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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.


Related in: MedlinePlus

Comparison of analytic (solid line) and numeric (dots) solutions for temperature.
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pone.0129814.g002: Comparison of analytic (solid line) and numeric (dots) solutions for temperature.

Mentions: It is noted that to solve the above system of equations as an initial value problem, we require the values f″(0), θ1(0) and φ1(0) whereas no such values are given initially. In order to find these values we initially selected an initial guesses and then applied the fourth-order Runge-Kutta method to approximate the values upto the desired accuracy of 10−5. Figs 1 and 2 are prepared to show a comparison between the numeric and HAM solution. It is evident from these plots that both the solutions are in a nice agreement with each other. An abstract computer code “S1 File” for the Shooting method with Runge-Kutta fourth order algorithm is also presented for the young researchers to excel in the numerical computations.


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)

Comparison of analytic (solid line) and numeric (dots) solutions for temperature.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0129814.g002: Comparison of analytic (solid line) and numeric (dots) solutions for temperature.
Mentions: It is noted that to solve the above system of equations as an initial value problem, we require the values f″(0), θ1(0) and φ1(0) whereas no such values are given initially. In order to find these values we initially selected an initial guesses and then applied the fourth-order Runge-Kutta method to approximate the values upto the desired accuracy of 10−5. Figs 1 and 2 are prepared to show a comparison between the numeric and HAM solution. It is evident from these plots that both the solutions are in a nice agreement with each other. An abstract computer code “S1 File” for the Shooting method with Runge-Kutta fourth order algorithm is also presented for the young researchers to excel in the numerical computations.

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