Algebraic solutions of flow and heat for some nanofluids over deformable and permeable surfaces

2017 ◽  
Vol 27 (10) ◽  
pp. 2259-2267 ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Heat Transfer ◽  
Design Methodology ◽  
Temperature Jump ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Jump Conditions ◽  
Content Type ◽  
Layer Flow ◽  
Working Out ◽  
Algebraic Solutions

Purpose This paper aims to working out exact solutions for the boundary layer flow of some nanofluids over porous stretching/shrinking surfaces with different configurations. To serve to this aim, five types of nanoparticles together with the water as base fluid are under consideration, namely, Ag, Cu, CuO, Al2O3 and TiO2. Design/methodology/approach The physical flow is affected by the presence of velocity slip as well as temperature jump conditions. Findings The knowledge on the influences of nanoparticle volume fraction on the practically significant parameters, such as the skin friction and the rate of heat transfer, for the above considered nanofluids, is easy to gain from the extracted explicit formulas. Originality/value Particularly, formulas clearly point that the heat transfer rate is not only dependent on the thermal conductivity of the material but it also highly relies on the heat capacitance as well as the density of the nanofluid under consideration.

Investigation of Heat Transfer Over a Rotating Disk in Case of Temperature and Velocity Jump Conditions by Using Differential Transform Method

2010 ◽  
Author(s):  
A. Y. Gunes ◽  
G. Komurgoz ◽  
A. Arikoglu ◽  
I. Ozkol
Keyword(s):  
Heat Transfer ◽  
Knudsen Number ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Rotating Disk ◽  
Jump Conditions ◽  
Governing Equations ◽  
Transform Method ◽  
Differential Transform ◽  
Velocity Jump

The energy crisis in the last two decades has turned the attention of scientific and engineering communities to redesigned and developed heat-fluid interaction systems. All of the details in analyses are reconsidered to reduce energy consumption. The present work examines the effects of temperature and velocity jump conditions on heat transfer, fluid flow over a single rotating disk. The flow due to rotating disks is of great interest in thermal engineering as it appears in many industrial and engineering applications such as gas turbine engines and micropumps. The related equation of flow, which is nonlinear and coupled, and heat transfer governing equations are reduced to ordinary differential equations by applying the so-called classical approach which was first introduced by Von Karman. Instead of this approach, a pure numerical one, the recently developed popular semi numerical analytical technique differential transform method (DTM), with Benton transformation, is employed to solve the reduced governing equations under the assumptions of velocity-slip and temperature jump conditions on the disk surface. The solution is valid for continuum and slip-flow regime which has a Knudsen number smaller than 0.1. The results attained for various physical cases are interpreted by using non-dimensional parameters related to flow and temperature fields. Velocity and temperature profiles are presented graphically. The effect of various parameters such as the Knudsen Number (Kn), Reynolds Number (Re) and Nusselt Numbers (Nu) are examined. The observed physical consequences are the velocity slip and temperature jump at the wall becoming strongly dependant on the Knudsen number. It is also observed that the temperature jump and velocity jump conditions have nonlinear effects on slip; these effects are investigated with great details and presented graphically.

Mixed convection boundary layer flow along vertical thin needles in nanofluids

2014 ◽  
Vol 24 (3) ◽  
pp. 579-594 ◽  
Author(s):  
Radu Trimbitas ◽  
Teodor Grosan ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Heat Transfer Characteristics ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Convection Boundary ◽  
Layer Flow

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.

Natural convection in a rectangular cavity filled with nanofluids

2018 ◽  
Vol 28 (6) ◽  
pp. 1410-1432 ◽  
Author(s):  
Cornelia Revnic ◽  
Eiyad Abu-Nada ◽  
Teodor Grosan ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Design Methodology ◽  
Volume Fraction ◽  
Numerical Study ◽  
Rectangular Cavity ◽  
Heat Transfer Characteristics ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Comprehensive Survey

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.

Two-phase model for mixed convection and flow enhancement of a nanofluid in an inclined channel patterned with heated slip stripes

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Subhasree Dutta ◽  
Somnath Bhattacharyya ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Temperature Jump ◽  
Volume Fraction ◽  
Volume Flow Rate ◽  
Homogeneous Model ◽  
Jump Condition ◽  
Two Phase ◽  
Content Type ◽  
The Impact

Purpose The purpose of this study is to analyze the heat transfer and flow enhancement of an Al2O3-water nanofluid filling an inclined channel whose lower wall is embedded with periodically placed discrete hydrophobic heat sources. Formation of a thin depletion layer of low viscosity over each hydrophobic heated patch leads to the velocity slip and temperature jump condition at the interface of the hydrophobic patch. Design/methodology/approach The mixed convection of the nanofluid is analysed based on the two-phase non-homogeneous model. The governing equations are solved numerically through a control volume approach. A periodic boundary condition is adopted along the longitudinal direction of the modulated channel. A velocity slip and temperature jump condition are imposed along with the hydrophobic heated stripes. The paper has validated the present non-homogeneous model with existing experimental and numerical results for particular cases. The impact of temperature jump condition and slip velocity on the flow and thermal field of the nanofluid in mixed convection is analysed for a wide range of governing parameters, namely, Reynolds number (50 ≤ Re ≤ 150), Grashof number ( 103≤Gr≤5×104), nanoparticle bulk volume fraction ( 0.01≤φb≤0.05), nanoparticle diameter ( 30≤dp≤60) and the angle of inclination ( −60°≤σ≤60°). Findings The presence of the thin depletion layer above the heated stripes reduces the heat transfer and augments the volume flow rate. Consideration of the nanofluid as a coolant enhances the rate of heat transfer, as well as the entropy generation and friction factor compared to the clear fluid. However, the rate of increment in heat transfer suppresses by a significant margin of the loss due to enhanced entropy generation and friction factor. Heat transfer performance of the channel diminishes as the channel inclination angle with the horizontal is increased. The paper has also compared the non-homogeneous model with the corresponding homogeneous model. In the non-homogeneous formulation, the nanoparticle distribution is directly affected by the slip conditions by virtue of the no-normal flux of nanoparticles on the slip planes. For this, the slip stripes augment the impact of nanoparticle volume fraction compared to the no-slip case. Originality/value This paper finds that the periodically arranged hydrophobic heat sources on the lower wall of the channel create a significant augmentation in the volume flow rate, which may be crucial to augment the transport process in mini- or micro-channels. This type of configuration has not been addressed in the existing literature.

Thermal performance of optimum exponential fin profiles subjected to a temperature jump

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Heat Transfer ◽  
Design Methodology ◽  
Temperature Jump ◽  
Physical Parameters ◽  
Transfer Enhancement ◽  
Cross Sectional ◽  
Content Type ◽  
Fin Efficiency ◽  
Fin Thickness ◽  
Fin Length

Purpose This paper aims to seek purely analytical results relying on the physical parameters including the temperature jump parameter. Design/methodology/approach The exponential fin profiles and heat transfer enhancement influenced by a temperature jump at the base are the main targets of this paper. Findings The introduced temperature slip at the base penetrates through the surface of the fin and reorganizes the distribution of temperature all over the surface. The overall impact of the temperature jump on the fin efficiency is such that it acts to lower the fin efficiency. However, the efficiency of the exponential fin is increasing for growing shape exponential fins as compared to the rectangular and decaying ones. Hence, exponential fins amenable to certain temperature jump has significance in technological cooling processes. Finally, the optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed by means of optimizing the base heat transfer rate given a cross-sectional area. Originality/value Exact solutions are provided for optimum exponential type fins subjected to a temperature jump. The optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed.

Heat and mass transfer characteristics of MHD three-dimensional flow over a stretching sheet filled with water-based alumina nanofluid

2018 ◽  
Vol 28 (3) ◽  
pp. 532-546 ◽  
Author(s):  
P. Sudarsan A. Reddy ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Content Type ◽  
Transfer Rates ◽  
Alumina Nanofluid

Purpose This paper aims to understand the influence of velocity slip, nanoparticle volume fraction, chemical reaction and non-linear thermal radiation on MHD three-dimensional heat and mass transfer boundary layer flow over a stretching sheet filled with water-based alumina nanofluid. To get more meaningful results, the authors have taken nonlinear thermal radiation in the heat transfer process. Design/methodology/approach Suitable similarity variables are introduced to convert governing partial differential equations into the set of ordinary differential equations, and are solved numerically using a versatile, extensively validated finite element method with Galerkin’s weighted residual simulation. The velocity, temperature and concentration profiles of nanoparticles as well as skin friction coefficient, Nusselt number and Sherwood number for different non-dimensional parameters such as volume fraction, magnetic, radiation and velocity slip parameters as well as the Prandtl number are examined in detail, and are presented through plots and tables. Findings It is noticed that the rate of heat transfer enhances with higher values of nanoparticle volume fraction parameter. It is worth mentioning that the heat transfer rates improve as the values of increase. Increasing values of M, R, θw and β decelerates the thickness of the thermal boundary layer in the fluid regime. The heat transfer rates decelerate as the values of suction parameter increase. Originality/value The authors have written this paper based on the best of their knowledge on heat and mass transfer analysis of nanofluids. The information in this paper is new and not copied from any other sources.

Slip velocity and temperature jump of a non-Newtonian nanofluid, aqueous solution of carboxy-methyl cellulose/aluminum oxide nanoparticles, through a microtube

2019 ◽  
Vol 29 (5) ◽  
pp. 1606-1628 ◽  
Author(s):  
Marjan Goodarzi ◽  
Saeed Javid ◽  
Ali Sajadifar ◽  
Mehdi Nojoomizadeh ◽  
Seyed Hossein Motaharipour ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Aqueous Solution ◽  
Aluminum Oxide ◽  
Temperature Jump ◽  
Methyl Cellulose ◽  
Oxide Nanoparticles ◽  
Carboxy Methyl Cellulose ◽  
Aluminum Oxide Nanoparticles ◽  
Content Type ◽  
Carboxy Methyl

Purpose With respect to two new subjects, i.e. nanofluids and microchannels, in heat transfer systems and modern techniques used for building them, this paper aims to study on effect of using aluminum oxide nanoparticles in non-Newtonian fluid of aqueous solution of carboxy-methyl cellulose in microtube and through application of different slip coefficients to achieve various qualities on surface of microtube. Design/methodology/approach Simultaneously, the effect of presence of nanoparticles and phenomenon of slip and temperature jump has been explored in non-Newtonian nanofluid in this essay. The assumption of homogeneity of nanofluid and fixed temperature of wall in microtube has been used in modeling processes. Findings The results have been presented as diagrams of velocity, temperature and Nusselt Number and the investigations have indicated that addition of nanoparticles to the base fluid and increase in microtube slip coefficient might improve rate of heat transfer in microtube. Originality/value The flow of non-Newtonian nanofluid of aqueous solution of carboxy methyl cellulose-aluminum oxide has been determined in a microtube for the first time.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

2019 ◽  
Vol 29 (8) ◽  
pp. 2524-2544 ◽  
Author(s):  
Mikhail A. Sheremet ◽  
Ioan Pop ◽  
A. Cihat Baytas
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Good Control ◽  
Solid Matrix ◽  
Content Type ◽  
Practical Applications ◽  
Nanofluid Viscosity ◽  
Non Equilibrium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

Fluid flow and heat transfer of a stratified system during natural convection – influence of chamfered corners

2019 ◽  
Vol 29 (2) ◽  
pp. 470-486 ◽  
Author(s):  
Alireza Rahimi ◽  
Aravindhan Surendar ◽  
Aygul Z. Ibatova ◽  
Abbas Kasaeipoor ◽  
Emad Hasani Malekshah
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Natural Convection ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Three Dimensional ◽  
Immiscible Fluids ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose This paper aims to investigate the three-dimensional natural convection and entropy generation in the rectangular cuboid cavities included by chamfered triangular partition made by polypropylene. Design/methodology/approach The enclosure is filled by multi-walled carbon nanotubes (MWCNTs)-H2O nanofluid and air as two immiscible fluids. The finite volume approach is used for computation. The fluid flow and heat transfer are considered with combination of local entropy generation due to fluid friction and heat transfer. Moreover, a numerical method is developed based on three-dimensional solution of Navier–Stokes equations. Findings Effects of side ratio of triangular partitions (SR = 0.5, 1 and 2), Rayleigh number (103 < Ra < 105) and solid volume fraction (f = 0.002, 0.004 and 0.01 Vol.%) of nanofluid are investigated on both natural convection characteristic and volumetric entropy generation. The results show that the partitions can be a suitable method to control fluid flow and energy consumption, and three-dimensional solutions renders more accurate results. Originality/value The originality of this work is to study the three-dimensional natural convection and entropy generation of a stratified system.

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