scholarly journals Boundary Layer Flow and Heat Transfer of Al2O3-TiO2/Water Hybrid Nanofluid over a Permeable Moving Plate

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1064
Author(s):  
Nur Adilah Liyana Aladdin ◽  
Norfifah Bachok
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Opposite Direction ◽  
Free Stream ◽  
Nonlinear Partial Differential Equation ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Moving Plate ◽  
Heat Transfer Efficiency ◽  
Layer Flow

Hybrid nanofluid is considered a new type of nanofluid and is further used to increase the heat transfer efficiency. This paper explores the two-dimensional steady axisymmetric boundary layer which contains water (base fluid) and two different nanoparticles to form a hybrid nanofluid over a permeable moving plate. The plate is suspected to move to the free stream in the similar or opposite direction. Similarity transformation is introduced in order to convert the nonlinear partial differential equation of the governing equation into a system of ordinary differential equations (ODEs). Then, the ODEs are solved using bvp4c in MATLAB 2019a software. The mathematical hybrid nanofluid and boundary conditions under the effect of suction, S, and the concentration of nanoparticles, ϕ 1 (Al2O3) and ϕ 2 (TiO2) are taken into account. Numerical results are graphically described for the skin friction coefficient, C f , and local Nusselt number, N u x , as well as velocity and temperature profiles. The results showed that duality occurs when the plate and the free stream travel in the opposite direction. The range of dual solutions expand widely for S and closely reduce for ϕ . Thus, a stability analysis is performed. The first solution is stable and realizable compared to the second solution. The C f and N u x increase with the increment of S. It is also noted that the increase of ϕ 2 leads to an increase in C f and decrease in N u x .

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat Transfer and Mean Profile Development, Part I—Experimental Data

1983 ◽  
Vol 105 (1) ◽  
pp. 33-40 ◽  
Author(s):  
M. F. Blair
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Full Range ◽  
Stream Velocity ◽  
Free Stream Turbulence ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

An experimental research program was conducted to determine the influence of free-stream turbulence on zero pressure gradient, fully turbulent boundary layer flow. Connective heat transfer coefficients and boundary layer mean velocity and temperature profile data were obtained for a constant free-stream velocity of 30 m/s and free-stream turbulence intensities ranging from approximately 1/4 to 7 percent. Free-stream multicomponent turbulence intensity, longitudinal integral scale, and spectral distributions were obtained for the full range of turbulence levels. The test results with 1/4 percent free-stream turbulence indicate that these data were in excellent agreement with classic two-dimensional, low free-stream turbulence, turbulent boundary layer correlations. For fully turbulent boundary layer flow, both the skin friction and heat transfer were found to be substantially increased (up to ∼ 20 percent) for the higher levels of free-stream turbulence. Detailed results of the experimental study are presented in the present paper (Part I). A comprehensive analysis is provided in a companion paper (Part II).

Boundary-layer flow of a micropolar fluid on a continuous flatplate moving in a parallel stream with uniform surface heat flux

2007 ◽  
Vol 85 (8) ◽  
pp. 869-878 ◽  
Author(s):  
A Ishak ◽  
R Nazar ◽  
I Pop
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Boundary Layer Flow ◽  
Surface Heat Flux ◽  
Micropolar Fluid ◽  
Free Stream ◽  
Velocity Ratio ◽  
Skin Friction Coefficient ◽  
Surface Heat ◽  
Layer Flow

The laminar boundary-layer flow of a micropolar fluid on a fixed or continuously moving flat plate with uniform surface heat flux is investigated. The plate is assumed to move in the same oropposite direction to the free stream. The resulting system of nonlinear ordinary differential equations is solved numerically using the Keller-box method. Numerical results are obtained for the skin-friction coefficient and the local Nusselt number as well as the velocity, microrotation, and temperature profiles for some values of the governing parameters, namely, the velocity ratio parameter, material parameter, and Prandtl number. The results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.PACS No.: 47.15.Cb

scholarly journals Boundary Layer Flow and Heat Transfer with Variable Fluid Properties on a Moving Flat Plate in a Parallel Free Stream

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Norfifah Bachok ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Fluid Viscosity ◽  
Flow And Heat Transfer ◽  
Variable Fluid Properties ◽  
Fluid Properties ◽  
Layer Flow

The steady boundary layer flow and heat transfer of a viscous fluid on a moving flat plate in a parallel free stream with variable fluid properties are studied. Two special cases, namely, constant fluid properties and variable fluid viscosity, are considered. The transformed boundary layer equations are solved numerically by a finite-difference scheme known as Keller-box method. Numerical results for the flow and the thermal fields for both cases are obtained for various values of the free stream parameter and the Prandtl number. It is found that dual solutions exist for both cases when the fluid and the plate move in the opposite directions. Moreover, fluid with constant properties shows drag reduction characteristics compared to fluid with variable viscosity.

scholarly journals Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

2021 ◽  
Vol 50 (12) ◽  
pp. 3753-3764
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Theoretical Investigations ◽  
Suitable Form ◽  
Layer Flow

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

scholarly journals Inherent irreversibility impacts on thermal boundary layer flow over a mobile plate with convective surface boundary conditions

2019 ◽  
Vol 5 (2) ◽  
pp. 45
Author(s):  
Sajjad Haider ◽  
Adnan Saeed Butt ◽  
Asif Ali ◽  
Yun-Zhang Li ◽  
Tufail Hussain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Profile ◽  
Entropy Generation ◽  
Free Stream ◽  
Entropy Generation Rate ◽  
Surface Boundary ◽  
Entropy Generation Number ◽  
Surface Boundary Conditions ◽  
Layer Flow

<p class="abstract"><strong>Background:</strong> The irreversibility impacts on flow and heat transfer processes can be quantified through entropy analysis. It is a significant tool which can be utilized to deduce about the energy losses. The current study investigates the inherent irreversibility impacts during a flow of boundary layer and heat transfer on a mobile plate.</p><p class="abstract"><strong>Methods:</strong> The flow is examined under thermal radiation and convective heat conditions. The fundamental governing equations of flow and heat phenomenon are transmuted into ordinary differential equations by employing similarity transmutations and shooting technique is utilized in order to solve the resultant equations. The temperature and velocity profiles are acquired to reckon Bejan and entropy generation number. Pertinent results are elucidated graphically for the movement of plate and flow in same and opposite directions.  </p><p class="abstract"><strong>Results:</strong> A decline in temperature profile is noted with rise in values of <em>Pr</em> in both cases when the movement of surface and free stream is in similar and converse directions. A decrease in temperature is observed for both cases with increase in <em>N<sub>R</sub></em> while with the rise in Biot number <em>a</em>, the temperature profile also increases. Entropy generation rate near the surface is high in case when surface and free stream are moving in opposite directions as compared to case when they move in same directions.</p><p class="abstract"><strong>Conclusions:</strong> It is observed that irreversibility impacts are more remarkable when the movement of fluid and plate is in opposite direction. Moreover, irreversibility impacts of heat transfer are prominent in free stream region.</p><p class="abstract"> </p><br /><em></em>

scholarly journals Comparison of k-ε Models in Predicting Heat Transfer and Skin Friction Under High Free Stream Turbulence

1996 ◽  
Author(s):  
Ganesh R. Iyer ◽  
Savash Yavuzkurt
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Skin Friction Coefficient ◽  
Empirical Correlations ◽  
Free Stream Turbulence ◽  
Boundary Layer Equations

Calculations of the effects of high free stream turbulence (FST) on heat transfer and skin friction in a flat plate turbulent boundary layer using different k-ε models (Launder-Sharma, K-Y Chien, Lam-Bremhorsi and Jones-Launder) are presented. This study was carried out in order to investigate the prediction capabilities of these models under high FST conditions. In doing so, TEXSTAN, a partial differential equation solver which is based on the ideas of Patankar and Spalding and solves steady-flow boundary layer equations, was used. Firstly, these models were compared as to how they predicted very low FST (≤ 1% turbulence intensity) cases. These baseline cases were tested by comparing predictions with both experimental data and empirical correlations. Then, these models were used in order to determine the effect of high FST (>5% turbulence intensity) on heat transfer and skin friction and compared with experimental data. Predictions for heat transfer and skin friction coefficient for all the turbulence intensities tested by all the models agreed well (within 1–8%) with experimental data. However, all these models predicted poorly the dissipation of turbulent kinetic energy (TKE) in the free stream and TKE profiles. Physical reasoning as to why the aforementioned models differ in their predictions and the probable cause of poor prediction of free-stream TKE and TKE profiles are given.

Heat Transfer Measurements and Calculations in Transitionally Rough Flow

1991 ◽  
Vol 113 (3) ◽  
pp. 404-411 ◽  
Author(s):  
M. H. Hosni ◽  
H. W. Coleman ◽  
R. P. Taylor
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Rough Surface ◽  
Element Model ◽  
Discrete Element ◽  
Skin Friction Coefficient ◽  
Stanton Number ◽  
Transfer Model ◽  
Layer Flow ◽  
Prediction Approach

Experimental data on a rough surface for both transitionally rough and fully rough turbulent flow regimes are presented for Stanton number distribution, skin friction coefficient distribution, and turbulence intensity profiles. The rough surface is composed of 1.27-mm-dia hemispheres spaced in a staggered array four base diameters apart on an otherwise smooth wall. Special emphasis is placed on the characteristics of heat transfer in the transitionally rough flows. Stanton number data are reported for zero pressure gradient incompressible turbulent boundary layer air flow for nominal free-stream velocities of 6, 12, 28, 43, 58, and 67 m/s, which give x-Reynolds numbers up to 10,000,000. These data are compared with previously published rough surface data, and the classification of a boundary layer flow into transitionally rough and fully rough regimes is explored. Moreover, a new heat transfer model for use in the previously published discrete element prediction approach is presented. Computations using the discrete element model are presented and compared with data obtained from two different rough surfaces. The discrete element predictions for both surfaces are found to be in substantial agreement with the data.

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