Flow and Heat Transfer Over a Stretched Microsurface

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Suhil Kiwan ◽  
M. A. Al-Nimr
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Flat Plate ◽  
Skin Friction ◽  
Convection Heat Transfer ◽  
Skin Friction Coefficient ◽  
Slip Parameter ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer

The convection heat transfer induced by a stretching flat plate has been studied. Similarity conditions are obtained for the boundary layer equations for a flat plate subjected to a power law temperature and velocity variations. It is found that a similarity solution exists only for a linearly stretching plate and only when the plate is isothermal. The analysis shows that three parameters control the flow and heat transfer characteristics of the problem. These parameters are the velocity slip parameter K1, the temperature slip parameter K2, and the Prandtl number. The effect of these parameters on the flow and heat transfer of the problem has been studied and presented. It is found that the slip velocity parameter affect both the flow and heat transfer characteristics of the problem. It is found that the skin friction coefficient decreases with increasing K1 and most of the changes in the skin friction takes place in the range 0<K1<1. A correlation between the skin friction coefficient and K1 and Rex has been found and presented. It is found that cf=23Rex−0.5(K1+0.64)−0.884 for 0<K1<10 with an error of ±0.8%. Other correlations between Nu and K1 and K2 has been found and presented in Eq. 28.

scholarly journals Turbulent flow and heat transfer characteristics in U-tubes: A numerical study

2009 ◽  
Vol 13 (4) ◽  
pp. 175-181 ◽  
Author(s):  
Khalid Alammar
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Turbulent Flow ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Heat Transfer Characteristics ◽  
Local Skin ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer

Using the standard k-e model, 3-dimensional turbulent flow and heat transfer characteristics in U-tubes are investigated. Uncertainty is approximated using experimental correlations and grid independence study. Increasing the Dean number is shown to intensify a secondary flow within the curved section. The overall Nusselt number for the tube is found to decrease substantially relative to straight tubes, while the overall skin friction coefficient remains practically unaffected. Local skin friction coefficient, Nusselt number, and wall temperature along the tube wall are presented.

Investigation Into the Similarity Solution for Boundary Layer Flows in Microsystems

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Suhil Kiwan ◽  
M. A. Al-Nimr
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Heat Transfer Characteristics ◽  
Boundary Layer Flows ◽  
Flow And Heat Transfer

An investigation toward the existence of a complete similarity solution for boundary layer flows under the velocity slip and temperature jump conditions is carried out. The study is limited to the boundary layer flows resulting from an arbitrary freestream velocity U(x)=Uoxm and wall temperature given by Tw−T∞=Cxn. It is found that a similar solution exists only for m=1 and n=0, which represents stagnation flow on isothermal surface. This case has been thoroughly investigated. The analysis showed that three parameters control the flow and heat transfer characteristics of the problem. These parameters are the velocity slip parameter K1, the temperature jump parameter K2, and Prandtl number. The effect of these parameters on the flow and heat transfer of the problem has been studied and presented. It is found that the slip velocity parameter affects both the flow and heat transfer characteristics of the problem. It is found that the skin friction coefficient decreases with increasing K1 and most of changes in the skin friction takes place in the range 0<K1<1. The skin friction coefficient is found to be related to K1 and Rex according to the relation: Cf=3.38Rex−0.5(K1+1.279)−0.8 for 0<K1<5 with an error of ±4%. On the other hand, the correlation between Nu, K1, K2, and Pr has been found by the equation Nu=[(0.449+1.142K11.06)∕(0.515+K11.06)](K2+1.489Pr−0.44)−1, for 0<K1, K2<5, 0.7≤Pr≤5 within a maximum error of ±3%.

scholarly journals Uncertainties Analysis on the Prediction of Flow and Heat Transfer of Liquid Sodium with CFD Technology

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanwei Liu ◽  
Xinyu Li ◽  
Tenglong Cong ◽  
Rui Zhang ◽  
Lingyun Zheng ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Liquid Sodium ◽  
Heat Transfer Characteristics ◽  
Backward Facing Step ◽  
Heating Wall ◽  
Transfer Characteristics ◽  
Cfd Models ◽  
Flow And Heat Transfer

The prediction of flow and heat transfer characteristics of liquid sodium with CFD technology is of significant importance for the design and safety analysis of sodium-cooled fast reactor. The accuracies and uncertainties of the CFD models should be evaluated to improve the confidence of the numerical results. In this work, the uncertainties from the turbulent model, boundary conditions, and physical properties for the flow and heat transfer of liquid sodium were evaluated against the experimental data. The results of uncertainty quantization show that the maximum uncertainties of the Nusselt number and friction coefficient occurred in the transition zone from the inlet to the fully developed region in the circular tube, while they occurred near the reattachment point in the backward-facing step. Furthermore, in backward-facing step flow, the maximum uncertainty of temperature migrated from the heating wall to the geometric center of the channel, while the maximum uncertainty of velocity occurred near the vortex zone. The results of sensitivity analysis illustrate that the Nusselt number was negatively correlated with the thermal conductivity and turbulent Prandtl number, while the friction coefficient was positively correlated with the density and Von Karman constant. This work can be a reference to evaluate the accuracy of the standard k-ε model in predicting the flow and heat transfer characteristics of liquid sodium.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

Investigation of Flat-Plate Hypersonic, Turbulent Boundary Layers With Heat Transfer

1961 ◽  
Vol 28 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Eva M. Winkler
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Mach Number ◽  
Flat Plate ◽  
Skin Friction ◽  
Boundary Layers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy

Naturally turbulent boundary layers on a cooled flat plate have been investigated at several distances from the leading edge of the plate at a Mach number of 5.2 for three rates of steady-state heat transfer to the surface. Measurements of Pitot and static pressures and of total and wall temperatures made it possible to compute velocity profiles, static-temperature profiles, and boundary-layer parameters without resorting to assumptions. The data demonstrate that the Reynolds analogy between skin friction and heat transfer is valid for all conditions of the present experiments. With increasing rate of heat transfer to the surface, the skin-friction coefficient was found to decrease, a phenomenon opposite to that predicted by theories and empirical relations. On the basis of the present data and other published results of compressible and incompressible turbulent boundary-layer skin friction, a simple relation was devised which describes closely the variation of the skin-friction coefficient with Mach number, heat-transfer rate, and momentum-thickness Reynolds number.

scholarly journals Flow and heat transfer in a rectangular converging (diverging) channel: new formulation

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Roohi Laila ◽  
Dil Nawaz Khan Marwat ◽  
Azhar Ali
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Model Problem ◽  
Skin Friction Coefficient ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Controlling Parameter ◽  
Diverging Channel ◽  
New Formulation

AbstractIn this paper, a model problem of viscous flow and heat transfer in a rectangular converging (diverging) channel has been investigated. The governing equations are presented in Cartesian Coordinates and consequently they are simplified and solved with perturbation and numerical methods. Initially, symmetrical solutions of the boundary value problem are found for the upper half of the channel. Later on, these solutions are extended to the lower half and then to the whole channel. The numerical and perturbation solutions are compared and exactly matched with each other for a small value of the parameters involved in the problem. It is also confirmed that the solutions for the converging/diverging channel are independent of the sign of m (the slope). Moreover, the skin friction coefficient and heat transfer at the upper wall are calculated and graphed against the existing parameters in different figures. It is observed that the heat transfer at walls is decreased (increased) with increasing $${c}_{1}$$ c 1 (thermal controlling parameter) for diverging (converging). It is also decreased against Pr (Prandtle number). For $${c}_{1}=0$$ c 1 = 0 , the temperature profiles may be exactly determined from the governing equations and the rate of heat transfer at the upper wall is $$\theta^{\prime } (1) = \frac{m}{{(1 + m^{2} )\tan^{ - 1} m}}$$ θ ′ ( 1 ) = m ( 1 + m 2 ) tan - 1 m . It is confirmed that the skin friction coefficient behaves linearly against Re* (modified Reynolds number) and it is increased with increasing of Re* (changed from negative to positive). Moreover, it is increased asymptotically against m and converges to a constant value i.e. zero.

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