Amplitude Equation and Heat Transport for Rayleigh–Bénard Convection in Newtonian Liquids with Nanoparticles

Siddheshwar, P. G.; Meenakshi, N.

doi:10.1007/s40819-015-0106-y

Cited by 50 publications

(23 citation statements)

References 30 publications

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“…Linear and weakly nonlinear stability analyses of Rayleigh-Bénard convection for free-free and rigid-rigid, isothermal boundaries using LTNE model is studied. The thermophysical properties of ethylene-glycol [17] as the base liquid, copper [17] as the nanoparticle and 30% glass fiber reinforced polycarbonate porous material [8] are considered. The thermophysical properties of porous material and ethylene-glycol copper saturated porous medium is calculated and the same is tabulated in Tables 1 and 2.…”

Section: Resultsmentioning

confidence: 99%

Study of Rayleigh–Bénard Convection of a Newtonian Nanoliquid in a High Porosity Medium Using Local Thermal Non-equilibrium Model

Siddheshwar

Sakshath

2019

Int. J. Appl. Comput. Math

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In the paper we make linear and non-linear stability analyses of Rayleigh-Bénard convection in a Newtonian, nanoliquid-saturated porous medium using local thermal non-equilibrium model (LTNE). The LTNE assumption results in advanced onset of convection and increase in heat transport when compared to that of local thermal equilibrium assumption. Freefree and rigid-rigid, isothermal boundaries are considered for investigation. The Galerkin method is used to obtain the critical eigen value. The influence of inter-phase heat transfer coefficient, ratio of thermal conductivities, Brinkman number, porous parameter on the onset of convection as well as on heat transport has been presented graphically and discussed in detail. The effect of increasing the value of porosity modified thermal conductivities advances the onset of convection and enhances the amount of heat transport whereas the remaining parameters have an opposing influence on both onset of convection as well as heat transport. Keywords Rayleigh-Bénard convection • Nanoliquid • Porous medium • LTNE • Free-free • Rigid-rigid • Linear • Non-linear List of Symbols A, B, C, D Amplitudes of convection C p Specific heat at constant pressure d Channel depth g Acceleration due to gravity h Inter-phase heat transfer coefficient H Dimensionless inter-phase heat transfer coefficient k Wavenumber in the x direction B P. G. Siddheshwar

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Section: Resultsmentioning

confidence: 99%

Study of Rayleigh–Bénard Convection of a Newtonian Nanoliquid in a High Porosity Medium Using Local Thermal Non-equilibrium Model

Siddheshwar

Sakshath

2019

Int. J. Appl. Comput. Math

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“…Typical values of the thermophysical properties of nanoliquids are documented in Table 3 that are calculated using values of thermophysical quantities of base liquids and nanoparticles extracted from the works of Ghasemi and Aminosadati [19], Siddheshwar and Meenakshi [20], Bergman et al [21], and the paper by Abu-Nada et al [22].…”

Section: Resultsmentioning

confidence: 99%

Steady Finite-Amplitude Rayleigh–Bénard Convection in Nanoliquids Using a Two-Phase Model: Theoretical Answer to the Phenomenon of Enhanced Heat Transfer

Siddheshwar

Kanchana

Kakimoto

et al. 2016

Journal of Heat Transfer

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Rayleigh-B enard convection in liquids with nanoparticles is studied in the paper considering a two-phase model for nanoliquids with thermophysical properties determined from phenomenological laws and mixture theory. In the absence of nanoparticle-modified thermophysical properties as used in the paper, the problem is essentially binary liquid convection with Soret effect. The base liquids chosen for investigation are water, ethylene glycol, engine oil, and glycerine, and the nanoparticles chosen are copper, copper oxide, silver, alumina, and titania. Using data on these 20 nanoliquids, our theoretical model clearly explains advanced onset of convection in nanoliquids in comparison with that in the base liquid without nanoparticles. The paper sets to rest the tentativeness regarding the boundary condition to be chosen in the study of Rayleigh-B enard convection in nanoliquids. The effect of thermophoresis is to destabilize the system and so is the effect of other parameters arising due to nanoparticles. However, Brownian motion effect does not have a say on onset of convection. In the case of nonlinear theory, the five-mode Lorenz model is derived under the assumptions of Boussinesq approximation and small-scale convective motions, and using it enhancement of heat transport due to the presence of nanoparticles is clearly explained for steady-state motions. Subcritical motion is shown to be possible in all 20 nanoliquids.

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“…It is also helpful to achieve the energy efficiency and the thermal comfort of buildings. Several numerical and experimental studies have been carried out on thermal comfort in the building [1][2][3].The lattice Boltzmann method (LBM) that has been rapidly progressing in developing new models and applications in many fields has attracted much attention and interest [4][5][6][7]. Unlike traditional methods which solve macroscopic equations, the LBM simulates fluid flow based on microscopic models or mesoscopic kinetic equations.…”

Section: Introductionmentioning

confidence: 99%

Study of thermal comfort: numerical simulation in a closed cavity using the lattice Boltzmann method

2020

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In this work, a study on thermal comfort in building is presented as it has great interest given its impact on the quality of indoor environments. The thermal comfort depends on several parameters such as air temperature and velocity, relative humidity and so on. With this in mind, numerical investigation is carried out on natural convection induced by temperature gradient between the lower and upper walls in a square enclosure filled with a Newtonian fluid. To approach the real case of underfloor heating subject to real weather conditions, periodic time varying temperature is imposed on the lower wall of the enclosure. The mathematical problem has been formulated by considering the Boussinesq's approximation, and the resulted governing equations are solved using the Lattice Boltzmann Method. The study has been carried out for Rayleigh numbers in the range 10 3 ≤ Ra ≤ 10 6 , while Prandtl number and aspect ratio are kept constant at 0.71 and 1, respectively. The results obtained show that the flow's behaviour is strongly dependent on the values of Rayleigh numbers and heating amplitude. The temporal evolution of the spatially averaged Nusselt number indicate that the transfer regime is periodic for low values of Ra and switches to a perturbed unsteady flow for hight values.

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Amplitude Equation and Heat Transport for Rayleigh–Bénard Convection in Newtonian Liquids with Nanoparticles

Cited by 50 publications

References 30 publications

Study of Rayleigh–Bénard Convection of a Newtonian Nanoliquid in a High Porosity Medium Using Local Thermal Non-equilibrium Model

Study of Rayleigh–Bénard Convection of a Newtonian Nanoliquid in a High Porosity Medium Using Local Thermal Non-equilibrium Model

Steady Finite-Amplitude Rayleigh–Bénard Convection in Nanoliquids Using a Two-Phase Model: Theoretical Answer to the Phenomenon of Enhanced Heat Transfer

Study of thermal comfort: numerical simulation in a closed cavity using the lattice Boltzmann method

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