Abstract: This paper deals with the theoretical and numerical
investigation of magneto hydrodynamic boundary layer flow of a
nanofluid past a wedge shaped wick in heat pipe used for the cooling
of electronic components and different type of machines. To
incorporate the effect of nanoparticle diameter, concentration of
nanoparticles in the pure fluid, nanothermal layer formed around the
nanoparticle and Brownian motion of nanoparticles etc., appropriate
models are used for the effective thermal and physical properties of
nanofluids. To model the rotation of nanoparticles inside the base
fluid, microfluidics theory is used. In this investigation ethylene
glycol (EG) based nanofluids, are taken into account. The non-linear
equations governing the flow and heat transfer are solved by using a
very effective particle swarm optimization technique along with
Runge-Kutta method. The values of heat transfer coefficient are
found for different parameters involved in the formulation viz.
nanoparticle concentration, nanoparticle size, magnetic field and
wedge angle etc. It is found that, the wedge angle, presence of
magnetic field, nanoparticle size and nanoparticle concentration etc.
have prominent effects on fluid flow and heat transfer characteristics
for the considered configuration.
Abstract: In this paper, the problem of steady laminar boundary
layer flow and heat transfer over a permeable exponentially
stretching/shrinking sheet with generalized slip velocity is
considered. The similarity transformations are used to transform the
governing nonlinear partial differential equations to a system of
nonlinear ordinary differential equations. The transformed equations
are then solved numerically using the bvp4c function in MATLAB.
Dual solutions are found for a certain range of the suction and
stretching/shrinking parameters. The effects of the suction parameter,
stretching/shrinking parameter, velocity slip parameter, critical shear
rate and Prandtl number on the skin friction and heat transfer
coefficients as well as the velocity and temperature profiles are
presented and discussed.
Abstract: The convective heat and mass transfer in nanofluid
flow through a porous media due to a permeable stretching sheet with
magnetic field, viscous dissipation, chemical reaction and Soret
effects are numerically investigated. Two types of nanofluids, namely
Cu-water and Ag-water were studied. The governing boundary layer
equations are formulated and reduced to a set of ordinary differential
equations using similarity transformations and then solved
numerically using the Keller box method. Numerical results are
obtained for the skin friction coefficient, Nusselt number and
Sherwood number as well as for the velocity, temperature and
concentration profiles for selected values of the governing
parameters. Excellent validation of the present numerical results has
been achieved with the earlier linearly stretching sheet problems in
the literature.
Abstract: The main objective of aircraft aerodynamics is to
enhance the aerodynamic characteristics and maneuverability of the
aircraft. This enhancement includes the reduction in drag and stall
phenomenon. The airfoil which contains dimples will have
comparatively less drag than the plain airfoil. Introducing dimples on
the aircraft wing will create turbulence by creating vortices which
delays the boundary layer separation resulting in decrease of pressure
drag and also increase in the angle of stall. In addition, wake
reduction leads to reduction in acoustic emission. The overall
objective of this paper is to improve the aircraft maneuverability by
delaying the flow separation point at stall and thereby reducing the
drag by applying the dimple effect over the aircraft wing. This project
includes both computational and experimental analysis of dimple
effect on aircraft wing, using NACA 0018 airfoil. Dimple shapes of
Semi-sphere, hexagon, cylinder, square are selected for the analysis;
airfoil is tested under the inlet velocity of 30m/s and 60m/s at
different angle of attack (5˚, 10˚, 15˚, 20˚, and 25˚). This analysis
favors the dimple effect by increasing L/D ratio and thereby
providing the maximum aerodynamic efficiency, which provides the
enhanced performance for the aircraft.
Abstract: For a bluff body, dimples behave like roughness
elements in stimulating a turbulent boundary layer, leading to delayed
flow separation, a smaller wake and lower form drag. This is very
different in principle from the application of dimples to streamlined
body, where any reduction in drag would be predominantly due to a
reduction in skin friction. In the present work, a car model with
different dimple geometry is simulated using k-ε turbulence modeling
to determine its effect to the aerodynamics performance. Overall, the
results show that the application of dimples manages to reduce the
drag coefficient of the car model.
Abstract: An analysis is carried out to investigate the effect of
magnetic field and heat source on the steady boundary layer flow and
heat transfer of a Casson nanofluid over a vertical cylinder stretching
exponentially along its radial direction. Using a similarity
transformation, the governing mathematical equations, with the
boundary conditions are reduced to a system of coupled, non –linear
ordinary differential equations. The resulting system is solved
numerically by the fourth order Runge – Kutta scheme with shooting
technique. The influence of various physical parameters such as
Reynolds number, Prandtl number, magnetic field, Brownian motion
parameter, thermophoresis parameter, Lewis number and the natural
convection parameter are presented graphically and discussed for non
– dimensional velocity, temperature and nanoparticle volume
fraction. Numerical data for the skin – friction coefficient, local
Nusselt number and the local Sherwood number have been tabulated
for various parametric conditions. It is found that the local Nusselt
number is a decreasing function of Brownian motion parameter Nb
and the thermophoresis parameter Nt.
Abstract: Parameters of flow are calculated in vaneless diffusers
with relative width 0,014–0,10. Inlet angles of flow and similarity
criteria were varied. There is information on flow separation,
boundary layer development, configuration of streamlines.
Polytrophic efficiency, loss coefficient and recovery coefficient are
used to compare effectiveness of diffusers. The sample of
optimization of narrow diffuser with conical walls is presented. Three
wide diffusers with narrowing walls are compared. The work is made
in the R&D laboratory “Gas dynamics of turbo machines” of the TU
SPb.
Abstract: Solar air heater is a type of heat exchanger which
transforms solar radiation into heat energy. The thermal performance
of conventional solar air heater has been found to be poor because of
the low convective heat transfer coefficient from the absorber plate to
the air. It is attributed to the formation of a very thin boundary layer
at the absorber plate surface commonly known as viscous sub-layer.
Thermal efficiency of solar air heater can be improved by providing
the artificial roughness on absorber plate is the most efficient
technique. In this paper an attempt is made to provide artificial
roughness by incorporating inclined multiple V-ribs in the underside
of the absorber plate. 60˚V – ribs are arranged inclined to the
direction of air flow. Performance of collector estimated theoretically
and experimentally. Results of the investigation reveal that thermal
efficiency of collector with multiple V-ribs increased by 14%.
Abstract: A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.
Abstract: The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.
Abstract: The aim of this work is to analyze a viscous flow
around the axisymmetric blunt body taken into account the mesh size
both in the free stream and into the boundary layer. The resolution of
the Navier-Stokes equations is realized by using the finite volume
method to determine the flow parameters and detached shock
position. The numerical technique uses the Flux Vector Splitting
method of Van Leer. Here, adequate time stepping parameter, CFL
coefficient and mesh size level are selected to ensure numerical
convergence. The effect of the mesh size is significant on the shear
stress and velocity profile. The best solution is obtained with using a
very fine grid. This study enabled us to confirm that the
determination of boundary layer thickness can be obtained only if the
size of the mesh is lower than a certain value limits given by our
calculations.
Abstract: This numerical study aims to develop a coupled,
passive and active control strategy of the flow around a cylinder of
diameter D, and Re=4000. The strategy consists to put a cylindrical
rod in front of a deforming cylinder. The quasi- elliptical deformation
of cylinder follow a sinusoidal law in order to reduce the drag force.
To analyze the evolution of unsteady vortices, the Large Eddy
Simulation approach is used in this 2D simulation, carried out using
ANSYS – Fluent. The movement of deformation is reproduced using
an internal subroutine, introduced in the form of a User Defined
Function UDF. Two diameters of the rod were tested for a rod placed
at a distance L = 3 ×d, with an amplitudes of deformation A = 5%, A
= 25% and A = 50% of the cylinder diameter, the frequency of
deformation take the values fd = 1fn, 5fn and 8fn, which fn
represents the naturel vortex shedding frequency. The results show
substantial changes in the flow behavior and for a rod of 6mm (1%
D) with amplitude A = 25%, and with a 2fn frequency, drag
reduction of 60% was recorded.
Abstract: This study involves numerical simulation of the flow
around a NACA2415 airfoil, with a 18° angle of attack, and flow
separation control using a rod, It involves putting a cylindrical rod -
upstream of the leading edge- in vertical translation movement in
order to accelerate the transition of the boundary layer by interaction
between the rod wake and the boundary layer. The viscous, nonstationary
flow is simulated using ANSYS FLUENT 13. The rod
movement is reproduced using the dynamic mesh technique and an
in-house developed UDF (User Define Function). The frequency
varies from 75 to 450 Hz and the considered amplitudes are 2%, and
3% of the foil chord. The frequency chosen closed to the frequency
of separation. Our results showed a substantial modification in the
flow behavior and a maximum drag reduction of 61%.
Abstract: The effect of mass transfer on MHD mixed convective flow along inclined porous plate with thermodiffusion have been analyzed on the basis of boundary layer approximations. The fluid is assumed to be incompressible and dense, and a uniform magnetic field is applied normal to the direction of the flow. A Similarity transformation is used to transform the problem under consideration into coupled nonlinear boundary layer equations which are then solved numerically using the Runge-Kutta sixth-order integration scheme together with Nachtsheim-Swigert shooting iteration technique. The behavior of velocity, temperature, concentration, local skin-friction, local Nusselt number and local Sherwood number for different values of parameters have been computed and the results are presented graphically, and analyzed thereafter. The validity of the numerical methodology and the results are questioned by comparing the findings obtained for some specific cases with those available in the literature, and a comparatively good agreement is reached.
Abstract: The problem of magnetohydrodynamics boundary layer flow and heat transfer on a permeable stretching surface in a second grade nanofluid under the effect of heat generation and partial slip is studied theoretically. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the PDE’s are transformed into a set of ODE’s with the help of local similarity transformations. The differential equations are solved by variational finite element method. The effects of different controlling parameters on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The comparison confirmed excellent agreement. The present study is of great interest in coating and suspensions, cooling of metallic plate, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers technology, materials processing exploiting.
Abstract: This paper presents a complete dynamic modeling
of a membrane distillation process. The model contains two
consistent dynamic models. A 2D advection-diffusion equation
for modeling the whole process and a modified heat equation
for modeling the membrane itself. The complete model describes
the temperature diffusion phenomenon across the feed, membrane,
permeate containers and boundary layers of the membrane. It gives
an online and complete temperature profile for each point in the
domain. It explains heat conduction and convection mechanisms that
take place inside the process in terms of mathematical parameters, and
justify process behavior during transient and steady state phases. The
process is monitored for any sudden change in the performance at any
instance of time. In addition, it assists maintaining production rates
as desired, and gives recommendations during membrane fabrication
stages. System performance and parameters can be optimized
and controlled using this complete dynamic model. Evolution of
membrane boundary temperature with time, vapor mass transfer along
the process, and temperature difference between membrane boundary
layers are depicted and included. Simulations were performed over
the complete model with real membrane specifications. The plots
show consistency between 2D advection-diffusion model and the
expected behavior of the systems as well as literature. Evolution
of heat inside the membrane starting from transient response till
reaching steady state response for fixed and varying times is
illustrated.
Abstract: The present analysis considers the steady stagnation point flow and heat transfer towards a permeable shrinking sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow and a local heat generation within the boundary layer, with a heat generation rate proportional to (T-T)p Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the stretching/shrinking parameter λ, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value λc whose value depends on the value of M, K, and s. In the presence of internal heat absorption (Q
Abstract: In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.
Abstract: In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.
Abstract: This study involves a numerical simulation of the flow around a NACA2415 airfoil, with a 15°angle of attack, and flow separation control using a rod, It reposes inputting a cylindrical rod upstream of the leading edge in order to accelerate the transition of the boundary layer by interaction between the rod wake and the boundary layer. The viscous, non-stationary flow is simulated using ANSYS FLUENT 13. Our results showed a substantial modification in the flow behavior and a maximum drag reduction of 51%.