An analytical heat transfer assessment and modeling in a natural convection between two infinite vertical parallel flat plates

Etbaeitabari, Amir; Barakat, Mohammad; Imani, Ali; Domairry, G.; Jalili, Payam

doi:10.1016/j.molliq.2013.09.010

Cited by 29 publications

(18 citation statements)

References 14 publications

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“…The system of coupled non-linear ordinary differential equations (6 and 7) with boundary conditions (equation (8)) are solved for the flow velocity and temperature using the FDM. The following linearized form should be applied because of nonlinearity in this system…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The natural convection of non-Newtonian fluids has been studied by many authors. [1][2][3][4][5][6][7][8][9][10][11] The natural convection problem between vertical flat plates for a certain class of non-Newtonian fluids has been carried out by Bruce and Na. 1 Rajagopal and Na 2 introduced a numerical solution for natural convection flow of Rivlin-Ericksen fluid and heat transfer between parallel plates.…”

Section: Introductionmentioning

confidence: 99%

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Natural convection flow of Rivlin–Ericksen fluid and heat transfer through non-Darcy medium with radiation

Ewis

2019

Advances in Mechanical Engineering

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The natural convection of non-Newtonian fluids between parallel plates has many engineering applications such as heat exchangers, cooling of electronic equipments, nuclear reactors, solar devices, polymer processing industries, food industries, and petroleum reservoirs. Numerical solution is introduced to solve the governing equations of natural convection of non-Newtonian (Rivlin–Ericksen) fluid flow and heat transfer under the influences of non-Darcy resistance force, constant pressure gradient, dissipation, and radiation. The novelty of this article is to solve this problem between parallel plates channel instead of one plate. The fluid flows between two heated parallel plates that are kept at constant temperatures. Second-order accurate finite difference schemes transform the coupled non-linear differential (momentum and energy) equations to linearized system of algebraic equations. Some comparisons are made to study the convergence and stability of the present results. Effects of parameters of fluid and heat on the velocity field, temperature, skin friction factor, and Nusselt number are illustrated and discussed. The present results and their comparisons with available results are listed and shown in tables and figures. The present results show that the numerical solution is of good agreement with previous analytical and numerical solutions.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Natural convection flow of Rivlin–Ericksen fluid and heat transfer through non-Darcy medium with radiation

Ewis

2019

Advances in Mechanical Engineering

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“…This interest can be attributed due to its wide range of applications in chemical catalytic reactors, fiber and granular insulation, packed beds, geothermal systems, petroleum reservoirs, heat exchangers and nuclear waste repositories (see for example [14][15][16][17] and the references therein). Also, a very common industrial application of natural convection is free air cooling without the aid of fans such as cooling towers and computer chips [15,16]. The flow of Newtonian and non-Newtonian fluids through two infinite parallel vertical plates has been studied by several researchers.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, Etbaeitabari et al [15] applied the reconstruction of variational iteration method for computing the natural convection of an incompressible fluid between two infinite parallel vertical plates. Ziabakhsh and Domairy [21] solved the same problem by homotopy analysis method.…”

Section: Introductionmentioning

confidence: 99%

Sinc-collocation method for solving sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates

Saadatmandi

Shateri

2019

J Braz. Soc. Mech. Sci. Eng.

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This paper seeks to develop an efficient method for solving natural convection of a non-Newtonian nanofluid flow between two vertical flat plates. Sodium alginate is considered as the non-Newtonian fluid, and then two distinct types of nanoparticles, namely silver and copper, are added to it. To do so, the governing boundary layer and temperature equations are reduced to a set of ordinary differential equations. This approach is based on a global collocation method using Sinc basis functions, and the resulting set of ordinary differential equations are replaced by a system of algebraic equations. It is well known that the Sinc procedure converges to the solution at an exponential rate. Numerical results are included to demonstrate the validity and applicability of the method, and a comparison is made with the existing results. Also, the effect of various parameters such as Prandtl number (Pr), dimensionless non-Newtonian viscosity number () and nanoparticle volume fraction () on non-dimensional velocity and temperature profiles are discussed. It was concluded from this study that velocity and temperature increased with increasing Pr. Moreover, our results indicate that both the velocity and temperature decrease as increases. Finally, the results demonstrated that, when increases, the velocity increases but the temperature values decrease. Keywords Natural convection • Sinc-collocation • Non-Newtonian fluid • Nanoparticles List of symbols 2b Distance between the plates (m) C p Specific heat at constant pressure (J kg K −1) Ec Eckert number k Thermal conductivity (W m −1 K −1) Pr Prandtl number T Temperature (K) Greek symbols Dynamic viscosity (N s m −2) Density (kg m −3) Dimensionless temperature Solid volume fraction Dimensionless non-Newtonian viscosity Subscripts f Pure fluid s Nanoparticle nf Nanofluid

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“…It is worth mentioning that the aforementioned methods offer accurate successive approximations for solution of ODEs. Etbaeitabari and Domairy (Etbaeitabari et al, 2013) employed VIM to evaluate the natural convection of a non-Newtonian fluid streaming between two infinite vertical plates (Etbaeitabari et al, 2013). Ziabakhsh and Domairy (Ziabakhsh and Domairry, 2009) analytically investigated the natural convection of a non-Newtonian fluid between two infinite parallel vertical flat plates considering the nature of the fluid.…”

Section: Introductionmentioning

confidence: 99%

Natural Convection of Third Grade Non-Newtonian Fluid Flow in a Changeable Semi-permeable Medium Considering the Effects of Variable Heat Source and Magnetic Field

Maghsoudi

Sadeghi

Rasam

et al. 2018

European Journal of Sustainable Development Research

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The main purpose of this paper is to conduct momentum and energy analysis on non-Newtonian fluid flow in a semi-permeable medium between two infinite vertical flat plates considering the influences of medium porosity, heat source and magnetic field. In this study, porosity, heat source and magnetic field terms are considered to be variable. Initially, partial differential equations of momentum and energy are derived and turned into ordinary differential equations utilizing a similarity solution. Afterwards, a system of differential equations is solved by Least Square Method (LSM) and subsequently reliable functions are proposed for temperature and velocity distributions. To assess the precision of this method, the equations are also solved by a numerical method and an analytical approach known as Galerkin Method (GM). Regarding the comparisons, it can be implied that when the values of magnetic field, heat source and porosity are constant along the channel width, both LSM and GM methods are efficient and appropriate agreement is observed between the results. However, for the case in which these parameters linearly vary along the channel width, Galerkin approach shows more accurate results. Ultimately, the influences of Hartman number, porosity and heat source parameters on the velocity and temperature distributions are discussed.

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An analytical heat transfer assessment and modeling in a natural convection between two infinite vertical parallel flat plates

Cited by 29 publications

References 14 publications

Natural convection flow of Rivlin–Ericksen fluid and heat transfer through non-Darcy medium with radiation

Natural convection flow of Rivlin–Ericksen fluid and heat transfer through non-Darcy medium with radiation

Sinc-collocation method for solving sodium alginate (SA) non-Newtonian nanofluid flow between two vertical flat plates

Natural Convection of Third Grade Non-Newtonian Fluid Flow in a Changeable Semi-permeable Medium Considering the Effects of Variable Heat Source and Magnetic Field

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