Abstract
In many industrial applications, heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention, owing to their immense importance in technology, engineering, and science. These processes are relevant for polymer solutions, porous industrial materials, ceramic processing, oil recovery, and fluid beds. The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics. Therefore, the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation (quadratic/nonlinear Boussinesq approximation) is performed in the present study. The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow, heat transfer, and entropy generation are analyzed. The governing nonlinear equations are solved with the spectral quasi-linearization method (SQLM). The obtained results are compared with those calculated with a finite element method and the bvp4c routine. In addition, the effects of key parameters on the velocity of the hyperbolic tangent material, the entropy generation, the temperature, and the Nusselt number are discussed. The entropy generation increases with the buoyancy force, the pressure gradient factor, the non-linear convection, and the Eckert number. The non-Newtonian fluid factor improves the magnitude of the velocity field. The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field. The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.
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References
BEJAN, A. Entropy Generation Minimization, CRC Press, Boca Raton (1996)
PAKDEMIRLI, M. and YILBAS, B. S. Entropy generation in a pipe due to non-Newtonian fluid flow: constant viscosity case. Sadhana—Academy Proceedings in Engineering Sciences, 31, 21–29 (2006)
DAS, S., BANU, A. S., JANA, R. N., and MAKINDE, O. D. Entropy analysis on MHD pseudoplastic nanofluid flow through a vertical porous channel with convective heating. Alexandria Engineering Journal, 54, 325–337 (2015)
TING, T. W., HUNG, Y. M., and GUO, N. Entropy generation of viscous dissipative nanofluid flow in thermal non-equilibrium porous media embedded in microchannels. International Journal of Heat and Mass Transfer, 81, 862–877 (2015)
IBÁÑEZ, G. Entropy generation in MHD porous channel with hydrodynamic slip and convective boundary conditions. International Journal of Heat and Mass Transfer, 80, 274–280 (2015)
LÓPEZ, A., IBÁÑEZ, G., PANTOJA, J., MOREIRA, J., and LASTRES, O. Entropy generation analysis of MHD nanofluid flow in a porous vertical microchannel with nonlinear thermal radiation, slip flow and convective-radiative boundary conditions. International Journal of Heat and Mass Transfer, 107, 982–994 (2017)
MAKINDE, O. D. and EEGUNJOBI, A. S. Effects of convective heating on entropy generation rate in a channel with permeable walls. Entropy, 15, 220–233 (2013)
NAGARAJU, G., JANGILI, S., RAMANAMURTHY, J. V., BEG, O. A., and KADIR, A. Second law analysis of flow in a circular pipe with uniform suction and magnetic field effects. Journal of Heat Transfer, 141, 012004 (2019)
SHEIKHOLESLAMI, M. New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media. Computer Methods in Applied Mechanics and Engineering, 344, 319–333 (2019)
JANGILI, S., ADESANYA, S. O., OGUNSEYE, H. A., and LEBELO, R. Couple stress fluid flow with variable properties: a second law analysis. Mathematical Methods in the Applied Sciences, 42, 85–98 (2019)
AFRIDI, M. I. and QASIM, M. Entropy generation and heat transfer in boundary layer flow over a thin needle moving in a parallel stream in the presence of nonlinear Rosseland radiation. International Journal of Thermal Sciences, 123, 117–128 (2018)
HAYAT, T., SHAHA, F., KHAN, M. I., and ALSAEDI, A. Entropy analysis for comparative study of effective Prandtl number and without effective Prandtl number via γAl2O3-H2O and γAl2O3-C2H6O2 nanoparticles. Journal of Molecular Liquids, 266, 814–823 (2018)
ADESANYA, S. O., OGUNSEYE, H. A., FALADE, J. A., and LEBELO, R. S. Thermodynamic analysis for buoyancy-induced couple stress nanofluid flow with constant heat flux. Entropy, 19, 580 (2017)
EEGUNJOBI, A. S. and MAKINDE, O. D. MHD mixed convection slip flow of radiating Casson fluid with entropy generation in a channel filled with porous media. Defect and Diffusion Forum, 374, 47–66 (2017)
SHEIKHOLESLAMI, M. and MAHIAN, O. Enhancement of PCM solidification using inorganic nanoparticles and an external magnetic field with application in energy storage systems. Journal of Cleaner Production, 215, 963–977 (2019)
ABBAS, S. Z., KHAN, W. A., KADRY, S., KHAN, M. I., WAQAS, M., and KHAN, M. I. Entropy optimized Darcy-Forchheimer nanofluid (silicon dioxide, molybdenum disulfide) subject to temperature dependent viscosity. Computer Methods and Programs in Biomedicine, 190, 105363 (2020)
KHAN, W. A. and ALI, M. Recent developments in modeling and simulation of entropy generation for dissipative cross material with quartic autocatalysis. Applied Physics A, 125(6), 1–9 (2019)
WANG, J., KHAN, W. A., ASGHAR, Z., WAQAS, M., ALI, M., and IRFAN, M. Entropy optimized stretching flow based on non-Newtonian radiative nanoliquid under binary chemical reaction. Computer Methods and Programs in Biomedicine, 188, 105274 (2020)
SULTAN, F., KHAN, W. A., ALI, M., SHAHZAD, M., SUN, H., and IRFAN, M. Importance of entropy generation and infinite shear rate viscosity for non-Newtonian nanofluid. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(10), 1–13 (2019)
ALI, M., SULTAN, F., KHAN, W. A., and SHAHZAD, M. Exploring the physical aspects of nanofluid with entropy generation. Applied Nanoscience, 10(8), 3215–3225 (2020)
FRIEDMAN, A. J., DYKE, S. J., and PHILLIPS, B. M. Over-driven control for large-scale MR dampers. Smart Materials and Structures, 22, 045001 (2013)
NADEEM, S. and AKRAM, S. Peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel. Zeitschrift für Naturforschung, 64, 559–567 (2009)
NADEEM, S. and AKRAM, S. Effects of partial slip on the peristaltic transport of a hyperbolic tangent fluid model in an asymmetric channel. International Journal for Numerical Methods in Fluids, 63, 374–394 (2010)
HAYAT, T., KHAN, M. I., WAQAS, M., and ALSAEDI, A. Stagnation point flow of hyperbolic tangent fluid with Soret-Dufour effects. Results in Physics, 7, 2711–2717 (2017)
SALEEM, N. and MUNAWAR, S. Entropy analysis in cilia driven pumping flow of hyperbolic tangent fluid with magnetic field effects. Fluid Dynamics Research, 52, 025503 (2020)
SALAHUDDIN, T., TANVEER, A., and MALIK, M. Y. Homogeneous-heterogeneous reaction effects in flow of tangent hyperbolic fluid on a stretching cylinder. Canadian Journal of Physics, 98, 125–129 (2020)
IBRAHIM, W. and GIZEWU, T. Nonlinear mixed convection flow of a tangent hyperbolic fluid with activation energy. Heat Transfer, 49, 2427–2448 (2020)
SRINIVASACHARYA, D. and BINDU, K. H. Entropy generation in a micropolar fluid flow through an inclined channel with slip and convective boundary conditions. Energy, 91, 72–83 (2015)
IBÁÑEZ, G., LÓPEZ, A., LÓPEZ, I., PANTOJA, J., MOREIRA, J., and LASTRES, O. Optimization of MHD nanofluid flow in a vertical microchannel with a porous medium, nonlinear radiation heat flux, slip flow and convective-radiative boundary conditions. Journal of Thermal Analysis and Calorimetry, 135, 3401–3420 (2019)
MADHU, M., SHASHIKUMAR, N. S., MAHANTHESH, B., GIREESHA, B. J., and KISHAN, N. Heat transfer and entropy generation analysis of non-Newtonian flu flow through vertical microchannel with convective boundary condition. Applied Mathematics and Mechanics (English Edition), 40(9), 1285–1300 (2019) https://doi.org/10.1007/s10483-019-2516-9
GIREESHA, B. J., SRINIVASA, C. T., SHASHIKUMAR, N. S., MACHA, M., SINGH, J. K., and MAHANTHESH, B. Entropy generation and heat transport analysis of Casson fluid flow with viscous and Joule heating in an inclined porous microchannel. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 233, 1173–1184 (2019)
LOPEZ, A., IBANEZ, G., PANTOJA, J., MOREIRA, J., and LASTRES, O. Entropy generation analysis of MHD nanofluid flow in a porous vertical microchannel with nonlinear thermal radiation, slip flow and convective-radiative boundary conditions. International Journal of Heat and Mass Transfer, 107, 982–994 (2017)
SHASHIKUMAR, N. S., GIREESHA, B. J., MAHANTHESH, B., PRASANNAKUMARA, B. C., and CHAMKHA, A. J. Entropy generation analysis of magneto-nanoliquids embedded with aluminium and titanium alloy nanoparticles in microchannel with partial slips and convective conditions. International Journal of Numerical Methods for Heat and Fluid Flow, 29, 3638–3658 (2019)
SINDHU, S. and GIREESHA, B. J. Heat and mass transfer analysis of chemically reactive tangent hyperbolic fluid in a microchannel. Heat Transfer, 50, 1410–1427 (2020)
DHLAMINI, M., KAMESWARAN, P. K., SIBANDA, P., MOTSA, S., and MONDAL, H. Activation energy and binary chemical reaction effects in mixed convective nanofluid flow with convective boundary conditions. Journal of Computational Design and Engineering, 6, 149–158 (2019)
SITHOLE, H., MONDAL, H., and SIBANDA, P. Entropy generation in a second grade magneto-hydrodynamic nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation. Results in Physics, 9, 1077–1085 (2018)
ACHARYA, N. Spectral simulation to investigate the effects of active passive controls of nanoparticles on the radiative nanofluidic transport over a spinning disk. Journal of Thermal Science and Engineering Applications, 13, 1–13 (2021)
BELLMAN, R. E. and KALABA, R. E. Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York (1965)
Acknowledgements
The authors would like to thank the editor and anonymous reviewers for their constructive suggestions. One of the authors (B. MAHANTHESH) would like to thank the management of CHRIST (Deemed to be University), Bangalore, India, for support.
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Srinivas Reddy, C., Mahanthesh, B., Rana, P. et al. Entropy generation analysis of tangent hyperbolic fluid in quadratic Boussinesq approximation using spectral quasi-linearization method. Appl. Math. Mech.-Engl. Ed. 42, 1525–1542 (2021). https://doi.org/10.1007/s10483-021-2773-8
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DOI: https://doi.org/10.1007/s10483-021-2773-8
Key words
- tangent hyperbolic fluid
- nonlinear Boussinesq approximation
- entropy production
- convective boundary condition
- spectral quasi-linearization method (SQLM)