal for Science and Engineering, 44 (2018), June, pp. 531-540
  3. Ahmed, N., et al., Transient MHD Convective Flow of Fractional Nanofluid Between Vertical Plates, Journal of Applied and Computational Mechanics, 5 (2019), 4, pp. 592-602
  4. Rahimi-Gorji, M., et al., Modelling of the Air Conditions Effects on the Power and Fuel Consumption of the SI Engine Using Neural Networks and Regression, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39 (2017), 2, pp. 375-384
  5. Rahimi-Gorji, M., et al., The CFD Simulation of Air-flow Behavior and Particle Transport and Deposition in Different Breathing Conditions through the Realistic Model of Human Airways, Journal of Molecular Liquids, 209 (2015), Sept., pp. 121-133
  6. Saqib, M., et al., Application of Atangana-Baleanu fractional Derivative to MHD Channel Flow of CMC- Based- CNT's Nanofluid through a Porous Medium, Chaos, Solitons and Fractals, 116 (2018), Nov., pp. 79-85
  7. Khanafer, K., et al., Buoyancy-Driven Heat Transfer Enhancement in a 2-D Enclosure Utilizing Nanofluids, International Journal of Heat and Mass Transfer, 46 (2003), 19, pp. 3639-3653
  8. Buongiorno, J., Convective Transport in Nanofluids, Journal of Heat Transfer, 128 (2006), 3, pp. 240-250
  9. Tiwari, R. K., Das, M. K., Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids, International Journal of Heat and Mass Transfer, 50 (2007), 9-10, pp. 2002-2018
  10. Ahmad, S., Pop, I., Mixed Convection Boundary-Layer Flow from a Vertical Flat Plate Embedded in a Porous Medium Filled with Nanofluids, International Communications in Heat and Mass Transfer, 37 (2010), 8, pp. 987-991
  11. Biglarian, M., et al., The H2O Based Different Nanofluids with Unsteady Condition and an External Magnetic Field on Permeable Channel Heat Transfer, International Journal of Hydrogen Energy, 42 (2017), 34, pp. 22005-22014
  12. Mosayebidorcheh, S., et al., Transient Thermal Behavior of Radial Fins of Rectangular, Triangular and Hyperbolic Profiles with Temperature-Dependent Properties Using DTM-FDM, Journal of Central South University, 24 (2017), 3, pp. 675-682
  13. Pourmehran, O., et al., Rheological Behaviour of Various Metal-Based Nanofluids Between Rotating Discs: A New Insight, Journal of the Taiwan Institute of Chemical Engineers, 88 (2018), July, pp. 37-48
  14. Rahimi-Gorji, M., et al., Unsteady Squeezing Nanofluid Simulation and Investigation of its Effect on Important heat Transfer Parameters in Presence of Magnetic Field, Journal of the Taiwan Institute of Chemical Engineers, 67 (2016), Oct., pp. 467-475
  15. Saqib, M., et al., Convection in Ethylene Glycol-Based Molybdenum Disulfide Nanofluid, Journal of Thermal Analysis and Calorimetry, 135 (2018), Feb., pp. 523-532
  16. Trisaksri, V., Wongwises, S., Critical Review of Heat Transfer Characteristics of Nanofluids, Renewable and Sustainable Energy Reviews, 11 (2007), 3, pp. 512-523
  17. Sheikh, N. A., et al., On the Applications of Nanofluids to Enhance the Performance of Solar Collectors: A Comparative Analysis of Atangana-Baleanu and Caputo-Fabrizio fractional Models, The European Physical Journal Plus, 132 (2017), 12, 540
  18. Oztop, H. F., et al., A Brief Review of Natural-Convection in Enclosures under Localized Heating with and without Nanofluids, International Communications in Heat and Mass Transfer, 60 (2015), Jan., pp. 37-44
  19. Hussanan, A., et al., Convection Heat Transfer in Micropolar Nanofluids with Oxide Nanoparticles in Water, Kerosene and Engine Oil, Journal of Molecular Liquids, 229 (2017), Mar., pp. 482-488
  20. Tesfai, W., et al., Rheology and Microstructure of Dilute Graphene Oxide Suspension, Journal of Nanoparticle Research, 15 (2013), 10, 1989
  21. Wu, J. M., Zhao, J., A Review of Nanofluid Heat Transferand Critical Heat Flux Enhancement - Research Gap to EngineeringApplication, Progress in Nuclear Energy, 66 (2013), July, pp. 13-24
  22. Khan, I., Shape Effects of MoS2 Nanoparticles on MHD Slip Flow of Molybdenum Disulphide Nanofluid in a Porous Medium, Journal of Molecular Liquids, 233 (2017), May, pp. 442-451
  23. Sheikholeslami, M., Bhatti, M. M., Active Method for Nanofluid Heat Transfer Enhancement by Means of EHD, International Journal of Heat and Mass Transfer, 109 (2017), June, pp. 115-122
  24. Abdelsalam, S. I., Bhatti, M. M., The Impact of Impinging TiO2 Nanoparticles in Prandtl Nanofluid Along with Endoscopic and Variable Magnetic Field Effects on Peristaltic Blood Flow, Multidiscipline Modelling in Materials and Structures, 14 (2018), 3, pp. 530-548
  25. Abdelsalam, S. I., Bhatti, M. M., The Study of Non-Newtonian Nanofluid with Hall and Ion Slip Effects on PeristalticallyInduced Motion in a Non-Uniform Channel, RSC Advances, 8 (2018), 15, pp. 7904-7915
  26. Brinkman, H. C., The Viscosity of Concentrated Suspensions and Solutions, The Journal of Chemical Physics, 20 (1952), 4, pp. 571-571
  27. Aminossadati, S. M., Ghasemi, B., Natural-Convection Cooling of a Localised Heat Source at the Bottom of a Nanofluid Filled Enclosure, European Journal of Mechanics - B/Fluids, 28 (2009), 5, pp. 630-640
  28. Matin, M. H., Pop, I., Forced Convection Heat and Mass Transfer Flow of a Nanofluid through a Porous Channel with a First Order Chemical Reaction on the Wall, International Communication in Heat and Mass Transfer, 46 (2013), Aug., pp. 134-141
  29. Khan, I., et al., Convective Heat Transfer in Drilling Nanofluid with Clay Nanoparticles: Applications in Water Cleaning Process, BioNanoScience, 9 (2019), Mar., pp. 453-460
  30. Baleanu, D., Fractional Calculus Models and Numerical Methods, World Scientific, Singapore, 2012
  31. Petras, I., Fractional-order Non-linear Systems: Modelling Analysis and Simulation, Springer and Beijing, London, HEP, 2011
  32. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006
  33. Baleanu, et al., On a Fractional Operator Combining Proportional and Classical Differintegrals, Mathematics, 8 (2020), 3, 860
PDF VERSION [DOWNLOAD]
New analytical solutions of heat transfer flow of clay-water base nanoparticles with the application of novel hybrid fractional derivative

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence