Journal of Applied and Computational Mechanics
Entropy Analysis of Darcy-Forchheimer Model of Prandtl Nanofluid over a Curved Stretching Sheet and Heat Transfer Optimization by ANOVA-Taguchi Technique
Document Type : Research Paper
Authors
1 Department of Mathematics, School of Engineering, Presidency University, Rajanakunte, Yelahanka, Bengaluru-560064, Karnataka, India
2 Department of Mathematics, Kuvempu University, Jnanasahyadri, Shankarghatta, Shivamogga-577451, India
Abstract
Darcy-Forchheimer model has been used to consider the mathematical and statistical aspects of Prandtl nanofluid flow on a stretched curvy geometry, with homogenic-heterogenic reactions, nonlinear radiation, exponential heat, Joule heating, velocity slip, and convective heat conditions. An account of entropy significance has been given to boost the applicability of the study. The 4-5th ordered numerical tool, Runge-Kutta-Fehlberg, has been employed to establish the plots for the considered flow. ANOVA and Taguchi optimisation technique is used to obtain the optimal condition in enhancing the heat transfer rate for modelled mathematical problem. Here, the study reveals that the increasing homo-heterogenic strength parameters foster the concentration profile. The study also found that the thermal curves are positively affected by the radiation parameter and the temperature differential parameter. In addition to this, graphical portraits of isotherms and streamlines have been given to characterise the flow and heat pattern. Taguchi method reveal that first level of Prandtl number, magnetic parameter, Weissenberg number, heat source parameter and third level of curvature parameter, produce maximum Nusselt number. Heat source parameter has large contribution of about 49.45% among the other parameters and Prandtl number has the least contribution of about 1.4% for optimisation.
Keywords
- Statistical interpretation
- Homogeneous-heterogeneous reactions
- Slip flow
- Convection
- non-Newtonian nanofluid
Main Subjects
Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
[1] Sajid, M., Ali, N., Javed, T., Abbas, Z., Stretching a curved surface in a viscous fluid, Chinese Physics Letters, 27, 2010, 024703.
[2] Hayat, T., Kiran, A., Imtiaz, M., Alsaedi, A., Hydromagnetic mixed convection flow of copper and silver water nanofluids due to a curved stretching sheet, Results in physics, 6, 2016, 904-910.
[3] Narla, V.K., Biswas, C., Rao, G.A., Entropy analysis of MHD fluid flow over a curved stretching sheet, AIP Conference Proceedings, 2246, 2020, 020099.
[4] Nagaraja, B., Gireesha, B.J., Exponential space-dependent heat generation impact on MHD convective flow of Casson fluid over a curved stretching sheet with chemical reaction, Journal of Thermal Analysis and Calorimetry, 143, 2021, 4071-4079.
[5] Usman, A.H., Hamisu, A., Khan, N.S., Rano, S.A., Maitama, M., Study of Heat and Mass Transfer in MHD Flow of Sutterby Nanofluid over a Curved Stretching Sheet with Magnetic Dipole and Effect, Thai Journal of Mathematics, 19, 2021, 1037-1055.
[6] Khan, M.I., Alzahrani, F., Optimized framework for slip flow of viscous fluid towards a curved surface with viscous dissipation and Joule heating features, Applied Mathematics and Computation, 417, 2022, 126777.
[7] Nadeem, S., Ijaz, S., Akbar, N.S., Nanoparticle analysis for blood flow of Prandtl fluid model with stenosis, International Nano Letters, 3, 2013, 1-13.
[8] Khan, I., Malik, M.Y., Hussain, A., Salahuddin, T., Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet, Results in Physics, 7, 2017, 4226-4231.
[9] Hamid, M., Zubair, T., Usman, M., Khan, Z.H., Wang, W., Natural convection effects on heat and mass transfer of slip flow of time-dependent Prandtl fluid, Journal of Computational Design and Engineering, 6, 2019, 584-592.
[10] Salmi, A., Madkhali, H.A., Ali, B., Nawaz, M., Alharbi, S.O., Alqahtani, A.S., Numerical study of heat and mass transfer enhancement in Prandtl fluid MHD flow using Cattaneo-Christov heat flux theory, Case Studies in Thermal Engineering, 33, 2022, 101949.
[11] Patil, A.B., Patil, N.S., Patil, V.S., Humane, P.P., Rajput, G.R., Unsteady thermally radiative Prandtl fluid flow past a magnetized inclined porous stretching device with double-diffusion, viscous dissipation, and Joule heating, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 237, 2023, 762-770.
[12] Hayat, T., Saif, R.S., Ellahi, R., Muhammad, T., Ahmad, B., Numerical study for Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions, Results in Physics, 7, 2017, 2886-2892.
[13] Gireesha, B.J., Nagaraja, B., Sindhu, S., Sowmya, G., Consequence of exponential heat generation on non-Darcy-Forchheimer flow of water-based carbon nanotubes driven by a curved stretching sheet, Applied Mathematics and Mechanics, 41, 2020, 1723-1734.
[14] Muhammad, T., Rafique, K., Asma, M., Alghamdi, M., Darcy–Forchheimer flow over an exponentially stretching curved surface with Cattaneo–Christov double diffusion, Physica A: Statistical Mechanics and its Applications, 556, 2020, 123968.
[15] Muhammad, R., Khan, M.I., Jameel, M., Khan, N.B., Fully developed Darcy-Forchheimer mixed convective flow over a curved surface with activation energy and entropy generation, Computer Methods and Programs in Biomedicine, 188, 2020, 105298.
[16] Hayat, T., Qayyum, S., Alsaedi, A., Waqas, M., Simultaneous influences of mixed convection and nonlinear thermal radiation in stagnation point flow of Oldroyd-B fluid towards an unsteady convectively heated stretched surface, Journal of Molecular Liquids, 224, 2016, 811-817.
[17] Patel, H.R., Singh, R., Thermophoresis Brownian motion and non-linear thermal radiation effects on mixed convection MHD micropolar fluid flow due to nonlinear stretched sheet in porous medium with viscous dissipation joule heating and convective boundary condition, International Communications in Heat and Mass Transfer, 107, 2019, 68-92.
[18] Raza, R., Mabood, F., Naz, R., Abdelsalam, S.I., Thermal transport of radiative Williamson fluid over stretchable curved surface, Thermal Science and Engineering Progress, 23, 2021, 100887.
[19] Algehyne, E.A., Aldhabani, M.S., Saeed, A., Dawar, A., Kumam, P., Mixed convective flow of Casson and Oldroyd-B fluids through a stratified stretching sheet with nonlinear thermal radiation and chemical reaction, Journal of Taibah University for Science, 16, 2022, 193-203.
[20] Imtiaz, M., Hayat, T. Alsaedi, A., Hobiny, A., Homogeneous-heterogeneous reactions in MHD flow due to an unsteady curved stretching surface, Journal of Molecular Liquids, 221, 2016, 245-253.
[21] Pal, D., Mandal, G., Effects of aligned magnetic field on heat transfer of water-based carbon nanotubes nanofluid over a stretching sheet with homogeneous–heterogeneous reactions, International Journal of Ambient Energy, 42, 2021, 1-13.
[22] Imtiaz, M., Mabood, F., Hayat, T., Alsaedi, A., Homogeneous-heterogeneous reactions in MHD radiative flow of second grade fluid due to a curved stretching surface, International Journal of Heat and Mass Transfer, 145, 2019, 118781.
[23] Ashraf, M.B., Ul Haq, S., The convective flow of Carreau fluid over a curved stretching surface with homogeneous-heterogeneous reactions and viscous dissipation, Waves in Random and Complex Media, 32, 2022, 1-15.
[24] Manjunatha, S., Puneeth, V., Gireesha, B.J., Chamkha, A.J., Theoretical Study of Convective Heat Transfer in Ternary Nanofluid Flowing past a Stretching Sheet, Journal of Applied and Computational Mechanics, 8, 2022, 1279-1286.
[25] Sharma, R.P., Shaw, S., MHD Non-Newtonian Fluid Flow past a Stretching Sheet under the Influence of Non-linear Radiation and Viscous Dissipation, Journal of Applied and Computational Mechanics, 8, 2022, 949-961.
[26] Felicita, A., Berrehal, H., Venkatesh, P., Gireesha, B.J., Sowmya, G., Slip flow of Walter’s B liquid through the channel possessing stretched walls by employing optimal homotopy asymptotic method (OHAM), Journal of Molecular Liquids, 353, 2022, 118731.
[27] Nagaraja, B., Ajaykumar, A.R., Felicita, A., Pradeep, K., Rudraswamy, N.G., Non-Darcy-Forchheimer flow of Casson-Williamson nanofluid on melting curved stretching sheet influenced by magnetic dipole, ZAMM-Journal of Applied Mathematics and Mechanics, 2023, https://doi.org/10.1002/zamm.202300134.
[28] Animasaun, I.L., Adebile, E.A., Fagbade, A.I., Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method, Journal of the Nigerian Mathematical Society, 35, 2016, 1-17.
[29] Zia, Q.M., Ullah, I., Waqas, M., Alsaedi, A., Hayat, T., Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface, Results in Physics, 8, 2018, 1275-1282.
[30] Kumar, A., Reddy, J.V.R., Sugunamma, V., Sandeep, N., Impact of cross diffusion on MHD viscoelastic fluid flow past a melting surface with exponential heat source, Multidiscipline Modelling in Materials and Structures, 14, 2018, 999-1016.
[31] Nagaraja, B., Gireesha, B.J., Soumya, D.O., Almeida, F., Characterization of MHD convective flow of Jeffrey nanofluid driven by a curved stretching surface by employing Darcy–Forchheimer law of porosity, Waves in Random and Complex Media, 2022, https://doi.org/10.1080/17455030.2021.2020933.
[32] Kumar, P., Nagaraja, B., Almeida, F., AjayKumar, A.R., Al-Mdallal, Q., Jarad, F., Magnetic dipole effects on unsteady flow of Casson-Williamson nanofluid propelled by stretching slippery curved melting sheet with buoyancy force, Scientific Reports, 13, 2023, 12770.
[33] Bejan, A., Entropy generation minimization: The new thermodynamics of finite‐size devices and finite‐time processes, Journal of Applied Physics, 79, 1996, 1191-1218.
[34] Hayat, T., Qayyum, S., Alsaedi, A., Ahmad, B., Entropy generation minimization: Darcy-Forchheimer nanofluid flow due to curved stretching sheet with partial slip, International Communications in Heat and Mass Transfer, 111, 2020, 104445.
[35] Almeida, F., Venkatesh, P., Gireesha, B.J., Nagaraja, B., Eshwarappa, K.M., Compressed flow of hybridized nanofluid entwined between Two rotating plates exposed to radiation, Journal of Nanofluids, 10, 2021, 186-199.
[36] Mishra, S.R., Sharma, R.P., Tinker, S., Panda, G.K., Impact of Slip and the Entropy Generation in a Darcy-Forchhimer Nanofluid Past a Curved Stretching Sheet with Heterogeneous and Homogenous Chemical Reactions, Journal of Nanofluids, 11, 2022, 48-57.
[37] Almeida, F., Gireesha, B.J., Venkatesh, P., Ramesh, G.K., Intrinsic irreversibility of Al2O3–H2O nanofluid Poiseuille flow with variable viscosity and convective cooling, International Journal of Numerical Methods for Heat & Fluid Flow, 31, 2022, 2042-2063.
[38] Sheikholeslami, M., Efficacy of porous foam on discharging of phase change material with inclusion of hybrid nanomaterial, Journal of Energy Storage, 62, 2023, 106925.
[39] Sheikholeslami, M., Numerical investigation for concentrated photovoltaic solar system in existence of paraffin equipped with MWCNT nanoparticles, Sustainable Cities and Society, 99, 2023, 104901.
[40] Sheikholeslami, M., Numerical investigation of solar system equipped with innovative turbulator and hybrid nanofluid, Solar Energy Materials and Solar Cells, 243, 2022, 111786.
[41] Upreti, H., Pandey, A.K., Kumar, M., Makinde, O.D., Darcy–Forchheimer flow of CNTs-H2O nanofluid over a porous stretchable surface with Xue model, International Journal of Modern Physics B, 37, 2023, 2350018.
[42] Upreti, H., Bartwal, P., Pandey, A.K., Makinde, O.D., Heat transfer assessment for Au-blood nanofluid flow in Darcy-Forchheimer porous medium using induced magnetic field and Cattaneo-Christov model, Numerical Heat Transfer, Part B: Fundamentals, 2023, 1-17.
[43] Nayak, M.K., Shaw, S., Khan, M.I., Makinde, O.D., Yu-Ming, C., Khan, S.U., Interfacial layer and shape effects of modified Hamilton’s Crosser model in entropy optimized Darcy-Forchheimer flow, Alexandria Engineering Journal, 60, 2021, 4067-4083.
[44] Tadesse, F.B., Makinde, O.D., Enyadene, L.G., Hydromagnetic stagnation point flow of a magnetite ferrofluid past a convectively heated permeable stretching/shrinking sheet in a Darcy–Forchheimer porous medium, Sadhana, 46, 2021, 115.
[45] Shaw, S., Dogonchi, A.S., Nayak, M.K., Makinde, O.D., Impact of entropy generation and nonlinear thermal radiation on Darcy–Forchheimer flow of MnFe2O4-Casson/water nanofluid due to a rotating disk: Application to brain dynamics, Arabian Journal for Science and Engineering, 45, 2020, 5471-5490.
[46] Nagaraja, B., Felicita, A., Ali, Y., Pradeep, K., Ajaykumar, A.R., Al-Mdallal, Q., Empirical study for Nusselt number optimization for the flow using ANOVA and Taguchi method, Case Studies in Thermal Engineering, 50, 2023, 103505.
[47] Pradeep, K., Ajaykumar, A.R., Felicita, A., Nagaraja, B., Qasem, Al-M., Youssef El-K., Model Designed to Acquire an Optimized Performance Implementing L27 Orthogonal Array for the Prandtl Fluid Flow Maneuvering Grey Relational Theory, International Journal of Thermofluids, 20, 2023, 100490.
[48] Prakash, D., Kumar, S., Muthtamilselvan, M., Al-Mdallal Q.M., Heat transfer enhancement in a nanofluid saturated porous medium with cross diffusion and nonequilibrium: A regression approach, Numerical Heat Transfer, Part A: Applications, 83, 2023, 1408-1420.
[49] Barman, T., Roy, S., Chamkha, A.J., Magnetized Bi-convective Nanofluid Flow and Entropy Production Using Temperature-sensitive Base Fluid Properties: A Unique Approach, Journal of Applied and Computational Mechanics, 8, 2022, 1163-1175.
[50] Sankar, M., Swamy, H.A.K., Al-Mdallal, Q., Wakif, A., Non-Darcy nanoliquid buoyant flow and entropy generation analysis in an inclined porous annulus: Effect of source-sink arrangement, Alexandria Engineering Journal, 68, 2023, 239-261.
[51] Almeida, F., Gireesha, B.J., Venkatesh, P., Magnetohydrodynamic flow of a micropolar nanofluid in association with Brownian motion and thermophoresis: Irreversibility analysis, Heat Transfer, 52, 2023, 2032-2055.
[52] Felicita, A., Pradeep, K., Nagaraja, B., Gireesha, B.J., Venkatesh, P., Parametric optimisation of entropy using sensitivity analysis and response surface methodology for the compressed flow of hybrid nanoliquid in a stretchable channel, Pramana, 97, 2023, 159.
[53] Singh, V.D., Hussain, M.M., Experimental investigation and optimization of coefficient of friction of brass sheet metal using Taguchi technique, AIP Conf. Proc., 2754, 2023, 100003.
[54] Jou, Y.T., Lin, W.T., Lee, W.C., Yeh, T.M., Integrating the Taguchi method and response surface methodology for process parameter optimization of the injection molding, Applied Mathematics & Information Sciences, 8(3), 2014, 1277.
[55] Rana, P., Gupta, S., Gupta, G., FEM computations and Taguchi optimization in nonlinear radiative MHD MWCNT-MgO/EG hybrid nanoliquid flow and heat transfer over a 3D wedge surface, Case Studies in Thermal Engineering, 41, 2023, 102639.
[56] Rana, P., Gupta, S., Gupta, G., Optimization of heat transfer by nonlinear thermal convection flow past a solid sphere with Stefan blowing and thermal slip using Taguchi method, International Communications in Heat and Mass Transfer, 141, 2023, 106580.
[2] Hayat, T., Kiran, A., Imtiaz, M., Alsaedi, A., Hydromagnetic mixed convection flow of copper and silver water nanofluids due to a curved stretching sheet, Results in physics, 6, 2016, 904-910.
[3] Narla, V.K., Biswas, C., Rao, G.A., Entropy analysis of MHD fluid flow over a curved stretching sheet, AIP Conference Proceedings, 2246, 2020, 020099.
[4] Nagaraja, B., Gireesha, B.J., Exponential space-dependent heat generation impact on MHD convective flow of Casson fluid over a curved stretching sheet with chemical reaction, Journal of Thermal Analysis and Calorimetry, 143, 2021, 4071-4079.
[5] Usman, A.H., Hamisu, A., Khan, N.S., Rano, S.A., Maitama, M., Study of Heat and Mass Transfer in MHD Flow of Sutterby Nanofluid over a Curved Stretching Sheet with Magnetic Dipole and Effect, Thai Journal of Mathematics, 19, 2021, 1037-1055.
[6] Khan, M.I., Alzahrani, F., Optimized framework for slip flow of viscous fluid towards a curved surface with viscous dissipation and Joule heating features, Applied Mathematics and Computation, 417, 2022, 126777.
[7] Nadeem, S., Ijaz, S., Akbar, N.S., Nanoparticle analysis for blood flow of Prandtl fluid model with stenosis, International Nano Letters, 3, 2013, 1-13.
[8] Khan, I., Malik, M.Y., Hussain, A., Salahuddin, T., Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet, Results in Physics, 7, 2017, 4226-4231.
[9] Hamid, M., Zubair, T., Usman, M., Khan, Z.H., Wang, W., Natural convection effects on heat and mass transfer of slip flow of time-dependent Prandtl fluid, Journal of Computational Design and Engineering, 6, 2019, 584-592.
[10] Salmi, A., Madkhali, H.A., Ali, B., Nawaz, M., Alharbi, S.O., Alqahtani, A.S., Numerical study of heat and mass transfer enhancement in Prandtl fluid MHD flow using Cattaneo-Christov heat flux theory, Case Studies in Thermal Engineering, 33, 2022, 101949.
[11] Patil, A.B., Patil, N.S., Patil, V.S., Humane, P.P., Rajput, G.R., Unsteady thermally radiative Prandtl fluid flow past a magnetized inclined porous stretching device with double-diffusion, viscous dissipation, and Joule heating, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 237, 2023, 762-770.
[12] Hayat, T., Saif, R.S., Ellahi, R., Muhammad, T., Ahmad, B., Numerical study for Darcy-Forchheimer flow due to a curved stretching surface with Cattaneo-Christov heat flux and homogeneous-heterogeneous reactions, Results in Physics, 7, 2017, 2886-2892.
[13] Gireesha, B.J., Nagaraja, B., Sindhu, S., Sowmya, G., Consequence of exponential heat generation on non-Darcy-Forchheimer flow of water-based carbon nanotubes driven by a curved stretching sheet, Applied Mathematics and Mechanics, 41, 2020, 1723-1734.
[14] Muhammad, T., Rafique, K., Asma, M., Alghamdi, M., Darcy–Forchheimer flow over an exponentially stretching curved surface with Cattaneo–Christov double diffusion, Physica A: Statistical Mechanics and its Applications, 556, 2020, 123968.
[15] Muhammad, R., Khan, M.I., Jameel, M., Khan, N.B., Fully developed Darcy-Forchheimer mixed convective flow over a curved surface with activation energy and entropy generation, Computer Methods and Programs in Biomedicine, 188, 2020, 105298.
[16] Hayat, T., Qayyum, S., Alsaedi, A., Waqas, M., Simultaneous influences of mixed convection and nonlinear thermal radiation in stagnation point flow of Oldroyd-B fluid towards an unsteady convectively heated stretched surface, Journal of Molecular Liquids, 224, 2016, 811-817.
[17] Patel, H.R., Singh, R., Thermophoresis Brownian motion and non-linear thermal radiation effects on mixed convection MHD micropolar fluid flow due to nonlinear stretched sheet in porous medium with viscous dissipation joule heating and convective boundary condition, International Communications in Heat and Mass Transfer, 107, 2019, 68-92.
[18] Raza, R., Mabood, F., Naz, R., Abdelsalam, S.I., Thermal transport of radiative Williamson fluid over stretchable curved surface, Thermal Science and Engineering Progress, 23, 2021, 100887.
[19] Algehyne, E.A., Aldhabani, M.S., Saeed, A., Dawar, A., Kumam, P., Mixed convective flow of Casson and Oldroyd-B fluids through a stratified stretching sheet with nonlinear thermal radiation and chemical reaction, Journal of Taibah University for Science, 16, 2022, 193-203.
[20] Imtiaz, M., Hayat, T. Alsaedi, A., Hobiny, A., Homogeneous-heterogeneous reactions in MHD flow due to an unsteady curved stretching surface, Journal of Molecular Liquids, 221, 2016, 245-253.
[21] Pal, D., Mandal, G., Effects of aligned magnetic field on heat transfer of water-based carbon nanotubes nanofluid over a stretching sheet with homogeneous–heterogeneous reactions, International Journal of Ambient Energy, 42, 2021, 1-13.
[22] Imtiaz, M., Mabood, F., Hayat, T., Alsaedi, A., Homogeneous-heterogeneous reactions in MHD radiative flow of second grade fluid due to a curved stretching surface, International Journal of Heat and Mass Transfer, 145, 2019, 118781.
[23] Ashraf, M.B., Ul Haq, S., The convective flow of Carreau fluid over a curved stretching surface with homogeneous-heterogeneous reactions and viscous dissipation, Waves in Random and Complex Media, 32, 2022, 1-15.
[24] Manjunatha, S., Puneeth, V., Gireesha, B.J., Chamkha, A.J., Theoretical Study of Convective Heat Transfer in Ternary Nanofluid Flowing past a Stretching Sheet, Journal of Applied and Computational Mechanics, 8, 2022, 1279-1286.
[25] Sharma, R.P., Shaw, S., MHD Non-Newtonian Fluid Flow past a Stretching Sheet under the Influence of Non-linear Radiation and Viscous Dissipation, Journal of Applied and Computational Mechanics, 8, 2022, 949-961.
[26] Felicita, A., Berrehal, H., Venkatesh, P., Gireesha, B.J., Sowmya, G., Slip flow of Walter’s B liquid through the channel possessing stretched walls by employing optimal homotopy asymptotic method (OHAM), Journal of Molecular Liquids, 353, 2022, 118731.
[27] Nagaraja, B., Ajaykumar, A.R., Felicita, A., Pradeep, K., Rudraswamy, N.G., Non-Darcy-Forchheimer flow of Casson-Williamson nanofluid on melting curved stretching sheet influenced by magnetic dipole, ZAMM-Journal of Applied Mathematics and Mechanics, 2023, https://doi.org/10.1002/zamm.202300134.
[28] Animasaun, I.L., Adebile, E.A., Fagbade, A.I., Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method, Journal of the Nigerian Mathematical Society, 35, 2016, 1-17.
[29] Zia, Q.M., Ullah, I., Waqas, M., Alsaedi, A., Hayat, T., Cross diffusion and exponential space dependent heat source impacts in radiated three-dimensional (3D) flow of Casson fluid by heated surface, Results in Physics, 8, 2018, 1275-1282.
[30] Kumar, A., Reddy, J.V.R., Sugunamma, V., Sandeep, N., Impact of cross diffusion on MHD viscoelastic fluid flow past a melting surface with exponential heat source, Multidiscipline Modelling in Materials and Structures, 14, 2018, 999-1016.
[31] Nagaraja, B., Gireesha, B.J., Soumya, D.O., Almeida, F., Characterization of MHD convective flow of Jeffrey nanofluid driven by a curved stretching surface by employing Darcy–Forchheimer law of porosity, Waves in Random and Complex Media, 2022, https://doi.org/10.1080/17455030.2021.2020933.
[32] Kumar, P., Nagaraja, B., Almeida, F., AjayKumar, A.R., Al-Mdallal, Q., Jarad, F., Magnetic dipole effects on unsteady flow of Casson-Williamson nanofluid propelled by stretching slippery curved melting sheet with buoyancy force, Scientific Reports, 13, 2023, 12770.
[33] Bejan, A., Entropy generation minimization: The new thermodynamics of finite‐size devices and finite‐time processes, Journal of Applied Physics, 79, 1996, 1191-1218.
[34] Hayat, T., Qayyum, S., Alsaedi, A., Ahmad, B., Entropy generation minimization: Darcy-Forchheimer nanofluid flow due to curved stretching sheet with partial slip, International Communications in Heat and Mass Transfer, 111, 2020, 104445.
[35] Almeida, F., Venkatesh, P., Gireesha, B.J., Nagaraja, B., Eshwarappa, K.M., Compressed flow of hybridized nanofluid entwined between Two rotating plates exposed to radiation, Journal of Nanofluids, 10, 2021, 186-199.
[36] Mishra, S.R., Sharma, R.P., Tinker, S., Panda, G.K., Impact of Slip and the Entropy Generation in a Darcy-Forchhimer Nanofluid Past a Curved Stretching Sheet with Heterogeneous and Homogenous Chemical Reactions, Journal of Nanofluids, 11, 2022, 48-57.
[37] Almeida, F., Gireesha, B.J., Venkatesh, P., Ramesh, G.K., Intrinsic irreversibility of Al2O3–H2O nanofluid Poiseuille flow with variable viscosity and convective cooling, International Journal of Numerical Methods for Heat & Fluid Flow, 31, 2022, 2042-2063.
[38] Sheikholeslami, M., Efficacy of porous foam on discharging of phase change material with inclusion of hybrid nanomaterial, Journal of Energy Storage, 62, 2023, 106925.
[39] Sheikholeslami, M., Numerical investigation for concentrated photovoltaic solar system in existence of paraffin equipped with MWCNT nanoparticles, Sustainable Cities and Society, 99, 2023, 104901.
[40] Sheikholeslami, M., Numerical investigation of solar system equipped with innovative turbulator and hybrid nanofluid, Solar Energy Materials and Solar Cells, 243, 2022, 111786.
[41] Upreti, H., Pandey, A.K., Kumar, M., Makinde, O.D., Darcy–Forchheimer flow of CNTs-H2O nanofluid over a porous stretchable surface with Xue model, International Journal of Modern Physics B, 37, 2023, 2350018.
[42] Upreti, H., Bartwal, P., Pandey, A.K., Makinde, O.D., Heat transfer assessment for Au-blood nanofluid flow in Darcy-Forchheimer porous medium using induced magnetic field and Cattaneo-Christov model, Numerical Heat Transfer, Part B: Fundamentals, 2023, 1-17.
[43] Nayak, M.K., Shaw, S., Khan, M.I., Makinde, O.D., Yu-Ming, C., Khan, S.U., Interfacial layer and shape effects of modified Hamilton’s Crosser model in entropy optimized Darcy-Forchheimer flow, Alexandria Engineering Journal, 60, 2021, 4067-4083.
[44] Tadesse, F.B., Makinde, O.D., Enyadene, L.G., Hydromagnetic stagnation point flow of a magnetite ferrofluid past a convectively heated permeable stretching/shrinking sheet in a Darcy–Forchheimer porous medium, Sadhana, 46, 2021, 115.
[45] Shaw, S., Dogonchi, A.S., Nayak, M.K., Makinde, O.D., Impact of entropy generation and nonlinear thermal radiation on Darcy–Forchheimer flow of MnFe2O4-Casson/water nanofluid due to a rotating disk: Application to brain dynamics, Arabian Journal for Science and Engineering, 45, 2020, 5471-5490.
[46] Nagaraja, B., Felicita, A., Ali, Y., Pradeep, K., Ajaykumar, A.R., Al-Mdallal, Q., Empirical study for Nusselt number optimization for the flow using ANOVA and Taguchi method, Case Studies in Thermal Engineering, 50, 2023, 103505.
[47] Pradeep, K., Ajaykumar, A.R., Felicita, A., Nagaraja, B., Qasem, Al-M., Youssef El-K., Model Designed to Acquire an Optimized Performance Implementing L27 Orthogonal Array for the Prandtl Fluid Flow Maneuvering Grey Relational Theory, International Journal of Thermofluids, 20, 2023, 100490.
[48] Prakash, D., Kumar, S., Muthtamilselvan, M., Al-Mdallal Q.M., Heat transfer enhancement in a nanofluid saturated porous medium with cross diffusion and nonequilibrium: A regression approach, Numerical Heat Transfer, Part A: Applications, 83, 2023, 1408-1420.
[49] Barman, T., Roy, S., Chamkha, A.J., Magnetized Bi-convective Nanofluid Flow and Entropy Production Using Temperature-sensitive Base Fluid Properties: A Unique Approach, Journal of Applied and Computational Mechanics, 8, 2022, 1163-1175.
[50] Sankar, M., Swamy, H.A.K., Al-Mdallal, Q., Wakif, A., Non-Darcy nanoliquid buoyant flow and entropy generation analysis in an inclined porous annulus: Effect of source-sink arrangement, Alexandria Engineering Journal, 68, 2023, 239-261.
[51] Almeida, F., Gireesha, B.J., Venkatesh, P., Magnetohydrodynamic flow of a micropolar nanofluid in association with Brownian motion and thermophoresis: Irreversibility analysis, Heat Transfer, 52, 2023, 2032-2055.
[52] Felicita, A., Pradeep, K., Nagaraja, B., Gireesha, B.J., Venkatesh, P., Parametric optimisation of entropy using sensitivity analysis and response surface methodology for the compressed flow of hybrid nanoliquid in a stretchable channel, Pramana, 97, 2023, 159.
[53] Singh, V.D., Hussain, M.M., Experimental investigation and optimization of coefficient of friction of brass sheet metal using Taguchi technique, AIP Conf. Proc., 2754, 2023, 100003.
[54] Jou, Y.T., Lin, W.T., Lee, W.C., Yeh, T.M., Integrating the Taguchi method and response surface methodology for process parameter optimization of the injection molding, Applied Mathematics & Information Sciences, 8(3), 2014, 1277.
[55] Rana, P., Gupta, S., Gupta, G., FEM computations and Taguchi optimization in nonlinear radiative MHD MWCNT-MgO/EG hybrid nanoliquid flow and heat transfer over a 3D wedge surface, Case Studies in Thermal Engineering, 41, 2023, 102639.
[56] Rana, P., Gupta, S., Gupta, G., Optimization of heat transfer by nonlinear thermal convection flow past a solid sphere with Stefan blowing and thermal slip using Taguchi method, International Communications in Heat and Mass Transfer, 141, 2023, 106580.
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