Engineering Transactions, Online first

Thermodynamic Analysis of Radiating Nanofluids Mixed Convection within Concentric Pipes Filled with a Porous Medium

Oluwole Daniel MAKINDE
ORCID ID 0000-0002-3991-4948
Stellenbosch University
South Africa

Fanshawe College London

Waqar Ahmed KHAN
Prince Mohammad Bin Fahd University
Saudi Arabia

Anuoluwa Esther MAKINDE
Stellenbosch University
South Africa

In this study, the entropy generation resulting from heat and mass transfer of water-based nanofluid through an annulus within two concentric vertical pipes filled with a porous medium is investigated. This study considers the effects of thermal radiation, viscous dissipation, thermal buoyancy, and axial pressure gradient in addition to heat and mass transfer. Brownian motion and thermophoresis have been introduced through the Buongiorno model. The similarity solution was used to solve nonlinear ordinary differential equations. The Runge-Kutta-Fehlberg method is used to solve these equations with the related boundary conditions. The effects of pertinent parameters such as pressure gradient, thermal radiation, viscosity parameter, thermophoretic parameter, Brownian motion parameter, and Eckert number are investigated numerically. This study found that the Bejan number increases as the viscosity parameter increases and decreases as the other active parameters increase. As the radiation parameter, thermophoretic parameter, Brownian parameter, and Eckert number increase, the Nusselt number decreases. The total entropy generation rate is found to increase with the fluid viscosity rate, Grashof number, thermal Biot number, and variable pressure gradient. However, the Bejan number is found to decrease with these parameters, as well as the Prandtl number.

Keywords: nanofluid; concentric pipes; mixed convection; thermal radiation; porous medium; entropy analysis
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Watanabe T., Toya Y., Nakamura I., Development of free surface flow between concentric cylinders with vertical axes, Journal of Physics: Conference Series, 14: 9–19, 2005, doi: 10.1088/1742-6596/14/1/002.

Makinde O.D., Thermal analysis of a reactive generalized Couette flow of power law fluid between concentric cylindrical pipes, The European Physical Journal Plus, 129(2): 270 (9pages), 2014, doi: 10.1140/epjp/i2014-14270-4.

Lorenzini M., Daprà I., Scarpri G., Heat transfer for a Giesekus fluid in a rotating concentric annulus, Applied Thermal Engineering, 122: 118–125, 2017, doi: 10.1016/j.applthermaleng.2017.05.013.

Coelho P.M., Pinho F.T, A generalized Brinkman number for non-Newtonian duct flows, Journal of Non-Newtonian Fluid Mechanics, 156(3): 202–206, 2009, doi: 10.1016/j.jnnfm.2008.07.001.

Bejan A., Second-law analysis in heat transfer and thermal design, Advance in Heat Transfer, 15: 1–58, 1982, doi: 10.1016/S0065-2717(08)70172-2.

Makinde O.D., Eegunjobi A.S, Inherent irreversibility of mixed convection within concentric pipes in a porous medium with thermal radiation, Journal of Mathematical and Fundamental Sciences, 53(3): 395–414, 2021, doi: 10.5614/

Makinde O.D., Eegunjobi A.S., Entropy analysis of a variable viscosity MHD Couette flow between two concentric pipes with convective cooling, Engineering Transactions, 68(4): 317–334, 2020, doi: 10.24423/engtrans.1104.20200720.

Monaledi R.L, Makinde O.D., Entropy generation analysis in a microchannel Poiseuille flows of nanofuid with nanoparticles injection and variable properties, Journal of Thermal Analysis and Calorimetry, 143: 1855–1865, 2021, doi: 10.1007/s10973-020-09919-x.

Nayak M.K., Mabood F., Dogonchi A.S, Ramadan K.M., Tlili I., Khan W.A., Entropy optimized assisting and opposing nonlinear radiative flow of hybrid nanofluid, Waves in Random and Complex Media, 22 pages, 2022, doi: 10.1080/17455030.2022.2032474.

Mabood F., Farooq W., Abbasi A., Entropy generation analysis in the electro-osmosis-modulated peristaltic flow of Eyring-Powell fluid, Journal of Thermal Analysis and Calorimetry, 147(5): 3815–3830, 2022, doi: 10.1007/s10973-021-10736-z.

Shaw S., Mabood F., Muhammad T., Nayak M.K., Alghamdi M., Numerical simulation for entropy optimized nonlinear radiative flow of GO‐Al2O3 magneto nanomaterials with auto catalysis chemical reaction, Numerical Methods for Partial Differential Equations, 38(3): 329–358, 2022, doi: 10.1002/num.22623.

Mabood F., Fatunmbi E.O., Benos L., Sarris I.E., Entropy generation in the magnetohydrodynamic Jeffrey nanofluid flow over a stretching sheet with wide range of engineering application parameters, International Journal of Applied and Computational Mathematics, 8(3): 98, 2022, doi: 10.1007/s40819-022-01301-9.

Nayak M.K., Mabood F., Khan W.A., Makinde O.D., Cattaneo-Christov double diffusion on micropolar magneto cross nanofluids with entropy generation, Indian Journal Physics, 96(1): 193–208, 2022, doi: 10.1007/s12648-020-01973-3.

Shaw S., Chamkha A.J., Wakif A., Makinde O.D., Nayak M.K., Effects of Wu’s slip and non-uniform source/ sink on entropy optimized radiative magnetohydrodynamic up/down flow of nanofluids, Journal of Nanofluids, 11(3): 305–317, 2022, doi: 10.1166/jon.2022.1840.

Sathyanarayanan S.U.D, Mabood F., Jamshed W., Mishra S.R., Nisar K., Pattnaik P.K., Prakash M., Abdel-Aty A.H., Zakarya M., Irreversibility process characteristics of variant viscosity and conductivity on hybrid nanofluid flow through Poiseuille microchannel: A special case study, Case Studies in Thermal Engineering, 27: 101337, 2021, doi: 10.1016/j.csite.2021.101337.

Nayak M.K., Mabood F., Tlili I., Dogonchi A.S., Khan W.A., Entropy optimization analysis on nonlinear thermal radiative electromagnetic Darcy-Forchheimer flow of SWCNT/MWCNT nanomaterials, Applied Nanoscience, 11(2): 399–418, 2021, doi: 10.1007/s13204-020-01611-8.

Azam A., Mabood F., Xu T., Waly M., Tlili I., Entropy optimized radiative heat transportation in axisymmetric flow of Williamson nanofluid with activation energy, Results in Physics, 19: 103576, 2020, doi: 10.1016/j.rinp.2020.103576.

Berrehal H., Sowmya G., Makinde O.D., Shape effect of nanoparticles on MHD nanofluid flow over a stretching sheet in the presence of heat source/sink with entropy generation, International Journal of Numerical Methods for Heat & Fluid Flow, 32(5): 1643–1663, 2022, doi: 10.1108/HFF-03-2021-0225.

Nayak M.K., Shaw S., Khan M.I., Makinde O.D., Chu Y.M., Khan S.U., Interfacial layer and shape effects of modified Hamilton’s Crosser model in entropy optimized Darcy-Forchheimer flow, Alexandria Engineering Journal, 60(4): 4067–4083, 2021, doi: 10.1016/j.aej.2021.02.010.

Choi S.U.S., Eastman J.A., Enhancing thermal conductivity of fluids with nanoparticles, [in:] Developments and Applications of Non- Newtonian Flows, FED-V.231/MD, ASME, D.A. Siginer, H.P. Wang (Eds.), 66: 99–105, 1995.

Khan W.A., Pop I., Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, 53(11–12): 2477–2483, 2010, doi: 10.1016/j.ijheatmasstransfer.2010.01.032.

Shehzad S.A., Mabood F., Rauf A., Izadi M., Abbasi F.M., Rheological features of non-Newtonian nanofluids flows induced by stretchable rotating disk, Physica Scripta, 96(3): 035210, 2021, doi: 10.1088/1402-4896/abd652.

Ferdows M., Shamshuddin M.D., Salawu S.O., Zaimi K., Numerical simulation for the steady nanofluid boundary layer flow over a moving plate with suction and heat generation, SN Applied Sciences, 3(2): 1–11, 2021, doi: 10.1007/s42452-021-04224-0.

Mabood F., Muhammad T., Nayak M.K., Waqas H., Makinde O.D., EMHD flow of non-Newtonian nanofluids over thin needle with Robinson's condition and Arrhenius pre-exponential factor law, Physica Scripta, 95(11): 115219, 2020, doi: 10.1088/1402-4896/abc0c3.

Khan W.A., Makinde O.D., Khan Z.H., Non-aligned MHD stagnation point flow of variable viscosity nanofluids past a stretching sheet with radiative heat, International Journal of Heat and Mass Transfer, 96: 525–534, 2016, doi: 10.1016/j.ijheatmasstransfer.2016.01.052.

Ali A.O., Khamis S.A., Seif F.S., Makinde O.D., Entropy analysis of the unsteady Darcian nanofluid flow in a cylindrical pipe with a porous wall, International Journal of Ambient Energy, 43(1): 7321–7329, 2022, doi: 10.1080/01430750.2022.2063382.

Eegunjobi A.S., Makinde O.D., Entropy analysis in an unsteady MHD flow of a radiating fluid through a vertical channel filled with a porous medium, International Journal of Ambient Energy, 43(1): 6404–6416, 2022, doi: 10.1080/01430750.2021.2019112.

Rikitu B.H., Makinde O.D., Enyadene L.G., Modeling heat transfer enhancement of Ferrofluid (Fe3O4–H2O) flow in a microchannel filled with a porous medium, Journal of Nanofluids, 10(1): 31–44, 2021, doi: 10.1166/jon.2021.1764.

Abbasi A., Mabood F., Farooq W., Hussain Z., Non-orthogonal stagnation point flow of Maxwell nano-material over a stretching cylinder, International Communications in Heat and Mass Transfer, 120: 105043, 2021, doi: 10.1016/j.icheatmasstransfer.2020.105043.

Chakraborty S., Ray S., Performance optimisation of laminar fully developed flow through square ducts with rounded corners, International Journal of Thermal Sciences, 50(12): 2522–2535, 2011, doi: 10.1016/j.ijthermalsci.2011.06.006.

Lorenzini M., Suzzi N., The influence of geometry on the thermal performance of microchannels in laminar flow with viscous dissipation, Heat Transfer Engineering, 37(13/14): 1096–1104, 2016, doi: 10.1080/01457632.2015.1111100.

DOI: 10.24423/EngTrans.2249.20230601