Gradient Layer Entrainment in a Thermohaline System With Mixed Layer Circulation

1986 ◽  
Vol 108 (4) ◽  
pp. 267-274 ◽  
Author(s):  
F. P. Incropera ◽  
C. E. Lents ◽  
R. Viskanta
Keyword(s):  
Flow Visualization ◽  
Mixed Layer ◽  
Fluid Velocity ◽  
Horizontal Flow ◽  
Entrainment Rate ◽  
Dimensionless Parameters ◽  
Buoyancy Flow ◽  
Shear Mechanism ◽  
Bottom Heating ◽  
Layer Flow

Entrainment of salt-stratified fluid into a bottom mixed layer is investigated under conditions for which mixing is driven by bottom heating and/or an imposed horizontal flow. Entrainment rate measurements and mixed layer flow visualization suggest that entrainment is strongly influenced by a shear mechanism involving both horizontal and vertical fluid velocity components. Under certain conditions, imposition of the horizontal flow inhibits the buoyancy flow and entrainment rates for combined mixing are less than those for pure buoyant mixing. Attempts to correlate entrainment rates in terms of conventional dimensionless parameters were unsuccessful.

scholarly journals Kinematics of local entrainment and detrainment in a turbulent jet

2019 ◽  
Vol 871 ◽  
pp. 896-924 ◽  
Author(s):  
Dhiren Mistry ◽  
Jimmy Philip ◽  
James R. Dawson
Keyword(s):  
Convex Surface ◽  
Fluid Velocity ◽  
Surface Curvature ◽  
Frame Of Reference ◽  
Entrainment Rate ◽  
Local Exchange ◽  
Local Flow ◽  
Micro Scale ◽  
Entrainment Velocity ◽  
Fluorescence Measurements

In this paper we investigate the continuous, local exchange of fluid elements as they are entrained and detrained across the turbulent/non-turbulent interface (TNTI) in a high Reynolds number axisymmetric jet. To elucidate characteristic kinematic features of local entrainment and detrainment processes, simultaneous high-speed particle image velocimetry and planar laser-induced fluorescence measurements were undertaken. Using an interface-tracking technique, we evaluate and analyse the conditional dependence of local entrainment velocity in a frame of reference moving with the TNTI in terms of the interface geometry and the local flow field. We find that the local entrainment velocity is intermittent with a characteristic length scale of the order of the Taylor micro-scale and that the contribution to the net entrainment rate arises from the imbalance between local entrainment and detrainment rates that occurs with a ratio of two parts of entrainment to one part detrainment. On average, an increase in local entrainment is correlated with excursions of the TNTI towards jet centreline into regions of higher streamwise momentum, convex surface curvature facing the turbulent side of the jet and along the leading edges of the interface. In contrast, detrainment is correlated with excursions of the TNTI away from the jet centreline into regions of lower streamwise momentum, concave surface curvature and along the trailing edge. We find that strong entrainment is characterised by a local counterflow velocity field in the frame of reference moving with the TNTI which enhances the transport of rotational and irrotational fluid elements. On the other hand, detrainment is characterised by locally uniform flow fields with the local fluid velocity on either side of the TNTI advecting in the same direction. These local flow patterns and the strength of entrainment or detrainment rates are also observed to be strongly influenced by the presence and relative strength of vortical structures which are of the order of the Taylor micro-scale that populate the turbulent region along the jet boundary.

scholarly journals Finite Element Simulation of Multi-Slip Effects on Unsteady MHD Bioconvective Micropolar Nanofluid Flow Over a Sheet with Solutal and Thermal Convective Boundary Conditions

Coatings ◽  
2019 ◽  
Vol 9 (12) ◽  
pp. 842 ◽  
Author(s):  
Liaqat Ali ◽  
Xiaomin Liu ◽  
Bagh Ali ◽  
Saima Mujeed ◽  
Sohaib Abdal
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fluid Velocity ◽  
Mesh Size ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Micropolar Nanofluid ◽  
Layer Flow ◽  
Buoyancy Ratio

In this article, the intention is to explore the flow of a magneto-hydrodynamic (MHD) bioconvective micro-polar Nanofluid restraining microorganism. The numerical solution of 2-D laminar bioconvective boundary layer flow of micro-polar nanofluids are presented. The phenomena of multi-slip, convective thermal and Solutal boundary conditions have been integrated. A system of non-linear partial differential equations are transformed into the system of coupled nonlinear ordinary differential equations by applying appropriate transformations, the transformed equations are then solved by applying the variational finite element method (FEM). The fascinating features of assorted velocity parameter, microrotation, temperature, microorganism compactness, solutal and nanoparticles concentration have been inspected. The rate of heat transfer, the skin friction coefficient, couple stress and Sherwood number for microorganisms have also been discussed graphically and numerically. The investigations illustrated that increase in material parameters causes a reduction in microorganism compactness, concentration and temperature. As a result of enhancement in the unsteadiness parameter, the fluid velocity, concentration of microorganisms and the temperature are observed to be declines. Energy and microorganism compactness profile affected by the improvement in the buoyancy ratio parameter. As the improvement in results of buoyancy ratio parameter effects on improvement in the energy and the microorganism compactness profile while the velocity profile is condensed. In the end, rationalized convergence of the finite element solution has been inspected; the computations are found out via depreciating the mesh size.

scholarly journals Effect of magnetic field, heat generation and absorption on nanofluid flow over a nonlinear stretching sheet

2020 ◽  
Vol 11 ◽  
pp. 976-990
Author(s):  
Santoshi Misra ◽  
Govardhan Kamatam
Keyword(s):  
Magnetic Field ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Partial Slip ◽  
Nanoparticle Suspension ◽  
Dimensionless Parameters ◽  
Similarity Transformations ◽  
Highly Nonlinear ◽  
Layer Flow ◽  
The Impact

The study of magnetohydrodynamic flow of a nanoparticle suspension under the influence of varied dimensionless parameters has been the focus of research in contemporary times. This work models the effect of magnetic field, heat generation and absorption parameter in a steady, laminar, two-dimensional boundary layer flow of a nanofluid over a permeable stretching sheet at a given surface temperature and partial slip. The highly nonlinear governing equations are solved numerically using similarity transformations with suitable boundary conditions and converted to ordinary differential equations. A computational model is setup using FORTRAN, where a relevant Adam’s predictor–corrector method is employed to solve the equations. The impact of the dimensionless parameters, including the Brownian motion, thermophoresis, magnetic field, heat generation and absorption parameters, on the velocity, temperature and nanoparticle concentration of fluid flow are analysed systematically.

Role of heatlines on thermal management during Rayleigh-Bénard heating within enclosures with concave/convex horizontal walls

2017 ◽  
Vol 27 (9) ◽  
pp. 2070-2104 ◽  
Author(s):  
Pratibha Biswal ◽  
Tanmay Basak
Keyword(s):  
Heat Flow ◽  
Flow Visualization ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Content Type ◽  
Bénard Convection ◽  
Benard Convection ◽  
First Time ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Purpose This study aims to carry out the analysis of Rayleigh-Bénard convection within enclosures with curved isothermal walls, with the special implication on the heat flow visualization via the heatline approach. Design/methodology/approach The Galerkin finite element method has been used to obtain the numerical solutions in terms of the streamlines (ψ ), heatlines (Π), isotherms (θ), local and average Nusselt number ( Nut¯) for various Rayleigh numbers (103 ≤ Ra ≥ 105), Prandtl numbers (Pr = 0.015 and 7.2) and wall curvatures (concavity/convexity). Findings The presence of the larger fluid velocity within the curved cavities resulted in the larger heat transfer rates and thermal mixing compared to the square cavity. Case 3 (high concavity) exhibits the largest Nut¯ at the low Ra for all Pr. At the high Ra, Nut¯ is the largest for Case 3 (high concavity) at Pr = 0.015, whereas at Pr = 7.2, Nut¯ is the largest for Case 1 (high concavity and convexity). Practical implications The results may be useful for the material processing applications. Originality/value The study of Rayleigh-Bénard convection in cavities with the curved isothermal walls is not carried out till date. The heatline approach is used for the heat flow visualization during Rayleigh-Benard convection within the curved walled enclosures for the first time. Also, the existence of the enhanced fluid and heat circulation cells within the curved walled cavities during Rayleigh-Benard heating is illustrated for the first time.

scholarly journals Numerical Analysis of Heat Transfer of Eyring Powell Fluid Using Double Stratification of Magneto-Hydrodynamic Boundary Layer Flow

2020 ◽  
pp. 91-108
Author(s):  
Wekesa Waswa Simon ◽  
Winifred Nduku Mutuku
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Thermal Stratification ◽  
Fluid Velocity ◽  
Double Stratification ◽  
Hydrodynamic Boundary Layer ◽  
Layer Flow ◽  
The Magnetic Field

Heat transfer fluids play a vital role in many engineering and industrial sectors such as power generation, chemical production, air-conditioning, transportation and microelectronics. Aim: To numerically investigate the effect of double stratification on magneto-hydrodynamic boundary layer flow and heat transfer of an Eyring-Powell fluid. Study Design: Eyring-Powell fluid is one of the non-Newtonian fluid that possess different characteristics thus different mathematical models have been formulated to describe such fluids by appropriate substitution into Navier-Stoke’s equations. The challenging complexity and the nature of the resultant equations are of great interest hence attract many investigations. Place and Duration of Study: Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya between December 2019 and October 2020. Methodology: The resultant nonlinear equations are transformed to linear differential equations by introducing appropriate similarity transformations. The resulting equations are solved numerically by simulating the predictor-corrector (P-C) method in matlab ode113. The results are graphically depicted and analysed to illustrate the effects of magnetic field, thermophoresis, thermal stratification, solutal stratification, material fluid parameters and Grashoff number on the fluid velocity, temperature, concentration, local Sherwood number and local Nusselt number. Results: The results show that increasing the magnetic field strength, thermophoresis, thermal stratification and solutal stratification lead to a decrease in the fluid velocity, temperature, Sherwood number, Nusselt number and skin friction while an increase in the magnetic field strength, thermal stratification, solutal stratification, and thermophoresis increases the fluid concentration. Conclusion: The parameters in this study can be varied to enhance heat ejection of Eyring-Powell fluid and applied in industries as a coolant or heat transfer fluid.

scholarly journals Numerical method approach for magnetohydrodynamic radiative ferrofluid flows over a solid sphere surface

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 379-385
Author(s):  
Yasin Mat ◽  
Muhammad Mohamed ◽  
Zulkhibri Ismail ◽  
Basuki Widodo ◽  
Mohd Salleh
Keyword(s):  
Boundary Layer ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Solid Sphere ◽  
Skin Friction Coefficient ◽  
Fluid Temperature ◽  
Sphere Surface ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Layer Flow

In this paper, the theoretical study on the laminar boundary-layer flow of ferrofluid with influences of magnetic field and thermal radiation is investigated. The viscosity of ferrofluid flow over a solid sphere surface is examined theoretically for magnetite volume fraction by using boundary-layer equations. The governing equations are derived by applied the non-similarity transformation then solved numerically by utilizing the Keller-box method. It is found that the increments in ferro-particles (Fe3O4) volume fraction declines the fluid velocity but elevates the fluid temperature at a sphere surface. Consequently, the results showed viscosity is enhanced with the increase of the ferroparticles volume fraction and acts as a pivotal role in the distribution of velocity, temperature, reduced skin friction coefficient, and reduced Nusselt number of ferrofluid.

Transient Couple Stress Fluid Past a Vertical Cylinder With Bejan’s Heat and Mass Flow Visualization for Steady-State

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
H. P. Rani ◽  
G. Janardhan Reddy ◽  
Chang Nyung Kim ◽  
Y. Rameshwar
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Flow Visualization ◽  
Boundary Layer Flow ◽  
Couple Stress ◽  
Vertical Cylinder ◽  
Couple Stress Fluid ◽  
Layer Flow ◽  
Flow Variables ◽  
Mass Functions

In the present study, the transient, free convective, boundary layer flow of a couple stress fluid flowing over a vertical cylinder is investigated, and the heat and mass functions for the final steady-state of the present flow are developed. The solution of the time dependent nonlinear and coupled governing equations is obtained with the aid of an unconditionally stable Crank–Nicolson type of numerical scheme. Numerical results for the time histories of the skin-friction coefficient, Nusselt number, and Sherwood number as well as the steady-state velocity, temperature, and concentration are presented graphically and discussed. Also, it is observed that time required for the flow variables to reach the steady-state increases with the increasing values of Schmidt and Prandtl numbers, while the opposite trend is observed with respect to the buoyancy ratio parameter. To analyze the flow variables in the steady-state, the heatlines and masslines are used in addition to streamlines, isotherms, and isoconcentration lines. When the heat and mass functions are properly made dimensionless, its dimensionless values are related to the local and overall Nusselt and Sherwood numbers. Boundary layer flow visualization indicates that the heatlines and masslines are dense in the vicinity of the hot wall, especially near the leading edge.

On the scaling of stress-driven entrainment experiments

1979 ◽  
Vol 90 (3) ◽  
pp. 509-529 ◽  
Author(s):  
James F. Price
Keyword(s):  
Mixed Layer ◽  
Mixed Layer Depth ◽  
Side Wall ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Entrainment Rate ◽  
Surface Mixed Layer ◽  
Mean Velocity ◽  
Wide Range ◽  
Conservation Of Momentum

The entrainment experiments of Kato & Phillips (1969) and Kantha, Phillips & Azad (1977) (hereafter KP and KPA) are analysed to demonstrate a more general and effective scaling of the entrainment observations. The preferred scaling is \[ V^{-1} dh/dt = E(R_v), \] where h is the mixed-layer depth, V is the mean velocity of the mixed layer, Rv = B/V2 and B is the total mixed-layer buoyancy. This scaling effectively collapses entrainment data taken at various h/L, where L is the tank width, and in cases in which the interior is density stratified (KP) or homogeneous (KPA). The entrainment law E(Rv) is computed from the KP and KPA observations using the conservation equations for mean momentum and buoyancy. A side-wall drag term is included in the momentum conservation equation. In the range 0·5 < Rv < 1·0, which includes nearly all of the KP, KPA data, E ≃ 5 × 10−4R−4v. This is very similar to the entrainment law followed by a surface half-jet (Ellison & Turner 1959) and by the wind-driven ocean surface mixed layer (Price, Mooers & Van Leer 1978).The analysis shows that, when forcing is steady, Rv is quasi-steady and, provided that side-wall drag is not large, Rv ≃ 0·6 over a wide range of RT = B/U2*, where U* is the friction velocity of the imposed stress. In the absence of side-wall drag (vanishing h/L) the conservation of momentum then leads to U−1*dh/dt = n(0·6)½R−½T, where n = ½ or 1 if the interior is linearly stratified or homogeneous. The KP, KPA data show this dependence throughout the range 17 < RT < 160 where the effect of side-wall drag is negligible or can be removed by a linear extrapolation. This result, together with the form and magnitude of the observed side-wall effect, suggests that mean momentum conservation is a key constraint upon the entrainment rate in the KP, KPA experiments.

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