Teodor Grosan, Flavius-Olimpiu Patrulescu and Ioan Pop
The purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate…
Abstract
Purpose
The purpose of this work is the study of the steady free convection in a square differentially heated cavity filled by a Brinkman bidisperse porous medium. An appropriate mathematical model considering the Brinkman, momentum and energy interphase terms is proposed. The dependence of the stream functions, isotherms and of the Nusselt numbers on the governing parameters is analysed.
Design/methodology/approach
The both phases of flow and heat transfer are solved numerically using a modified finite difference technique. The algebraic system obtained after discretization is solved using the SOR method. The results are found to be in a significant agreement with the ones presented by the literature for a Darcy bidisperse porous medium and a Brinkman monodisperse porous medium.
Findings
The effects of the governing parameters on stream functions, isotherms and Nusselt numbers are discussed. It has been found that in the case of the Brinkman bidisperse model, the Nusselt numbers decrease compared to the Darcy model, and this behaviour is significant in comparison to the Brinkman monodisperse case.
Originality/value
A mathematical model for the free convection inside a cavity filled by a non-Darcy bidisperse porous medium, based on the Brinkman equation, is used. The effect of Darcy number, Rayleigh number, modified inter-phase heat transfer parameter, modified thermal conductivity ratio and the inertial parameters is studied. To the best of the authors’ knowledge, this problem has not been studied before, and the results are new and original.
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Mikhail A. Sheremet, Teodor Grosan and Ioan Pop
The purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the single-phase…
Abstract
Purpose
The purpose of this paper is to study numerically the steady thermal convection in a chamber filled with a nanoliquid affected by a chemical reaction using the single-phase nanofluid approximation.
Design/methodology/approach
Water was considered as a host fluid while nanoparticles are aluminum oxide. Homogeneous reactions are analyzed. The nonlinear partial differential equations describing the considered problem are simulated using the finite difference technique.
Findings
The results of streamlines, isotherms, isoconcentrations, nanofluid flow rate, mean Nusselt and Sherwood numbers are discussed. The data demonstrate that the mean Sherwood number increases with the homogeneous reaction rate. Further, nanofluid flow rate can be increased with nanoparticles concentration for high Rayleigh numbers owing to the homogeneous chemical reaction inside the cavity.
Originality/value
Searching the existent references illustrates that the homogeneous-heterogeneous reactions influence on the nanoliquid motion and energy transport within enclosures has not been investigated before. The results of this paper are completely original and the numerical results of the present paper were never published by any researcher.
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Mikhail Sheremet, Teodor Grosan and Ioan Pop
This paper aims to study the magnetohydrodynamic (MHD)-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganism.
Abstract
Purpose
This paper aims to study the magnetohydrodynamic (MHD)-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganism.
Design/methodology/approach
The benefits of adding motile microorganisms to the suspension include enhanced mass transfer, microscale mixing and anticipated improved stability of the nanofluid. The model includes equations expressing conservation of total mass, momentum, thermal energy, nanoparticles, microorganisms and oxygen. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model.
Findings
It has been found that the Hartmann number suppresses the heat and mass transfer, while the cavity and magnetic field inclination angles characterize a non-monotonic behavior of the all considered parameters. A rise of the Hartmann number leads to a reduction of the influence rate of the magnetic field inclination angle.
Originality/value
The present results are original and new for the study of MHD-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganisms.
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Mikhail Sheremet, Teodor Grosan and Ioan Pop
The purpose of this paper is to study steady natural convection flow and heat transfer in a triangular cavity filled with a micropolar fluid.
Abstract
Purpose
The purpose of this paper is to study steady natural convection flow and heat transfer in a triangular cavity filled with a micropolar fluid.
Design/methodology/approach
It is assumed that the left inclined wall is heated, whereas the other walls are cooled and maintained at constant temperatures. All four walls of the cavity are assumed to be rigid and impermeable. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the finite difference method of the second order accuracy over a wide range of the Rayleigh number, Prandtl number, vortex viscosity parameter and two values of micro-gyration parameter, namely, strong concentration (n = 0) and week concentration (n = 0.5).
Findings
The results are presented in the form of streamlines, isotherms, vorticity contours and variations of average Nusselt number and fluid flow rate depending on the Rayleigh number, Prandtl number, vortex viscosity parameter and micro-gyration parameter. The flow field and temperature distribution in the cavity are affected by these parameters. The heat transfer rate into the cavity is decreasing upon the raise of the vortex viscosity parameter.
Originality/value
This work studies the effects of vortex viscosity parameter and micro-gyration parameter in a triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants; for the design of solar collectors, room ventilation systems and electronic cooling systems; and so on.
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Cornelia Revnic, Eiyad Abu-Nada, Teodor Grosan and Ioan Pop
This paper aims to develop a numerical study of the steady natural convection in a rectangular cavity filled with the CuO–water-based nanofluid. It is assumed that the viscosity…
Abstract
Purpose
This paper aims to develop a numerical study of the steady natural convection in a rectangular cavity filled with the CuO–water-based nanofluid. It is assumed that the viscosity of nanofluids depends on the temperature and on the nanofluids volume fraction.
Design/methodology/approach
The mathematical nanofluid model has been formulated on the basis of the model proposed by Buongiorno (2006). The system of partial differential equations is written in terms of a dimensionless stream function, vorticity, temperature and the volume fraction of the nanoparticles, and is solved numerically using the finite difference method for different values of the governing parameters.
Findings
It is found that both fluid flow and heat transfer coefficient are affected by the considered parameters. Thus, the Nusselt number is slowly increasing with increasing volume fraction from 2 per cent to 5 per cent and it is more pronounced increasing with increasing Rayleigh number from 103 to 105.
Originality/value
Buongiorno’s (2006) nanofluid model has been applied for the flow with the characteristics as mentioned in the paper. A comprehensive survey on the behavior of flow and heat transfer characteristics has been presented. All plots presented in the paper are new and are not reported in any other study.
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M M Rahman, Teodor Grosan and Ioan Pop
The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity…
Abstract
Purpose
The laminar two-dimensional stagnation-point flow and heat transfer of a viscous incompressible nanofluid obliquely impinging on a shrinking surface is formulated as a similarity solution of the Navier-Stokes, energy and concentration equations. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the dimensionless strain rate, shrinking parameter, Brownian motion parameter and thermophoresis parameter on the flow, temperature and nanoparticle volume fraction is investigated in details. The paper aims to discuss these issues.
Design/methodology/approach
The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 10−10.
Findings
It is found that dimensionless strain rate and shrinking parameter causes a shift in the position of the point of zero skin friction along the stretching sheet. Obliquity of the flow toward the surface increases as the strain rate intensifies. The results indicate that dual solutions exist for the opposing flow case.
Research limitations/implications
The problem is formulated for an incompressible nanofluid with no chemical reactions, dilute mixture, negligible viscous dissipation and negligible radiative heat transfer assuming nanoparticles and base fluid are locally in thermal equilibrium. Beyond the critical point λ c to obtain further solutions, the full basic partial differential equations have to be solved.
Originality/value
The present results are original and new for the oblique stagnation-point flow of a nanofluid past a shrinking sheet. Therefore, this study would be important for the researchers working in the relatively new area of nanofluids in order to become familiar with the flow behavior and properties of such nanofluids.
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Radu Trimbitas, Teodor Grosan and Ioan Pop
The purpose of this paper is to theoretically study the problem of mixed convection boundary layer flow and heat transfer past a vertical needle with variable wall temperature…
Abstract
Purpose
The purpose of this paper is to theoretically study the problem of mixed convection boundary layer flow and heat transfer past a vertical needle with variable wall temperature using nanofluids. The similarity equations are solved numerically for copper nanoparticles in the based fluid of water to investigate the effect of the solid volume fraction parameter of the fluid and heat transfer characteristics. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles and are graphically presented and discussed.
Design/methodology/approach
The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 1e-10. For the study of the stability the authors also used the bvp4c function in combination with chebfun package from Matlab.
Findings
It is found that the solid volume fraction affects the fluid flow and heat transfer characteristics. The numerical results for a regular fluid and forced convection flow are compared with the corresponding results reported by Chen and Smith. The solutions exists up to a critical value of λ, beyond which the boundary layer separates from the surface and the solution based upon the boundary-layer approximations is not possible
Originality/value
The paper describes how multiple (dual) solutions for the flow reversals are obtained. A stability analysis for this flow reversal has been also done showing that the lower solution branches are unstable, while the upper solution branches are stable.
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Natalia C. Roşca, Alin V. Roşca, Teodor Groşan and Ioan Pop
The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium…
Abstract
Purpose
The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium filled by a nanofluid. The non-Darcy equation model along with the mathematical nanofluid model proposed by Tiwari and Das (2007) has been used.
Design/methodology/approach
Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the nanoparticle volume fraction, the mixed convection and the non-Darcy parameters using the bvp4c function from Matlab. A stability analysis has been also performed.
Findings
Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the opposing flow case (λ<0). The stability analysis indicates that for the opposing flow case, the lower solution branch is unstable, while the upper solution branch is stable. In addition, it is shown that for a regular fluid (φ=0) a very good agreement exists between the present numerical results and those reported in the open literature.
Research limitations/implications
The problem is formulated for three types of nanoparticles, namely, copper (Cu), alumina (Al2O3) and titania (TiO2). However, the paper present results here only for the Cu nanoparticles. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved.
Practical implications
Nanofluids have many practical applications, for example, the production of nanostructured materials, engineering of complex fluids, for cleaning oil from surfaces due to their excellent wetting and spreading behavior, etc.
Social implications
Nanofluids could be applied to almost any disease treatment techniques by reengineering the nanoparticle properties.
Originality/value
The present results are original and new for the boundary-layer flow and heat transfer past a vertical flat plate embedded in a porous medium saturated by a nanofluid. Therefore, this study would be important for the researchers working in porous media in order to become familiar with the flow behavior and properties of such nanofluids.