Published 12 issues per year
ISSN Print: 1091-028X
ISSN Online: 1934-0508
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Vertical Free Convective Boundary-Layer Flow in a Porous Medium Using a Thermal Nonequilibrium Model
ABSTRACT
In this article we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng and Minkowycz (1977) vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behavior of the flow relatively close to the leading edge, where the boundary layer is comprised of two distinct asymptotic regions. The numerical simulation of the developing boundary-layer relies heavily on near-leading-edge analysis to provide suitable boundary conditions. At increasing distances from the leading edge the difference between the temperatures of the fluid and solid phases decreases to zero, which corresponds to thermal equilibrium between the phases; this is confirmed by an asymptotic analysis.
-
Khadrawi A. F., Tahat M. S., Al-Nimr M. A., Validation of the Thermal Equilibrium Assumption in Periodic Natural Convection in Porous Domains, International Journal of Thermophysics, 26, 5, 2005. Crossref
-
Malashetty M. S., Swamy Mahantesh, Kulkarni Sridhar, Thermal convection in a rotating porous layer using a thermal nonequilibrium model, Physics of Fluids, 19, 5, 2007. Crossref
-
Sharma Poonam, Mahajan Amit, Onset of Darcy–Brinkman double-diffusive convection in a magnetized ferrofluid layer using a thermal non-equilibrium model: a nonlinear stability analysis, Journal of Geophysics and Engineering, 7, 4, 2010. Crossref
-
Rees D. A. S., Nield D. A., Kuznetsov A. V., Vertical Free Convective Boundary-Layer Flow in a Bidisperse Porous Medium, Journal of Heat Transfer, 130, 9, 2008. Crossref
-
REES D. ANDREW S., BASSOM ANDREW P., SIDDHESHWAR PRADEEP G., Local thermal non-equilibrium effects arising from the injection of a hot fluid into a porous medium, Journal of Fluid Mechanics, 594, 2008. Crossref
-
Malashetty M. S., Heera Rajashekhar, The onset of double diffusive convection in a sparsely packed porous layer using a thermal non-equilibrium model, Acta Mechanica, 204, 1-2, 2009. Crossref
-
Lee Jinho, Shivakumara I. S., Ravisha M., Effect of Thermal Non-Equilibrium on Convective Instability in a Ferromagnetic Fluid-Saturated Porous Medium, Transport in Porous Media, 86, 1, 2011. Crossref
-
Nouri-Borujerdi Ali, Noghrehabadi Amin R., Rees D. Andrew S., The effect of local thermal non-equilibrium on conduction in porous channels with a uniform heat source, Transport in Porous Media, 69, 2, 2007. Crossref
-
Malashetty M. S., Shivakumara I. S., Kulkarni Sridhar, Swamy Mahantesh, Convective Instability of Oldroyd-B Fluid Saturated Porous Layer Heated from Below using a Thermal Non-equilibrium Model, Transport in Porous Media, 64, 1, 2006. Crossref
-
Kumari M., Pop I., Mixed Convection Boundary Layer Flow Past a Horizontal Circular Cylinder Embedded in a Bidisperse Porous Medium, Transport in Porous Media, 77, 2, 2009. Crossref
-
Bayta?? A.C., Thermal non-equilibrium natural convection in a square enclosure filled with a heat-generating solid phase, non-Darcy porous medium, International Journal of Energy Research, 27, 10, 2003. Crossref
-
Al-Sumaily Gazy F., Hussen Hasanen M., Thompson Mark C., Validation of thermal equilibrium assumption in free convection flow over a cylinder embedded in a packed bed, International Communications in Heat and Mass Transfer, 58, 2014. Crossref
-
REES D.A.S., POP I., LOCAL THERMAL NON-EQUILIBRIUM IN POROUS MEDIUM CONVECTION, in Transport Phenomena in Porous Media III, 2005. Crossref
-
Shivakumara I. S., Mamatha A. L., Ravisha M., Boundary and thermal non-equilibrium effects on the onset of Darcy–Brinkman convection in a porous layer, Journal of Engineering Mathematics, 67, 4, 2010. Crossref
-
Malashetty M.S., Swamy Mahantesh, Effect of rotation on the onset of thermal convection in a sparsely packed porous layer using a thermal non-equilibrium model, International Journal of Heat and Mass Transfer, 53, 15-16, 2010. Crossref
-
Nazari Mohsen, Shakerinejad Esmaeel, Nazari Morteza, Rees D. Andrew S., Natural Convection Induced by a Heated Vertical Plate Embedded in a Porous Medium with Transpiration: Local Thermal Non-equilibrium Similarity Solutions, Transport in Porous Media, 98, 1, 2013. Crossref
-
Gao Dongyan, Chen Zhenqian, Chen Linghai, A thermal lattice Boltzmann model for natural convection in porous media under local thermal non-equilibrium conditions, International Journal of Heat and Mass Transfer, 70, 2014. Crossref
-
Baytas A.Cihat, Pop Ioan, Free convection in a square porous cavity using a thermal nonequilibrium model, International Journal of Thermal Sciences, 41, 9, 2002. Crossref
-
Haddad O.M., Al-Nimr M.A., Al-Khateeb A.N., Validation of the local thermal equilibrium assumption in natural convection from a vertical plate embedded in porous medium: non-Darcian model, International Journal of Heat and Mass Transfer, 47, 8-9, 2004. Crossref
-
Malashetty M.S., Shivakumara I.S., Kulkarni Sridhar, The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model, Physics Letters A, 373, 7, 2009. Crossref
-
Cheng Ching-Yang, A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model, International Communications in Heat and Mass Transfer, 34, 5, 2007. Crossref
-
Malashetty M.S., Shivakumara I.S., Kulkarni Sridhar, The onset of Lapwood–Brinkman convection using a thermal non-equilibrium model, International Journal of Heat and Mass Transfer, 48, 6, 2005. Crossref
-
Wong W.Sam, Rees D.Andrew S., Pop Ioan, Forced convection past a heated cylinder in a porous medium using a thermal nonequilibrium model: Finite Péclet number effects, International Journal of Thermal Sciences, 43, 3, 2004. Crossref
-
Sheu Long-Jye, An autonomous system for chaotic convection in a porous medium using a thermal non-equilibrium model, Chaos, Solitons & Fractals, 30, 3, 2006. Crossref
-
Muthtamilselvan M., Prakash D., Doh Deog-Hee, Effect of thermal non-equilibrium on transient hydromagnetic flow over a moving surface in a nanofluid saturated porous media, Journal of Mechanical Science and Technology, 28, 9, 2014. Crossref
-
Cheng Ching-Yang, Free Convection Heat Transfer From A Sphere In A Porous Medium Using A Thermal Non-equilibrium Model, Transport in Porous Media, 98, 1, 2013. Crossref
-
Rees D.Andrew S., Bassom Andrew P., Pop Ioan, Forced convection past a heated cylinder in a porous medium using a thermal nonequilibrium model: boundary layer analysis, European Journal of Mechanics - B/Fluids, 22, 5, 2003. Crossref
-
Cheng Ching-Yang, Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium, International Communications in Heat and Mass Transfer, 43, 2013. Crossref
-
Miansari Mehdi, Gorji M, Ganji D. D., Hooman Kamel, Comparison between continuum and porous continuum models in studying natural convection in porous cavity with random distribution of solid obstacles, International Journal of Numerical Methods for Heat & Fluid Flow, 25, 3, 2015. Crossref
-
Banu Nurzahan, Rees D.A.S., Onset of Darcy–Bénard convection using a thermal non-equilibrium model, International Journal of Heat and Mass Transfer, 45, 11, 2002. Crossref
-
Celli M., Rees D.A.S., Barletta A., The effect of local thermal non-equilibrium on forced convection boundary layer flow from a heated surface in porous media, International Journal of Heat and Mass Transfer, 53, 17-18, 2010. Crossref
-
Postelnicu Adrian, The onset of a Darcy–Brinkman convection using a thermal nonequilibrium model. Part II, International Journal of Thermal Sciences, 47, 12, 2008. Crossref
-
Bera P., Pippal Sarita, Sharma Abhishek K., A thermal non-equilibrium approach on double-diffusive natural convection in a square porous-medium cavity, International Journal of Heat and Mass Transfer, 78, 2014. Crossref
-
Nield D.A., Kuznetsov A.V., Natural convection about a vertical plate embedded in a bidisperse porous medium, International Journal of Heat and Mass Transfer, 51, 7-8, 2008. Crossref
-
Pippal Sarita, Bera P., A thermal non-equilibrium approach for 2D natural convection due to lateral heat flux: Square as well as slender enclosure, International Journal of Heat and Mass Transfer, 56, 1-2, 2013. Crossref
-
Bibliography, in Convective Heat Transfer, 2001. Crossref
-
Nield D.A., Kuznetsov A.V., The Cheng–Minkowycz problem for natural convection about a vertical plate embedded in a tridisperse porous medium, International Journal of Heat and Mass Transfer, 54, 15-16, 2011. Crossref
-
Malashetty M.S., Swamy Mahantesh, Heera Rajashekhar, Double diffusive convection in a porous layer using a thermal non-equilibrium model, International Journal of Thermal Sciences, 47, 9, 2008. Crossref
-
Kumar Anoj, Bhadauria B. S., Double diffusive convection in a porous layer saturated with viscoelastic fluid using a thermal non-equilibrium model, Physics of Fluids, 23, 5, 2011. Crossref
-
Shivakumara I S, Malashetty M S, Chavaraddi K B, Onset of convection in a viscoelastic-fluid-saturated sparselypacked porous layer using a thermal nonequilibrium model, Canadian Journal of Physics, 84, 11, 2006. Crossref
-
Al-Sumaily Gazy F., Nakayama Akira, Sheridan John, Thompson Mark C., The effect of porous media particle size on forced convection from a circular cylinder without assuming local thermal equilibrium between phases, International Journal of Heat and Mass Transfer, 55, 13-14, 2012. Crossref
-
Saeid Nawaf H., Analysis of free convection about a horizontal cylinder in a porous media using a thermal non-equilibrium model, International Communications in Heat and Mass Transfer, 33, 2, 2006. Crossref
-
Shivakumara I. S., Lee Jinho, Mamatha A. L., Ravisha M., Boundary and thermal non-equilibrium effects on convective instability in an anisotropic porous layer, Journal of Mechanical Science and Technology, 25, 4, 2011. Crossref
-
Khan W. A., Pop I., Heat Transfer Near Stretching Surface in Porous Medium Using Thermal Nonequilibrium Model, Journal of Thermophysics and Heat Transfer, 26, 4, 2012. Crossref
-
Goldstein R.J., Eckert E.R.G., Ibele W.E., Patankar S.V., Simon T.W., Kuehn T.H., Strykowski P.J., Tamma K.K., Bar-Cohen A., Heberlein J.V.R., Davidson J.H., Bischof J., Kulacki F.A., Kortshagen U., Garrick S., Heat transfer – a review of 2000 literature, International Journal of Heat and Mass Transfer, 45, 14, 2002. Crossref
-
Malashetty M.S., Kulkarni Sridhar, The convective instability of Maxwell fluid-saturated porous layer using a thermal non-equilibrium model, Journal of Non-Newtonian Fluid Mechanics, 162, 1-3, 2009. Crossref
-
Khan W. A., Pop I., Heat Transfer Near Stretching Surface in Porous Medium Using Thermal Nonequilibrium Model, Journal of Thermophysics and Heat Transfer, 26, 4, 2012. Crossref
-
Anjum Badruddin Irfan, Zainal Z.A., Aswatha Narayana P.A., Seetharamu K.N., Thermal non-equilibrium modeling of heat transfer through vertical annulus embedded with porous medium, International Journal of Heat and Mass Transfer, 49, 25-26, 2006. Crossref
-
Nield Donald A., Bejan Adrian, External Natural Convection, in Convection in Porous Media, 2017. Crossref
-
Shahmardan M. M., Nazari M., Samani A. A., NOVEL SIMILARITY-SOLUTION WHICH IS APPLICABLE FOR FREE CONVECTION OVER A BODY OF ARBITRARY SHAPE: THERMAL NON-EQUILIBRIUM IN A POROUS MEDIUM, Brazilian Journal of Chemical Engineering, 32, 1, 2015. Crossref
-
Saravanan S., Brinda R.K., Thermal nonequilibrium porous convection in a heat generating medium, International Journal of Mechanical Sciences, 135, 2018. Crossref
-
Sakamoto Hitoshi, Kulacki Francis A., Prior Research, in Buoyancy-Driven Flow in Fluid-Saturated Porous Media near a Bounding Surface, 2018. Crossref
-
Al-Sumaily Gazy F., Forced Convection Heat Transfer From a Bank of Circular Cylinders Embedded in a Porous Medium, Journal of Heat Transfer, 136, 4, 2014. Crossref
-
Sunil , Choudhary Shalu, Mahajan Amit, Stability analysis of a couple-stress fluid saturating a porous medium with temperature and pressure dependent viscosity using a thermal non-equilibrium model, Applied Mathematics and Computation, 340, 2019. Crossref
-
Hoghoughi Gholamreza, Izadi Mohsen, Oztop Hakan F., Abu-Hamdeh Nidal, Effect of geometrical parameters on natural convection in a porous undulant-wall enclosure saturated by a nanofluid using Buongiorno's model, Journal of Molecular Liquids, 255, 2018. Crossref
-
Prakash D., Muthtamilselvan M., Niu Xiao-Dong, Unsteady MHD Non-Darcian Flow Over a Vertical Stretching Plate Embedded in a Porous Medium with Thermal Non-Equilibrium Model, Advances in Applied Mathematics and Mechanics, 8, 1, 2016. Crossref
-
Nield Donald A., Bejan Adrian, External Natural Convection, in Convection in Porous Media, 2013. Crossref
-
Bai X., Nakayama A., A local thermal non-equilibrium integral analysis for forced convective thermal boundary development in a channel filled with a fluid-saturated porous medium, International Journal of Heat and Mass Transfer, 142, 2019. Crossref
-
Malashetty M. S., Shivakumara I. S., Kulkarni Sridhar, The Onset of Convection in an Anisotropic Porous Layer Using a Thermal Non-Equilibrium Model, Transport in Porous Media, 60, 2, 2005. Crossref
-
Rosali Haliza, Ishak Anuar, Pop Ioan, Mixed Convection Boundary Layer Flow Near the Lower Stagnation Point of a Cylinder Embedded in a Porous Medium Using a Thermal Nonequilibrium Model, Journal of Heat Transfer, 138, 8, 2016. Crossref
-
Rees D. Andrew S., Vortex instability from a near–vertical heated surface in a porous medium. I Linear instability, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 457, 2011, 2001. Crossref
-
Ando Kenji, Kuwahara Fujio, Yang Chen, Nakayama Akira, A Local Thermal Non-Equilibrium Analysis of Forced Convective Heat Transfer in a Metal Foam Filled Channel, KAGAKU KOGAKU RONBUNSHU, 39, 2, 2013. Crossref
-
Kudenatti Ramesh B., Gogate S. Shashi Prabha , Two-Phase Microscopic Heat Transfer Model for Three-Dimensional Stagnation Boundary-Layer Flow in a Porous Medium, Journal of Heat Transfer, 142, 2, 2020. Crossref
-
Sheremet Mikhail A., Pop Ioan, Baytas A. Cihat, Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium, International Journal of Numerical Methods for Heat & Fluid Flow, 29, 8, 2019. Crossref
-
Retraction: Ahmed, A. et al. Dual Solutions in a Boundary Layer Flow of a Power Law Fluid over a Moving Permeable Flat Plate with Thermal Radiation, Viscous Dissipation, and Heat Generation/Absorption. Fluids 2018, 3, 6, doi:10.3390/fluids3010006, Fluids, 4, 3, 2019. Crossref
-
Bidin Biliana, Rees D. Andrew S., Pattern selection for Darcy-Bénard convection with local thermal nonequilibrium, International Journal of Heat and Mass Transfer, 153, 2020. Crossref
-
Bai Xiaohui, Yi Yuan, Kuwahara Fujio, Nakayama Akira, A Unified Treatment for Local Thermal Nonequilibrium Free, Forced, and Mixed Convective Boundary Layer Flows Over an Arbitrarily Shaped Nonisothermal Body in a Fluid Saturated Porous Medium, Journal of Heat Transfer, 142, 6, 2020. Crossref
-
Yi Yuan, Kuwahara Fujio, Bai Xiaohui, Nakayama Akira, Similarity Solutions for Local Thermal Non-equilibrium Boundary-Layer Flows in a Fluid-Saturated Porous Medium, Transport in Porous Media, 134, 1, 2020. Crossref
-
S. Shashi Prabha Gogate, M. C. Bharathi, Kudenatti Ramesh B., Linear Stability on the Local Thermal Nonequilibrium Model of Mixed Convection Boundary Layer Flow over a Moving Wedge in a Porous Medium: Viscous Dissipation and Radiation Effects, Journal of Heat Transfer, 143, 4, 2021. Crossref
-
Pan Zhigang, Jia Lan, Mao Yiqiu, Wang Quan, Transitions and bifurcations in couple stress fluid saturated porous media using a thermal non-equilibrium model, Applied Mathematics and Computation, 415, 2022. Crossref
-
Krishnan Shankar, Murthy Jayathi Y., Garimella Suresh V., A Two-Temperature Model for the Analysis of Passive Thermal Control Systems, Journal of Heat Transfer, 126, 4, 2004. Crossref
-
Zhang Wenhao, Yi Yuan, Bai Xiaohui, Nakayama Akira, A local thermal non-equilibrium analysis for convective and radiative heat transfer in gaseous transpiration cooling through a porous wall, International Journal of Heat and Mass Transfer, 162, 2020. Crossref
-
Sheremet Mikhail A., Pop Ioan, Effect of local heater size and position on natural convection in a tilted nanofluid porous cavity using LTNE and Buongiorno's models, Journal of Molecular Liquids, 266, 2018. Crossref
-
Gupta Nitish , Bhargavi D. , NUMERICAL INVESTIGATION OF HEAT TRANSFER IN A DEVELOPING THERMAL FIELD IN THE POROUS-FILLED DUCT UNDER LOCAL THERMAL NONEQUILIBRIUM: CONSTANT WALL HEAT FLUX , Special Topics & Reviews in Porous Media: An International Journal, 13, 5, 2022. Crossref