The Thermal Performance Analysis of an Al2O3-Water Nanofluid Flow in a Composite Microchannel
Abstract
:1. Introduction
2. Problem Formulation
2.1. Problem Formulation
2.2. Problem Formulation
2.3. Analytical Solution
2.3.1. Temperature
2.3.2. Dimensional Temperature Variation with x and y
2.4. Problem Formulation
2.5. Verification of Results
3. Results and Discussion
3.1. Velcoity Profile
3.2. Temperature Profile
3.3. Nusselt Number
3.4. Microchannel Partially Filled with Porous Medium
3.4.1. Heat Transfer Coefficient
3.4.2. Temperature Field in a Microchannel
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A
References
- Bejan, A. Convection in Porous Media; Springer: Berlin/Heidelberg, Germany, 2006; ISBN 9780387290966. [Google Scholar]
- Vafai, K. Handbook of Porous Media, 3rd ed.; CRC Press: Boca Raton, FL, USA, 2015; ISBN 9781439885574. [Google Scholar]
- Mohamad, A.A. Heat Transfer Enhancements in Heat Exchangers Fitted with Porous Media. Part I: Constant Wall Temperature. Int. J. Therm. Sci. 2003, 42, 385–395. [Google Scholar] [CrossRef]
- Mahmoudi, Y.; Maerefat, M. Analytical Investigation of Heat Transfer Enhancement in a Channel Partially Filled with a Porous Material under Local Thermal Non-Equilibrium Condition. Int. J. Therm. Sci. 2011, 50, 2386–2401. [Google Scholar] [CrossRef]
- Vafai, K.; Thiyagaraja, R. Analysis of Flow and Heat Transfer at the Interface Region of a Porous Medium. Int. J. Heat Mass Transf. 1987, 30, 1391–1405. [Google Scholar] [CrossRef]
- Kiwan, S.; Khodier, M. Natural Convection Heat Transfer in an Open-Ended Inclined Channel-Partially Filled with Porous Media. Heat Transf. Eng. 2008, 29, 67–75. [Google Scholar] [CrossRef]
- Yang, K.; Wang, Y.; Mao, Y.; Zhang, W. Heat and Moisture Transfer in a Rectangular Cavity Partially Filled with Hygroscopic Porous Media. Heat Transf. Eng. 2020, 41, 814–824. [Google Scholar] [CrossRef]
- Beavers, G.S.; Joseph, D.D. Boundary Conditions at a Natural Permeable Wall. J. Fluid Mech. 1967, 30, 197–207. [Google Scholar] [CrossRef]
- Jang, J.Y.; Chen, J.L. Forced Convection in a Parallel Plate Channel Partially with a High Porosity Porous Medium. Int. Comm. Heat Mass Trasnf. 1992, 19, 263–273. [Google Scholar] [CrossRef]
- Kuznetsov, A.V. Analytical Investigation of Couette Flow in a Composite Channel Partially Filled with a Porous Medium and Partially with a Clear Fluid. Int. J. Heat Mass Transf. 1998, 41, 2556–2560. [Google Scholar] [CrossRef]
- Ochoa-Tapia, J.A.; Whitaker, S. Momentum Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid-I. Theoretical Development. Int. J. Heat Mass Transf. 1995, 38, 2635–2646. [Google Scholar] [CrossRef]
- Cekmer, O.; Mobedi, M.; Ozerdem, B.; Pop, I. Fully Developed Forced Convection in a Parallel Plate Channel with a Centered Porous Layer. Transp. Porous Media 2012, 93, 179–201. [Google Scholar] [CrossRef]
- Ucar, E.; Mobedi, M.; Pop, I. Effect of an Inserted Porous Layer Located at a Wall of a Parallel Plate Channel on Forced Convection Heat Transfer. Transp. Porous Media 2013, 98, 35–57. [Google Scholar] [CrossRef] [Green Version]
- Maerefat, M.; Mahmoudi, S.Y.; Mazaheri, K. Numerical Simulation of Forced Convection Enhancement in a Pipe by Porous Inserts. Heat Transf. Eng. 2011, 32, 45–56. [Google Scholar] [CrossRef]
- Guo, Z.; Kim, S.Y.; Sung, H.J. Pulsating Flow and Heat Transfer in a Pipe Partially Filled with a Porous Medium. Int. J. Heat Mass Transf. 1997, 40, 4209–4218. [Google Scholar] [CrossRef]
- Amiri, A.; Vafai, K.; Kuzay, T.M. Effects of Boundary Conditions on Non-Darcian Heat Transfer through Porous Media and Experimental Comparisons. Numer. Heat Transf. Part A Appl. 1995, 27, 651–664. [Google Scholar] [CrossRef]
- Ochoa-Tapia, J.A.; Whitaker, S. Heat Transfer at the Boundary between a Porous Medium and a Homogeneous Fluid: The One-Equation Model. J. Porous Media 1998, 1, 31–46. [Google Scholar] [CrossRef]
- Alazmi, B.; Vafai, K. Analysis of Fluid Flow and Heat Transfer Interfacial Conditions between a Porous Medium and a Fluid Layer. Int. J. Heat Mass Transf. 2001, 44, 1735–1749. [Google Scholar] [CrossRef]
- Yang, K.; Vafai, K. Analysis of Temperature Gradient Bifurcation in Porous Media—An Exact Solution. Int. J. Heat Mass Transf. 2010, 53, 4316–4325. [Google Scholar] [CrossRef]
- Yang, K.; Vafai, K. Restrictions on the Validity of the Thermal Conditions at the Porous-Fluid Interface—An Exact Solution. J. Heat Transf. 2011, 133, 112601. [Google Scholar] [CrossRef] [Green Version]
- Yang, K.; Vafai, K. Analysis of Heat Flux Bifurcation inside Porous Media Incorporating Inertial and Dispersion Effects—An Exact Solution. Int. J. Heat Mass Transf. 2011, 54, 5286–5297. [Google Scholar] [CrossRef]
- Xu, H.J.; Qu, Z.G.; Tao, W.Q. Analytical Solution of Forced Convective Heat Transfer in Tubes Partially Filled with Metallic Foam Using the Two-Equation Model. Int. J. Heat Mass Transf. 2011, 54, 3846–3855. [Google Scholar] [CrossRef]
- Yang, C.; Nakayama, A.; Liu, W. Heat Transfer Performance Assessment for Forced Convection in a Tube Partially Filled with a Porous Medium. Int. J. Therm. Sci. 2012, 54, 98–108. [Google Scholar] [CrossRef]
- Mahmoudi, Y.; Karimi, N.; Mazaheri, K. Analytical Investigation of Heat Transfer Enhancement in a Channel Partially Filled with a Porous Material under Local Thermal Non-Equilibrium Condition: Effects of Different Thermal Boundary Conditions at the Porous-Fluid Interface. Int. J. Heat Mass Transf. 2014, 70, 875–891. [Google Scholar] [CrossRef] [Green Version]
- Mahmoudi, Y.; Karimi, N. Numerical Investigation of Heat Transfer Enhancement in a Pipe Partially Filled with a Porous Material under Local Thermal Non-Equilibrium Condition. Int. J. Heat Mass Transf. 2014, 68, 161–173. [Google Scholar] [CrossRef] [Green Version]
- Li, Q.; Hu, P. Analytical Solutions of Fluid Flow and Heat Transfer in a Partial Porous Channel with Stress Jump and Continuity Interface Conditions Using LTNE Model. Int. J. Heat Mass Transf. 2019, 128, 1280–1295. [Google Scholar] [CrossRef]
- Xu, H.J.; Qu, Z.G.; Lu, T.J.; He, Y.L.; Tao, W.Q. Thermal Modeling of Forced Convection in a Parallel-Plate Channel Partially Filled with Metallic Foams. J. Heat Transfer 2011, 133, 20–22. [Google Scholar] [CrossRef]
- Qu, Z.G.; Xu, H.J.; Tao, W.Q. Fully Developed Forced Convective Heat Transfer in an Annulus Partially Filled with Metallic Foams: An Analytical Solution. Int. J. Heat Mass Transf. 2012, 55, 7508–7519. [Google Scholar] [CrossRef]
- Torabi, M.; Karimi, N.; Zhang, K. Heat Transfer and Second Law Analyses of Forced Convection in a Channel Partially Filled by Porous Media and Featuring Internal Heat Sources. Energy 2015, 93, 106–127. [Google Scholar] [CrossRef] [Green Version]
- Lu, W.; Zhang, T.; Yang, M. Analytical Solution of Forced Convective Heat Transfer in Parallel-Plate Channel Partially Filled with Metallic Foams. Int. J. Heat Mass Transf. 2016, 100, 718–727. [Google Scholar] [CrossRef]
- Yang, K.; Chen, H.; Wang, J. Analysis of Heat Transfer and Entropy Generation in a Channel Partially Filled with N-Layer Porous Media. J. Heat Transf. 2018, 140, 082601. [Google Scholar] [CrossRef]
- Karimi, N.; Agbo, D.; Khan, A.T.; Younger, P.L. On the Effects of Exothermicity and Endothermicity upon the Temperature Fields in a Partially-Filled Porous Channel. Int. J. Therm. Sci. 2015, 96, 128–148. [Google Scholar] [CrossRef]
- Torabi, M.; Zhang, K.; Yang, G.; Wang, J.; Wu, P. Heat Transfer and Entropy Generation Analyses in a Channel Partially Filled with Porous Media Using Local Thermal Non-Equilibrium Model. Energy 2015, 82, 922–938. [Google Scholar] [CrossRef]
- Baig, M.F.; Chen, G.M.; Tso, C.P. Viscous Dissipative Forced Convection in a Channel Partially Filled with Porous Medium. J. Thermophys. Heat Transf. 2021, 36, 276–290. [Google Scholar] [CrossRef]
- Dehghan, M. Effects of Heat Generations on the Thermal Response of Channels Partially Filled with Non-Darcian Porous Materials. Transp. Porous Media 2015, 110, 461–482. [Google Scholar] [CrossRef]
- Hunt, G.; Karimi, N.; Torabi, M. Analytical Investigation of Heat Transfer and Classical Entropy Generation in Microreactors—The Influences of Exothermicity and Asymmetry. Appl. Therm. Eng. 2017, 119, 403–424. [Google Scholar] [CrossRef]
- Bhargavi, D.; Reddy, J.S.K. Analytical Investigation of Laminar Forced Convection with Viscous Dissipation in Parallel Plate Channels Partially Filled with Porous Material: Constant Wall Heat Flux. J. Nanofluids 2019, 8, 238–251. [Google Scholar] [CrossRef]
- Hu, P.; Li, Q. Effect of Heat Source on Forced Convection in a Partially-Filled Porous Channel under LTNE Condition. Int. Commun. Heat Mass Transf. 2020, 114, 104578. [Google Scholar] [CrossRef]
- Al-Hadhrami, A.K.; Elliott, L.; Ingham, D.B. A New Model for Viscous Dissipation in Porous Media across a Range of Permeability Values. Transp. Porous Media 2003, 53, 117–122. [Google Scholar] [CrossRef]
- Chen, G.M.; Tso, C.P. Forced Convection with Viscous Dissipation Using a Two-Equation Model in a Channel Filled by a Porous Medium. Int. J. Heat Mass Transf. 2011, 54, 1791–1804. [Google Scholar] [CrossRef]
- Chen, G.M.; Tso, C.P. A Two-Equation Model for Thermally Developing Forced Convection in Porous Medium with Viscous Dissipation. Int. J. Heat Mass Transf. 2011, 54, 5406–5414. [Google Scholar] [CrossRef]
- Ting, T.W.; Hung, Y.M.; Guo, N. Viscous Dissipative Forced Convection in Thermal Non-Equilibrium Nanofluid-Saturated Porous Media Embedded in Microchannels. Int. Commun. Heat Mass Transf. 2014, 57, 309–318. [Google Scholar] [CrossRef]
- Farrukh B, M.; Chen, G.M.; Tso, C.P. Viscous Dissipation Effect on CuO-Water Nanofluid-Cooled Microchannel Heat Sinks. Case Stud. Therm. Eng. 2021, 26, 101159. [Google Scholar] [CrossRef]
Thickness of | [40] | [41] | |||||
---|---|---|---|---|---|---|---|
1 | 0 | 0.01 | 100 | 10 | 4.122 | 4.117 | - |
1 | 0 | 1 | 0.01 | 1 | 123.9 | - | 123.9 |
1 | 0 | 1 | 100 | 5.901 | - | 5.901 | |
1 | 0 | 1 | 100 | 1 | 4.171 | - | 4.171 |
1 | 1 | 0.01 | 100 | 10 | 0.2444 | 0.2439 | - |
1 | 1 | 10 | 0.01 | 1 | 132.4 | - | 132.4 |
1 | 1 | 1 | 0.01 | 1 | 49.33 | - | 49.33 |
1 | 1 | 1 | 100 | 1 | 1.622 | - | 1.622 |
1 | 1 | 1 | 0.01 | 0.01 | 143.3 | - | 143.3 |
1 | 10 | 0.01 | 100 | 10 | 0.0258 | 0.0257 | - |
1 | 10 | 1 | 0.01 | 0.01 | 122.6 | - | 122.6 |
1 | 10 | 1 | 0.01 | 0.04 | 85.37 | - | 85.37 |
10 | 1.6450 | 0.16855 | −3.3145 | 0.09494 | |
20 | −3.43828 | 0.17674 | −10.326 | 0.10406 | |
10 | −2.9101 | 0.62406 | −5.9737 | 0.36085 | |
20 | −7.5618 | 0.58943 | −12.987 | 0.37010 |
Nanofluid | Al2O3-Water |
---|---|
Solid | Silicon |
Length of the channel, (m) | 0.03 |
Channel height, | 50 |
Heat flux, (W/m2) | 1 104 |
Thermal conductivity of solid, (W/m·K) | 148 |
Porosity, | 0.9 |
Darcy number, | 0.1 |
Biot number, | 0.01 |
Properties | Nanoparticle (Al2O3) | Base Fluid (Water) |
---|---|---|
(kg/m3) | 3975 | 997 |
(J/kg·K) | 778.6 | 4179 |
(W/m·K) | 36 | 0.613 |
(N·s/m2) | - | 10−4 |
Working Fluid | at | |||
---|---|---|---|---|
Water | 25 | 0 | 116,191 | 0.10 |
0.006 | 116,086 | |||
4% volume fraction Al2O3-Water nanofluid | 0 | 132,800 | 2.44 | |
0.064 | 129,550 | |||
Water | 50 | 0 | 116,191 | 0.36 |
0.025 | 115,773 | |||
4% volume fraction Al2O3-Water nanofluid | 0 | 132,800 | 5.62 | |
0.255 | 125,054 |
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Baig, M.F.; Chen, G.M.; Tso, C.P. The Thermal Performance Analysis of an Al2O3-Water Nanofluid Flow in a Composite Microchannel. Nanomaterials 2022, 12, 3821. https://doi.org/10.3390/nano12213821
Baig MF, Chen GM, Tso CP. The Thermal Performance Analysis of an Al2O3-Water Nanofluid Flow in a Composite Microchannel. Nanomaterials. 2022; 12(21):3821. https://doi.org/10.3390/nano12213821
Chicago/Turabian StyleBaig, Mirza Farrukh, Gooi Mee Chen, and Chih Ping Tso. 2022. "The Thermal Performance Analysis of an Al2O3-Water Nanofluid Flow in a Composite Microchannel" Nanomaterials 12, no. 21: 3821. https://doi.org/10.3390/nano12213821