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Heat Generation/Absorption Effects in a Boundary Layer Stretched Flow of Maxwell Nanofluid: Analytic and Numeric Solutions.

Awais M, Hayat T, Irum S, Alsaedi A - PLoS ONE (2015)

Bottom Line: Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations.Both numerical and analytic solutions are presented and found in nice agreement.Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Attock, 43600, Pakistan.

ABSTRACT
Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM) has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.

No MeSH data available.


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Stream lines for Maxwell model.
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pone.0129814.g004: Stream lines for Maxwell model.

Mentions: In this section we have prepared various plots and table to analyze different rheological aspects of the involved sundry parameters. Figs 3 and 4 presented the stream line behavior for the Newtonian and Maxwell fluid flow. It is observed that the stream line for Maxwell fluid are quite different as compared to the Newtonian fluid. Fig 5 presents the influence of the Deborah number β on the velocity profile f′. It is observed from this figure that Deborah number β retards the flow for the case of constant magnetic field. Basically Deborah number β defines the difference between the solid and liquids (or fluids). The material behaves like fluids for smaller Deborah number whereas for large value of Deborah number the material behaves like viscoelastic solids. This is quite obvious from the present analysis that velocity field shows declaration for larger Deborah number. The velocity profile and the boundary layer thickness monotonically decreases with an increase in η and finally approaches to zero when η−>η∞ (which for the present case equals to 6) representing the characteristics of the boundary layer flow. The influence of β on the temperature profile θ is shown in Fig 6. Since Deborah number β causes a reduction in the molecular movement which conclusively increases the temperature of the nanofluid as shown in the figure. The significant enhancement is noted in temperature profile θ when Nb and Nt are increases (Fig 7). Since an increase in the strength of Brownian motion process causes an effective movement of the nanoparticles which enhances the thermal conductivity of the fluid. Figs 8 and 9 elucidate that magnetic field M and Biot number γ (the conjugate parameter for convective cooling) enhance the temperature. The effects of heat source parameter (λ>0) and heat sink parameter (λ<0) on temperature profile θ are presented in Figs 10 and 11. It is noted from these plots that the temperature of the fluid increases with an increase in heat source whereas it decreases with an increase in heat sink parameter. It is also observed that the magnitude for the case of heat source parameter is larger when compared with the case when heat sink is present in the system. It is quite obvious because of the fact that nanoparticles has the property to enhance the temperature of the fluid and additionally when heat source is present into the system then the temperature is further increases as shown in Fig 10. Moreover we can also conclude that one can control the heat enhancement phenomenon can be controlled very efficiently by adding the heat sink into the system (Fig 11). Effects on Deborah number β on nanoparticle concentration ϕ are portrayed in Fig 12. It is seen that nanoparticle concentration increases due to an increase in β. Moreover the nanoparticle concentration boundary layer is also become thicker with an increase in β. Influences of magnetic field M, the Brownian motion parameter Nb and the thermophoresis parameter Nt on ϕ are shown in Figs 13 and 14. It is noted from these plots that ϕ increases with an increase in magnetic field M, the Brownian motion parameter Nb and the thermophoresis parameter Nt.


Heat Generation/Absorption Effects in a Boundary Layer Stretched Flow of Maxwell Nanofluid: Analytic and Numeric Solutions.

Awais M, Hayat T, Irum S, Alsaedi A - PLoS ONE (2015)

Stream lines for Maxwell model.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4482663&req=5

pone.0129814.g004: Stream lines for Maxwell model.
Mentions: In this section we have prepared various plots and table to analyze different rheological aspects of the involved sundry parameters. Figs 3 and 4 presented the stream line behavior for the Newtonian and Maxwell fluid flow. It is observed that the stream line for Maxwell fluid are quite different as compared to the Newtonian fluid. Fig 5 presents the influence of the Deborah number β on the velocity profile f′. It is observed from this figure that Deborah number β retards the flow for the case of constant magnetic field. Basically Deborah number β defines the difference between the solid and liquids (or fluids). The material behaves like fluids for smaller Deborah number whereas for large value of Deborah number the material behaves like viscoelastic solids. This is quite obvious from the present analysis that velocity field shows declaration for larger Deborah number. The velocity profile and the boundary layer thickness monotonically decreases with an increase in η and finally approaches to zero when η−>η∞ (which for the present case equals to 6) representing the characteristics of the boundary layer flow. The influence of β on the temperature profile θ is shown in Fig 6. Since Deborah number β causes a reduction in the molecular movement which conclusively increases the temperature of the nanofluid as shown in the figure. The significant enhancement is noted in temperature profile θ when Nb and Nt are increases (Fig 7). Since an increase in the strength of Brownian motion process causes an effective movement of the nanoparticles which enhances the thermal conductivity of the fluid. Figs 8 and 9 elucidate that magnetic field M and Biot number γ (the conjugate parameter for convective cooling) enhance the temperature. The effects of heat source parameter (λ>0) and heat sink parameter (λ<0) on temperature profile θ are presented in Figs 10 and 11. It is noted from these plots that the temperature of the fluid increases with an increase in heat source whereas it decreases with an increase in heat sink parameter. It is also observed that the magnitude for the case of heat source parameter is larger when compared with the case when heat sink is present in the system. It is quite obvious because of the fact that nanoparticles has the property to enhance the temperature of the fluid and additionally when heat source is present into the system then the temperature is further increases as shown in Fig 10. Moreover we can also conclude that one can control the heat enhancement phenomenon can be controlled very efficiently by adding the heat sink into the system (Fig 11). Effects on Deborah number β on nanoparticle concentration ϕ are portrayed in Fig 12. It is seen that nanoparticle concentration increases due to an increase in β. Moreover the nanoparticle concentration boundary layer is also become thicker with an increase in β. Influences of magnetic field M, the Brownian motion parameter Nb and the thermophoresis parameter Nt on ϕ are shown in Figs 13 and 14. It is noted from these plots that ϕ increases with an increase in magnetic field M, the Brownian motion parameter Nb and the thermophoresis parameter Nt.

Bottom Line: Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations.Both numerical and analytic solutions are presented and found in nice agreement.Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Attock, 43600, Pakistan.

ABSTRACT
Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM) has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.

No MeSH data available.


Related in: MedlinePlus