Abstract
The current exploration focuses on the ethylene glycol (EG) based nanoliquid flow in a microchannel. The effectiveness of the internal heat source and linear radiation is reflected in the present investigation. The estimation of suitable thermal conductivity model has affirmative impact on the convective heat transfer phenomenon. The examination is conceded with the nanoparticle aggregation demonstrated by the Maxwell-Bruggeman and Krieger-Dougherty models which tackle the formation of nanolayer. These models effectively describe the thermal conductivity and viscosity correspondingly. The dimensionless mathematical expressions are solved numerically by the Runge Kutta Fehlberg approach. A higher thermal field is attained for the Bruggeman model due to the formation of thermal bridge. A second law analysis is carried out to predict the sources of irreversibility associated with the thermal system. It is remarked that lesser entropy generation is obtained for the aggregation model. The entropy generation rate declines with the slip flow and the thermal heat flux. A notable enhancement in the Bejan number is attained by increasing the Biot number. It is established that the nanoparticle aggragation model exhibits a higher Bejan number in comparision with the usual flow model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- f :
-
axial velocity (m·s−1)
- y :
-
transversal coordinate (m)
- F(Y):
-
dimensionless velocity
- Y :
-
dimensionless transverse coordinate
- T :
-
temperature of fluid (K)
- T a :
-
ambient temperature (K)
- T h :
-
hot fluid temperature (K)
- θ(Y):
-
dimensionless temperature
- k* :
-
mean absorption coefficient (m−1)
- s 1 :
-
s2, slip lengths
- D :
-
fractal index
- k :
-
thermal conductivity (W·m−1·K−1)
- C p :
-
specific heat at constant pressure (J·kg−1·K−1)
- \(Re = {{{\nu_0}{\rho_{\rm{f}}}a} \over {{\mu_{\rm{f}}}}}\) :
-
Reynolds number
- \(B{i_i} = {{a{h_i}} \over {{k_{\rm{f}}}}},i = 1,2,\) :
-
Biot numbers
- \(Pr = {{{\nu_{\rm{f}}}} \over {{\alpha_{\rm{f}}}}},\) :
-
Prandtl number
- p :
-
modified pressure
- \(P = - {{{a^3}{\rho_{\rm{f}}}} \over {\mu_{\rm{f}}^2}}{{{\rm{d}}p} \over {{\rm{d}}x}},\) :
-
pressure gradient parameter
- \(Nr = {{16{\sigma ^*}T_{\rm{a}}^3} \over {3{{\rm{k}}^*}{k_{\rm{f}}}}},\) :
-
radiation parameter
- \(Ec = {{v_{\rm{f}}^2} \over {{a^2}{C_{p{\rm{f}}}}({T_{\rm{h}}} - {T_{\rm{a}}})}}\) :
-
Eckert number
- \(H = \frac{{Q_T^*{a^2}}}{{{k_f}}},\) :
-
heat source parameter
- S 1 :
-
{tiS}2, dimensionless slip parameters
- E G :
-
entropy generation rate
- [n]:
-
Einstein coefficient
- h1, h2 :
-
convective heat transfer coefficients
- ra, rp :
-
radii of aggregates and nanoparticle, respectively.
- β :
-
thermal expansion coefficient (K−1)
- ϕ m :
-
extreme volume fraction
- μ :
-
dynamic viscosity (kg-m−1·s−1)
- ρ :
-
fluid density (kg·m−3)
- σ* :
-
Stefan-Boltzmann constant (W·m−2·K−4)
- ϕ a :
-
effective volume fraction of aggregates
- ν 0 :
-
uniform suction/injection velocity
- ϕ :
-
solid volume fraction of nanoparticles.
- nf:
-
nanofluid
- s:
-
solid particle
- f:
-
fluid.
References
IJAM, A., SAIDUR, R., GANESAN, P., and GOLSHEIKH, A. M. Stability, thermo-physical properties, and electrical conductivity of graphene oxide-deionized water/ethylene glycol based nanofluid. International Journal of Heat and Mass Transfer, 87, 92–103 (2015)
SANDHYA, D., REDDY, M. C. S., and RAO, V. V. Improving the cooling performance of automobile radiator with ethylene glycol water based TiO2 nanofluids. International Communications in Heat and Mass Transfer, 78, 121–126 (2016)
CABALEIRO, D., COLLA, L., BARISON, S., LUGO, L., FEDELE, L., and BOBBO, S. Heat transfer capability of (ethylene glycol+water)-based nanofluids containing graphene nanoplatelets: design and thermophysical profile. Nanoscale Research Letters, 12, 53 (2017)
ZYLA, G. and FAL, J. Viscosity, thermal and electrical conductivity of silicon dioxide-ethylene glycol transparent nanofluids: an experimental study. Thermochimica Acta, 650, 106–113 (2017)
DOGONCHI, A. S. and HASHIM. Heat transfer by natural convection of Fe3O4-water nanofluid in an annulus between a wavy circular cylinder and a rhombus. International Journal of Heat and Mass Transfer, 130, 320–332 (2019)
DOGONCHI, A. S., WAQAS, M., SEYYEDI, S. M., TILEHNOEE, M. H., and GANJI, D. D. CVFEM analysis for Fe3O4-H2O nanofluid in an annulus subject to thermal radiation. International Journal of Heat and Mass Transfer, 132, 473–483 (2019)
HATAMI, M., KHEIRKHAH, A., RAD, H. G., and JING, D. Numerical heat transfer enhancement using different nanofluids flow through venturi and wavy tubes. Case Studies in Thermal Engineering, 13, 100368 (2019)
KARIMIPOUR, A., ORAZIO, A. D., and SHADLOO, M. The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump. Physica E: Low-Dimensional Systems and Nanostructures, 86, 146–153 (2017)
WANG, B. X., ZHOU, L. P., and PENG, X. F. A fractal model for predicting the effective thermal conductivity of liquid with suspension of nanoparticles. International Journal of Heat and Mass Transfer, 46, 2665–2672 (2003)
XIE, H., FUJII, M., and ZHANG, X. Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle-fluid mixture. International Journal of Heat and Mass Transfer, 48, 2926–2932 (2005)
PRASHER, R. Effect of aggregation kinetics on the thermal conductivity of nanoscale colloidal solutions (nanofluid). Nano Letters, 6(7), 1529–1534 (2006)
CHEN, H., DING, Y., HE, Y., and TAN, C. Rheological behaviour of ethylene glycol based titania nanofluids. Chemical Physics Letters, 444, 333–337 (2007)
ZHOU, D. and KELLER, A. A. Role of morphology in the aggregation kinetics of ZnO nanoparticles. Water Research, 44(9), 2948–2956 (2010)
HALELFADL, S., ESTELLÉ, P., ALADAG, B., DONER, N., and MARE, T. Viscosity of carbon nanotubes water-based nanofluids: influence of concentration and temperature. International Journal of Thermal Sciences, 71, 111–117 (2013)
SEDIGHI, M. and MOHEBBI, A. Investigation of nanoparticle aggregation effect on thermal properties of nanofluid by a combined equilibrium and non-equilibrium molecular dynamics simulation. Journal of Molecular Liquids, 197, 14–22 (2014)
HERIS, S. Z., RAZBANI, M. A., ESTELLÉ, P., and MAHIAN, O. Rheological behavior of zinc-oxide nanolubricants. Journal of Dispersion Science and Technology, 36(8), 1073–1079 (2015)
MOTEVASEL, M., NAZAR, A. R. S., and JAMIALAHMADI, M. The effect of nanoparticles aggregation on the thermal conductivity of nanofluids at very low concentrations: experimental and theoretical evaluations. Heat and Mass Transfer, 54, 125–133 (2018)
BENOS, L.T., KARVELAS, E. G., and SARRIS, I. E. Crucial effect of aggregations in CNT-water nanofluid magnetohydrodynamic natural convection. Thermal Science and Engineering Progress, 11, 263–271 (2019)
MACKOLIL, J. and MAHANTHESH, B. Sensitivity analysis of Marangoni convection in TiO2-EG nanoliquid with nanoparticle aggregation and temperature-dependent surface tension. Journal of Thermal Analysis and Calorimetry (2020) https://doi.org/10.1007/s10973-020-09642-7
MAKINDE, O. D. and EEGUNJOBI, A. S. Entropy generation in a couple stress fluid flow through a vertical channel filled with saturated porous media. Entropy, 15, 4589–4606 (2013)
MAHDAVI, M., AVVAL, M. S., TIARI, S., and MANSOORI, Z. Entropy generation and heat transfer numerical analysis in pipes partially filled with porous medium. International Journal of Heat and Mass Transfer, 79, 496–506 (2014)
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)
SHEREMET, M., POP, I., ÖZTOP, H. F., and HAMDEH, N. A. Natural convection of nanofluid inside a wavy cavity with a non-uniform heating: entropy generation analysis. International Journal of Numerical Methods for Heat and Fluid Flow, 27(4), 958–980 (2017)
TORABI, M., TORABI, M., GHIAASIAAN, S. M., and PETERSON, G. P. The effect of Al2O3-water nanofluid on the heat transfer and entropy generation of laminar forced convection through isotropic porous media. International Journal of Heat and Mass Transfer, 111, 804–816 (2017)
LIAKOPOULOS, A., SOFOS, F., and KARAKASIDIS, T. E. Darcy-Weisbach friction factor at the nanoscale: from atomistic calculations to continuum models. Physics of Fluids, 29(5), 052003 (2017)
MIAO, Q., YUAN, Q., and ZHAO, Y. P. Dissolutive flow in nanochannels: transition between pluglike and Poiseuille-like. Microfluidics and Nanofluidics, 22, 141 (2018)
IBANEZ, G., LOPEZ, A., LOPEZ, 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)
IBANEZ, G., LOPEZ, A., PANTOJA, J., and MOREIRA, J. Entropy generation analysis of a nanofluid flow in MHD porous microchannel with hydrodynamic slip and thermal radiation. International Journal of Heat and Mass Transfer, 100, 89–97 (2016)
KARIMIPOUR, A., D’ORAZIO, A., and SHADLOO, M. The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump. Physica E: Low-dimensional Systems and Nanostructures, 86, 146–153 (2017)
TLILI, I., HAMADNEH, N. N., KHAN, W. A., and ATAWNEH, S. Thermodynamic analysis of MHD Couette-Poiseuille flow of water based nanofluids in a rotating channel with radiation and Hall effects. Journal of Thermal Analysis and Calorimetry, 132(3), 1899–1912 (2018)
TOGHRAIE, D., MAHMOUDI, M., AKBARI, O. A., POURFATTAH, F., and HEYDARI, M. The effect of using water/CuO nanofluid and L-shaped porous ribs on the performance evaluation criterion of microchannels. Journal of Thermal Analysis and Calorimetry, 135(4), 145–159 (2018)
GIREESHA, B. J. and SINDHU, S. Entropy generation analysis of nanoliquid flow through microchannel considering heat source and different shapes of nanoparticle. International Journal of Numerical Methods for Heat and Fluid Flow, 30(3), 1457–1477 (2019)
SINDHU, S., GIREESHA, B. J., and SOWMYA, G. Entropy generation analysis of multi-walled carbon nanotube dispersed nanoliquid in the presence of heat source through a vertical microchannel. International Journal of Numerical Methods for Heat and Fluid Flow (2020) https://doi.org/10.1108/HFF-10-2019-0754
Acknowledgements
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed.
Author information
Authors and Affiliations
Corresponding author
Additional information
Citation: SINDHU, S. and GIREESHA, B. J. Flow of colloidal suspension and irreversibility analysis with aggregation kinematics of nanoparticles in a microchannel. Applied Mathematics and Mechanics, 41(11), 1671–1684 (English Edition) (2020) https://doi.org/10.1007/s10483-020-2669-9
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Sindhu, S., Gireesha, B.J. Flow of colloidal suspension and irreversibility analysis with aggregation kinematics of nanoparticles in a microchannel. Appl. Math. Mech.-Engl. Ed. 41, 1671–1684 (2020). https://doi.org/10.1007/s10483-020-2669-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-020-2669-9