Heat Transfer Improvement in a Double Backward-Facing Expanding Channel Using Different Working Fluids

This paper reports a numerical study on heat transfer improvement in a double backward-facing expanding channel using different convectional fluids. A finite volume method with the k-ε standard model is used to investigate the effects of step, Reynolds number and type of liquid on heat transfer enhancement. Three types of conventional fluids (water, ammonia liquid and ethylene glycol) with Reynolds numbers varying from 98.5 to 512 and three cases for different step heights at a constant heat flux (q = 2000 W/m2) are examined. The top wall of the passage and the bottom wall of the upstream section are adiabatic, while the walls of both the first and second steps downstream are heated. The results show that the local Nusselt number rises with the augmentation of the Reynolds number, and the critical effects are seen in the entrance area of the first and second steps. The maximum average Nusselt number, which represents the thermal performance, can be seen clearly in case 1 for EG in comparison to water and ammonia. Due to the expanding of the passage, separation flow is generated, which causes a rapid increment in the local skin friction coefficient, especially at the first and second steps of the downstream section for water, ammonia liquid and EG. The maximum skin friction coefficient is detected in case 1 for water with Re = 512. Trends of velocities for positions (X/H1 = 2.01, X/H2 = 2.51) at the first and second steps for all the studied cases with different types of convectional fluids are indicated in this paper. The presented findings also include the contour of velocity, which shows the recirculation zones at the first and second steps to demonstrate the improvement in the thermal performance.

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

Thermal Science ◽

10.2298/tsci0904175a ◽

2009 ◽

Vol 13 (4) ◽

pp. 175-181 ◽

Cited By ~ 1

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.

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-01-2019-0057 ◽

2019 ◽

Vol 29 (9) ◽

pp. 3110-3127 ◽

Cited By ~ 37

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.

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Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

Mathematical Problems in Engineering ◽

10.1155/2010/579162 ◽

2010 ◽

Vol 2010 ◽

pp. 1-20 ◽

Cited By ~ 20

Author(s):

Mostafa Mahmoud ◽

Shimaa Waheed

Keyword(s):

Nusselt Number ◽

Friction Coefficient ◽

Mixed Convection ◽

Skin Friction ◽

Heat Generation ◽

Local Nusselt Number ◽

Skin Friction Coefficient ◽

Convection Flow ◽

Local Skin ◽

Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

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Nanofluid Viscoelastic Fluid Flow with Thermophoresis

Nanoscience and Nanotechnology Letters ◽

10.1166/nnl.2019.3061 ◽

2019 ◽

Vol 11 (12) ◽

pp. 1739-1749

Author(s):

Gamal M. Abdel-Rahman ◽

Faiza M. N. El-Fayez

Keyword(s):

Nusselt Number ◽

Friction Coefficient ◽

Skin Friction ◽

Numerical Solutions ◽

Fluid Model ◽

Skin Friction Coefficient ◽

Jeffrey Fluid ◽

Deposition Flux ◽

Local Skin ◽

Linear Ordinary Differential Equations

We in this study investigated Brownian motion and thermophoresis effects embedded in a porous medium flow with heat transfer generation and chemical reaction on a stretching sheet and Jeffrey fluid model for viscoelastic nanofluid under the effects of magnetic field and thermal radiation. The nanofluid was assumed incompressible and the flow was laminar, with base fluid containing the following types of nanoparticles: Copper (Cu), Aluminum (Al2O3) and Titanium Oxide (TiO2). The governing continuity, momentum, and energy equations for the nanofluid were reduced using similarity transformation and converted into a system of non-Linear ordinary differential equations which were solved numerically. Numerical solutions were also obtained for the velocity, temperature and nanoparticle concentration fields, as well as for skin friction coefficient and Nusselt number. Finally, numerical values for the physical quantities, such as local skin-friction coefficient, local Nusselt number, local Sherwood number and wall deposition flux are herein presented in tabular form.

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Effect of Vertical Baffle Installation on Forced Convective Heat Transfer in Channel Having a Backward Facing Step

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.388.169 ◽

2013 ◽

Vol 388 ◽

pp. 169-175 ◽

Cited By ~ 7

Author(s):

Amirhossein Heshmati ◽

Hussein A. Mohammed ◽

Mohammad Parsazadeh ◽

Farshid Fathinia ◽

Mazlan A. Wahid ◽

...

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Friction Coefficient ◽

Convective Heat Transfer ◽

Skin Friction ◽

Convective Heat ◽

Average Nusselt Number ◽

Skin Friction Coefficient ◽

Expansion Ratio ◽

Forced Convective Heat Transfer

In this study, forced convective heat transfer is considered in channel over a backward facing step having a baffle on the top wall. Four different geometries with different expansion ratios and different type of baffles are numerically investigated. The study clearly shows that the geometry with expansion ratio 2 and solid baffle has the highest Nusselt number compared to other geometries. Considering both Nusselt number and skin friction coefficient for all four geometries clearly illustrated an increase in average Nusselt number by increasing the expansion ratio. This study clearly shows that mounting a slotted baffle at the top wall instead of a solid baffle caused a decline in average Nusselt number. It is also found that for geometry with expansion ratio of 3 and a slotted baffle on the top of the channel, skin friction coefficient in both bottom wall and step wall has its minimal compared to other geometries.

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Nanofluid Viscoelastic Fluid Flow with Thermophoresis

Nanoscience and Nanotechnology Letters ◽

10.1166/nnl.2019.30611739 ◽

2019 ◽

Vol 11 (12) ◽

pp. 1739-1749

Author(s):

Gamal M. Abdel-Rahman ◽

Faiza M. N. El-Fayez

Keyword(s):

Nusselt Number ◽

Friction Coefficient ◽

Skin Friction ◽

Numerical Solutions ◽

Fluid Model ◽

Skin Friction Coefficient ◽

Jeffrey Fluid ◽

Deposition Flux ◽

Local Skin ◽

Linear Ordinary Differential Equations

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Influence of moving plate velocity on conjugate heat transfer due to the impingement of an inclined slot jet

International Journal of Modern Physics C ◽

10.1142/s0129183120500060 ◽

2019 ◽

Vol 30 (12) ◽

pp. 2050006 ◽

Cited By ~ 1

Author(s):

Shashikant Pawar ◽

Devendra Kumar Patel

Keyword(s):

Heat Transfer ◽

Nusselt Number ◽

Friction Coefficient ◽

Skin Friction ◽

Numerical Study ◽

Finite Thickness ◽

Skin Friction Coefficient ◽

Moving Plate ◽

Potential Core ◽

Plate Velocity

In this paper, a dimensionless numerical study of the flow-field and heat transfer characteristics of an incompressible turbulent slot jet impinging obliquely over a moving surface of finite thickness is presented. Simulations were performed using [Formula: see text] eddy viscosity turbulence model. The temperature field was solved simultaneously in the solid and the fluid domain. For a fixed impingement distance and a fixed Reynolds number, the impingement angle ([Formula: see text]) and plate velocity ([Formula: see text]) were varied in the range of 30–75∘ and 0–0.3, respectively. In the results, the length of the potential core depends on the jet inclination, which increases with increase in jet angle. The jet angle and plate velocity have more influence on the uphill side compared to the downhill side. The location of stagnation displaces toward the uphill side as the inclination angle decreases, and the drifting of stagnation point is noted with the variation in plate velocity. The average skin-friction coefficient increases with increase in [Formula: see text] and [Formula: see text], and the influence of [Formula: see text] on the skin-friction coefficient is reduced as [Formula: see text] increases. The maximum Nusselt number ([Formula: see text]) increases with increase in [Formula: see text], and the drifting of [Formula: see text] is observed with increase in plate velocity. It is found that the average Nusselt number increases quickly with increase in plate velocity for lower angles of impingement. The distribution of local heat flux follows the same trend as the local Nusselt number.

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

Pertanika Journal of Science and Technology ◽

10.47836/pjst.29.3.42 ◽

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.

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Roughness effects in turbulent forced convection

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.900 ◽

2018 ◽

Vol 861 ◽

pp. 138-162 ◽

Cited By ~ 6

Author(s):

M. MacDonald ◽

N. Hutchins ◽

D. Chung

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Friction Coefficient ◽

Skin Friction ◽

Forced Convection ◽

Temperature Difference ◽

Skin Friction Coefficient ◽

Stanton Number ◽

Reynolds Analogy ◽

Momentum And Heat Transfer

We conducted direct numerical simulations of turbulent flow over three-dimensional sinusoidal roughness in a channel. A passive scalar is present in the flow with Prandtl number $Pr=0.7$, to study heat transfer by forced convection over this rough surface. The minimal-span channel is used to circumvent the high cost of simulating high-Reynolds-number flows, which enables a range of rough surfaces to be efficiently simulated. The near-wall temperature profile in the minimal-span channel agrees well with that of the conventional full-span channel, indicating that it can be readily used for heat-transfer studies at a much reduced cost compared to conventional direct numerical simulation. As the roughness Reynolds number, $k^{+}$, is increased, the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$, increases in the transitionally rough regime before tending towards the fully rough asymptote of $\unicode[STIX]{x1D705}_{m}^{-1}\log (k^{+})+C$, where $C$ is a constant that depends on the particular roughness geometry and $\unicode[STIX]{x1D705}_{m}\approx 0.4$ is the von Kármán constant. In this fully rough regime, the skin-friction coefficient is constant with bulk Reynolds number, $Re_{b}$. Meanwhile, the temperature difference between smooth- and rough-wall flows, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}^{+}$, appears to tend towards a constant value, $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. This corresponds to the Stanton number (the temperature analogue of the skin-friction coefficient) monotonically decreasing with $Re_{b}$ in the fully rough regime. Using shifted logarithmic velocity and temperature profiles, the heat-transfer law as described by the Stanton number in the fully rough regime can be derived once both the equivalent sand-grain roughness $k_{s}/k$ and the temperature difference $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$ are known. In meteorology, this corresponds to the ratio of momentum and heat-transfer roughness lengths, $z_{0m}/z_{0h}$, being linearly proportional to the inner-normalised momentum roughness length, $z_{0m}^{+}$, where the constant of proportionality is related to $\unicode[STIX]{x0394}\unicode[STIX]{x1D6E9}_{FR}^{+}$. While Reynolds analogy, or similarity between momentum and heat transfer, breaks down for the bulk skin-friction and heat-transfer coefficients, similar distribution patterns between the heat flux and viscous component of the wall shear stress are observed. Instantaneous visualisations of the temperature field show a thin thermal diffusive sublayer following the roughness geometry in the fully rough regime, resembling the viscous sublayer of a contorted smooth wall.

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Non-similar characteristics of mixed convective slip flow over a wedge with temperature-dependent thermo-physical properties

Modern Physics Letters B ◽

10.1142/s0217984919504554 ◽

2019 ◽

Vol 33 (36) ◽

pp. 1950455

Author(s):

Nepal Chandra Roy ◽

Sudharonjon Roy ◽

Naved Azum ◽

Anish Khan ◽

Abdullah M. Asiri ◽

...

Keyword(s):

Nusselt Number ◽

Friction Coefficient ◽

Skin Friction ◽

Sherwood Number ◽

Local Nusselt Number ◽

Slip Flow ◽

Skin Friction Coefficient ◽

Local Skin ◽

Local Skin Friction ◽

Local Sherwood Number

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

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