Form Of Streamlines Research Articles

Characterization of magnetized CNT-based hybrid nanofluid subjected to convective phenomenon

Hybrid nanofluid gains attention of scientists due to its dynamic properties in various fields, and thus, hybrid nanofluids can be taken as an innovative form of nanofluids. Even though analysts acquire tremendous results in the field of hybrid nanofluids but yet no study has been carried out to predict magnetohydrodynamic effects in such fluid models. In this present analysis, influence of MHD has been investigated for the micro hybrid nanofluid over a stretched surface under convective conditions. Combine boundary layer equations for the flow have been altered into a suitable form via boundary layer approximations. Further, complete nonlinear system of equations has been numerically solved via BVP-4C method. Interesting results have been demonstrated for an exponentially stretched surface and expressed in the form of shear stress and rate of heat transfer. Results have also been visualized in the form of streamlines and isotherms. This study reveals after observing the numeric values of skin friction and Nusselt number that micropolar hybrid nanofluid models have greater heat transfer rate as compared to nanofluids.

Mixed Convection Heat Transfer and Entropy Generation in a Water-filled Square Cavity Partially Heated from Below: The Effects of Richardson and Prandtl Numbers

In the present study, fluid flow, heat transfer, and entropy generation for mixed convection inside a water-filled square cavity were investigated numerically. The sidewalls of the cavity, which move upwards, are kept at low-temperature Tc while only a part in the center of the bottom wall is kept at high-temperature Th and the remaining parts are kept adiabatic. The governing equations, in stream function–vorticity form, are discretized and solved using the finite difference method. Particular attention was paid to the influence of the Prandtl numbers of 5.534, 3.045 and 2, corresponding respectively to the water temperatures of 303.15 K, 333.15 K and 363.15 K. The numerical results are presented in the form of streamlines, isotherms, and entropy generation contours for different values of the Richardson numbers at an arbitrary Reynolds number Re=102. Besides this, the evolution of the average Nusselt number and the average entropy generation is also reported. The obtained results show interesting behaviors of the flow and thermal fields, which mainly involve stable symmetric and non-symmetric steady-state solutions, as well as unsteady regimes, depending on specific values of the Richardson and Prandtl numbers. It is additionally observed that the average Nusselt number increases and the average entropy generation decreases when both the Richardson and Prandtl numbers increase.

Numerical Analysis of Natural Convection Driven Flow of a Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure with a U-Shaped Constructal

Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a U-shaped fin. The Boussinesq approximation is utilized to generate the mathematical attributes of factors describing natural convection, which are then used in the momentum equation. Furthermore, the Fourier law is applied to formulate the streaming heat inside the fluid flow region. The formulated system describing the problem is non-dimensionalized using similarity transformations. The geometry of the problem comprises a trapezoidal cavity with a non-uniformly heated U-shaped fin introduced at the center of the base of the enclosure. The boundaries of the cavity are at no-slip conditions. Non-uniform heating is provided at the walls (l1 and l2), curves (c1,c2 and c3) and surfaces (s1 and s2) of the fin; the upper wall is insulated whereas the base and sidewalls of the enclosure are kept cold. The solution of the non-dimensionalized equations is procured by the Galerkin finite element procedure. To acquire information regarding the change in displacement w.r.t time and temperature, supplementary quadratic interpolating functions are also observed. An amalgam meshing is constructed to elaborate the triangular and quadrilateral elements of the trapezoidal domain. Observation of significant variation in the flow configurations for a specified range of parameters is taken into consideration i.e., 0.5≤n≤1.5 and 104≤Ra≤106. Furthermore, flow structures in the form of velocity profiles, streamlines, and temperature contours are interpreted for the parameters taken into account. It is deduced from the study that ascending magnitude of (Ra) elevates level of kinetic energy and magnitude of heat flux; however, a contrary configuration is encapsulated for the power-law index. Navier–Stokes equations constituting the phenomenon are written with the help of non-dimensionalized stream function, temperature profiles, and vortices, and the solutions are acquired using the finite element method. Furthermore, the attained outcomes are accessible through velocity and temperature profiles. It is worth highlighting the fact that the following analysis enumerates the pseudo-plastic, viscous and dilatant behavior of the fluid for different values of (n). This study highlights that the momentum profile and the heat transportation increase by increasing (Ra) and decline as the viscosity of the fluid increases. Overall, it can be seen from the current study that heat transportation increases with the insertion of a fin in the cavity. The current communication signifies the phenomenon of a power-law fluid flow filling a trapezoidal cavity enclosing a U-shaped fin. Previously, researchers have studied such phenomena mostly in Newtonian fluids, hence the present effort presents novelty regarding consideration of a power-law liquid in a trapezoidal enclosure by the placement of a U-shaped fin.

A class of second‐order schemes with application to chemically reactive radiative natural convection flow in a rectangular enclosure

AbstractA new class of explicit second‐order schemes is proposed for solving time‐dependent partial differential equations. This class of proposed schemes is constructed on three‐time levels. Stability is found for the scalar two‐dimensional heat equation and the system of time‐dependent partial differential equations. This partial differential equations system comprises a non‐dimensional set of equations obtained from the governing equations of natural convection chemically reactive fluid flow in a rectangular enclosure with thermal radiations. Flow is generated by applying the force of pressure. Graphs of streamlines, contours plots of velocity, temperature and concentration profiles, local Nusselt number, and local Sherwood number are displayed with the variation of time and parameters in the considered partial differential equations. Results are shown in the form of streamlines and contour plots. It is found that local Nusselt number has dual behavior by enhancing radiation parameter whereas local Sherwood number de‐escalates by upraising the reaction rate parameter. It is hoped that the results in this pagination will serve as a valuable resource for future fluid‐flow studies in an enclosed industrial environment.

Numerical Study on Natural Convection of Alumina-water Nanofluid in a Square Cavity with Two Localized Heat Sources on Adjacent Surfaces

In the present work, results of a numerical study carried out using finite volume method, to investigate the fluid flow and heat transfer characteristics of Alumina ( Al2O3 ) nanoparticles in the base fluid (water) in a square cavity under natural convection mode are presented. The Semi Implicit Method for Pressure Linked Equations (SIMPLE) algorithm was used to solve the discretized momentum and energy equations. Constant temperature heat sources of same strength are placed on bottom and left vertical surfaces whereas the right surface was kept cold, while the top surface was maintained as adiabatic. The impact of Rayleigh number (RaN) ( 1000 to 106 ) and nanoparticles volume fraction (Φ = 0 %, 5 %, 10 %, 15 % and 20 %) on fluid and heat flow characteristics were numerically investigated and presented in the form of streamlines, isothermal lines, mid line horizontal and vertical velocity components, local Nusselt number ( Nuloc ) and average Nusselt number ( Nuavg ). The obtained results indicate, for lower RaN ( i.e; 103 ), conduction dominates over convection near heated surfaces and results in lower fluid velocities and poor heat transfer. For higher values of RaN ( RaN = 105 and 106 ) and volume fraction of nanoparticles, there was a significant increase in mid horizontal and vertical velocity components, Nuloc and Nuavg due to increase in convective heat transfer and thermal conductivity of nanofluid.

Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid

Abstract A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

NUMERICAL INVESTIGATION OF NATURAL CONVECTION WITH HEATED TUBES IN TUNNEL GREENHOUSE

In this research, a numerical study was carried out on heat transfer by natural convection, in a closed tunnel greenhouse, in the range of the Rayleigh number (103≤Ra≤106). Were considered in the study, the number of heating tubes used (1≤Nt≤7), which were equidistant inside the greenhouse volume, when the bottom at an average temperature and cold Roof. The governing equations written in a bicylindrical coordinates were discretized using the finite volume method and vorticity-stream function formulation; the resulting algebraic equations were solved using successive over relaxation method (S.O.R). First, the effect of the Rayleigh number on heat transfer was examined for a fixed number of tubes as reference (Nt = 3) and the number of tubes was varied to investigate the influence on heat transfer in the greenhouse. Finally, the results obtained were summarized in the form of isotherms and streamlines, and for the average Nusselt number profile; in addition to the horizontal and vertical velocities and temperatures. However, in the reference case, for low Rayleigh numbers, the heat transfer is dominated by pure conduction.With the increase of the Rayleigh number and the number of tubes Nt, the natural convection becomes more dominant and the heat transfer increases, and in general the heat transfer increase with the increasing number of tubes.

Double‐diffusive flow in a porous right‐angle trapezoidal enclosure with constant heat flux

A computation analysis is performed to study double‐diffusive natural convection in a right‐angle trapezoidal cavity packed with a porous medium. The horizontal top and bottom boundaries are insulated and impermeable. The vertical left sidewall is kept at a constant heat flux and high concentration, whereas the inclined sidewall is held at lower temperature and concentration. The dimensionless nonlinear system is solved by employing the finite difference method along the successive Under Relaxation technique. The findings are compared and validated with the existing literature for the Darcy flow driven through a single buoyancy effect (difference in density is only due to temperature variations) in a porous square enclosure. The numerical results are expressed in the form of streamlines, isotherms and iso‐concentrations, and local and average Nusselt and Sherwood numbers. It is observed that the buoyancy parameter reduces the dimensionless temperature of the cavity and increases the dimensionless concentration due to the strong impact of buoyancy. Smaller values of the Lewis number enhance heat transfer, whereas higher values reduce it. Moreover, the Rayleigh number and buoyancy parameter enhance both surface heat and concentration rates.

Thermal transport of radiative Williamson fluid over stretchable curved surface

The study of incompressible steady Williamson fluid flow is conducted in a curvilinear coordinate system. The flow is bounded below through curves stretchable sheet. Linear thermal radiation effects are considered to observe the heat flow in the system. The model was designed as an application to solar energy in thermal engineering processes. Employing suitable similarity transformations, a set of partial differential equations obtained from the flow situations are converted into a system of non-linear coupled ordinary differential equations. The subsequent equations are elucidated numerically via Runge-Kutta-4 along with the shooting algorithm. The outcomes for different flow properties are displayed and discussed both graphically and numerically. The observations shows that the curvature parameter reduces both velocity and temperature. Radiation parameter boosts the temperature of the fluid but reduces the local Nusselt number. Williamson fluid parameter has a reverse impact on velocity field but it works as a provoking agent for the case of thermal profile. The visual effects in the form of streamlines and isotherms are also presented for different Reynolds number.

Effect of partial magnetic field on thermo gravitational convection in an inclined cavity

The study presented gives a succinct overview of the effect of partially applied magnetic field on natural convective heat transfer in a differentially heated inclined cavity. The left and right sidewalls are differentially heated such that their temperatures are maintained (at T h and T c respectively), while the top and bottom walls have been assumed to be adiabatic, such that heat transfer through those walls can be neglected. The results are supposed to elucidate the effect of changing Rayleigh number (Ra), Hartmann number (Ha), and cavity inclination angle (f ) on the thermo-fluid phenomena. The analysis is carried out numerically utilizing finite volume based computing code. The results have been demonstrated in the form of streamlines, isotherms, and average Nusselt number. From the analysis, it is found that the flow structure and associated heat transfer characteristics are severely influenced by the studied range of governing parameters.

Oscillatory flow around a vertical wall-mounted cylinder: Flow pattern details

The interaction between surface gravity waves and a vertical wall-mounted rigid cylindrical structure such as a pier or vegetation involves various interdependent physical phenomena including the scouring process and the vertical mixing and horizontal dispersion of materials. As a step toward understanding this interaction, detailed flow fields of sinusoidal oscillatory flow passing a vertical wall-mounted cylinder are numerically investigated for three different wave conditions. With a moderately wide range of the Keulegan–Carpenter number from 6 to 20, numerical simulations are systematically performed, and the data are extensively investigated to determine the dynamic characteristics of the oscillatory flow past a wall-mounted cylinder. In this study, three-dimensional unsteady incompressible Navier–Stokes equations are solved using the open-source software, OpenFOAM®. Grid-convergence tests are conducted, and the undisturbed oscillating Stokes boundary-layer determined by numerical simulations is validated by a good agreement with the analytical solution. Flow details in the form of profiles, streamlines, and contours of calculated turbulence fields are presented. Coherent structure dynamics is illustrated using iso-surfaces of the Q-criterion. The synthesis of various flow variables presents a mechanistic view of the bed shear and processes responsible for scour near the cylinder-wall junction.

ISLAMIC MAQASHID APPROACH ON DROPSHIPPING PRACTICES

Dropshipping is a streamlined form of retail business. In this business, there are three actors involved; buyers, sellers (owners of goods), and drop shippers. The series of product sales through the dropshipping system is when the customer has paid for a product to the drop shipper. The drop shipper then pays the seller as well as sends the products ordered by the customer. Furthermore, the owner of the goods will send the product ordered by the customer directly. This study aims to explain the scheme of buying and selling online through the dropshipping system from the Islamic economic perspective. This research is descriptive qualitative research by analyzing the dropshipping from the Islamic perspective. The study concluded that dropshipping trading is allowed in the perspective of Islamic economics by using the syirkah contract, known as syirkah wujuh and simsarah (broker/agent). Both types of this transaction can legalize dropshipping as long as there are no elements of gharar/frauds. This dropshipping practice is following maqashid syariah which will provide a rational and substantial pattern of thinking in looking at forms of transactions to respond to the progress of growing business.

Effect of non-uniform diameter and fractal dimension of Al2O3 nanoparticle on double-diffusion in tilted enclosure

The present numerical work examines the effect of variable fractal dimension and non-uniform diameter of Al2O3 nanoparticle on heat and mass transfer due to natural convection in tilted square enclosures. Enclosures are filled with Al2O3/H2O nanofluid and under constant heat and mass fluxes boundary conditions. The Navier-Stokes, energy, and concentration equations are solved numerically by finite difference method. Xu’s model [1] and Jang’s model [2] have been used to compute effective thermal conductivity and dynamic viscosity, respectively. Present work validated with published work experimentally and numerically. Influence of Al2O3 nanoparticle’s non-uniform diameter, fractal dimension, and the ratio of minimum to maximum diameter are illustrated in the form of streamlines, heatlines, and masslines in addition to average Nusselt and Sherwood numbers at different enclosure tilt angles. Heat transfer increases with the decrement in mean nanoparticle diameter, and maximum at tilt angle of θ=45∘ is observed for all Rayleigh numbers. At weak buoyancy effect (Ra=5×103) and minimum mean nanoparticle diameter (dp=1nm), maximum of 30% enhancement in overall heat transfer is observed at tilt angle, θ=45∘ and nanoparticle volume fraction, ϕ=5%. At strong buoyancy effect (Ra=1×105), maximum of 66% enhancement in overall heat transfer is observed at same nanoparticle conditions and tilt angle. An increase in Rayleigh and Lewis number decreases the tilt angle at which maximum mass transfer occurred. Mass transfer is maximum in the range of mean nanoparticle diameter of dp=25−50 nm.

Upper Openings Ventilation System Study of the Building by the Lattice Boltzmann Model

We present in this work a numerical study of a ventilation system in a room with two openings in the ceiling and a floor heating indicated by constant heat temperature. The double population thermal lattice Boltzmann method is used, with nine velocities model D2Q9 for the dynamic field and a five velocities model D2Q5 for the temperature field. The results are presented in the form of streamlines, temperature contour and velocity profile, and analysed as a function of the Richardson number.

Numerical study of turbulent natural convection of nanofluids in differentially heated rectangular cavities

In this work we study numerically the turbulent natural convection of nanofluids (water + Al2O3/NTC/Cu) in rectangular cavities differentially heated. The objective is to compare the effect of the macro-structural aspect of the rectangular cavity and the effect of the types of nanofluids studied on the thermal exchange by turbulent natural convection in this type of geometry. Therefore, we have numerically treated the cases of these three nanofluids, for different particles volume fractions (0 ? ? ? 0.06) and for different form ratios of the rectangular cavity. The standard k-? turbulence model is used to take into account the effects of turbulence. The governing equations are discretized by the finite volume method using the power law scheme which offers a good stability characteristic in this type of flow. The results are presented in the form of streamlines and isothermal lines. The variation of the average Nusselt number is calculated as a function of the types of nanoparticles, of theirs particles volume fractions, for different form ratios of the cavity, and for different Rayleigh numbers. The results show that the average Nusselt number is greater as the form ratio is large and that the effect of the use of CNT in suspension in a water prevails for voluminal fractions and large Rayleigh numbers.

NATURAL CONVECTION HEAT TRANSFER INSIDE HORIZONTAL CIRCULAR ENCLOSURE WITH TRIANGULAR CYLINDER AT DIFFERENT ANGLES OF INCLINATION

Numerical simulation study by using Fluent CFD software has been carried out to investigate the steady. laminar natural convective heat transfer for air formed by heated inner equilateral triangular cylinder inside cold circular enclosure. The triangular cylinder was located at center of enclosure with four radius ratio RR=1.5, 2, 2.5, and 3; and four inclination angles, θ=0o (the base of triangle cylinder at bottom), 20o, 40o and 60o (the base of triangle at top). All numerical calculations were performed in the range of Rayleigh number extends from 103 to 107. The fluid and temperature fields were represented in the form of streamlines and isotherms. Results show that, As Rayleigh number increases, the streamlines become more concentrated next to the walls and the center of vortex displays upward towards the central plane of enclosure. Also, there is no effect for the inclination angle of triangular cylinder on the peak values of local Nusselt number along the inner surface of circular cylinder except the positions of these peaks due to turning of thermal plumes.

Increase in high-lift devices efficiency of swept wing

The use of Fowler flaps and slotted slats in sweptwing aircraft is the standard solution to increase wing lift at take off and landing. In the literature this solution is known as a classical option of high-lift system of commercial subsonic aircraft. The results of numerical and experimental studies of some solutions intended to increase the efficiency of classical high-lift devices are presented. The concept of the trailing-edge devices called "the adaptive flap" is considered as a way to improve flap efficiency. The adaptive concept is characterized by the integration of spoiler downward deflection to the Fowler flap function. Integration of the spoiler with a movable flap provided an increase of lift in the linear region due to flaps deflected to a higher angle. The steeper upwash angle at a leading-edge device may be the reason of an early stall of the main wing. To protect the leading edge a slotted Kruger flap with streamline form has been used. Preliminary design of classical and improved high-lift systems included the determination of aerodynamic shapes and the optimized position for the high-lift devices. Aerodynamic analysis and design were carried out using 2D RANS Navier-Stokes method. A comparison of computed results has shown visible aerodynamic advantages of an improved high-lift system for maximum lift coefficient and refining the behavior of stall characteristics at high angles of attack. The results of wind tunnel tests of aircraft model with adaptive flap showed its effectiveness.

Numerical Simulation of Free Convection in a Three-Dimensional Enclosure Full of Nanofluid with the Existence a Magnetic Field

A numerical analysis was performed to study the influence of a magnetic field in free convection in a cube full with nanofluid. To solve the equation, we appeal to finite volume method. The SIMPLEC algorithm is used for pressure-velocity coupling. All walls are adiabatic, except for the left and right walls that are heated differently. The effects of the Rayleigh and Hartmann numbers, as well as the volume fraction of nanometric particles were studied. Results are conveyed in the form of isotherms, streamlines, velocity curves and Nusselt numbers. It has been shown that as the percentage of nanoparticles increases and the number of Rayleigh increases, heat transfer improves. Hartman number has considerable influence on hydrodynamic and thermal field.

The Effects of Internal Heat Generation or Absorption on Mixed Convection in a Lid-Driven Rectangular Cavity using Finite Volume Method

Mixed convection heat transfer in cavities is a significant phenomenon in numerous engineering fields, such as nuclear reactors, solar energy storage, and heat exchangers. Despite acknowledging that a square is a basic shape found in these systems, not all the figures are geometrical. Less attention was given to the rectangle cavity even though it could be found in these systems. Various internal reactions could occur inside the systems, especially in geothermal heat exchangers. Therefore, this research aims to analyze the effect of internal heat generation or absorption in a two-dimensional (2D) horizontal cavity to the fluid flow and heat transfer process numerically. The vertical walls are well insulated. Meanwhile, the top and bottom walls are kept at and , respectively, where . The top wall moves at a constant speed from left to right. The finite volume method (FEM) and SIMPLE algorithm are employed to discretize the governing equations. Next, the algebraic equations are solved iteratively using the tri-diagonal matrix algorithm (TDMA). The influences of heat generation or absorption parameters are investigated in terms of the flow, heat transfer, and Nusselt number. The numerical results are plotted in the form of streamlines and isotherms. It is found that the presence of heat generation or absorption has a significant effect on the fluid flow and heat transfer process in the horizontal cavity. Overall, for internal heat generation, the heat transfer rate decreases, while the opposite pattern can be observed for the case of internal heat absorption. However, for Ri = 10.0, as the heat generation's value increases from 2 to 4, the heat transfer rate is the same.

FINITE ELEMENT SIMULATIONS OF FREE CONVECTION FLOW INSIDE A POROUS INCLINED CAVITY FILLED WITH MICROPOLAR FLUID

The present study predicts the effects of inclined magnetic field and thermal boundary conditions on the natural convection flow inside a porous conduit filled with micropolar fluid. The lower wall is cold and the inclined walls of the conduit are constantly or sinusoidally heated. The nonlinear partial differential equations are solved by employing a robust Galerkin finite element scheme. The pressure term in this scheme is eliminated by using a penalty method. The value of penalty parameter ∏ is set at 107 to ensure consistent solutions. The results are presented in the form of streamlines, temperature contours, and local and average Nusselt numbers. The results show that the magnitude of the stream function decreases with increasing the inclination angle of the applied magnetic field, Hartmann number, and micropolar parameter while an opposite trend is noted against Darcy number, Prandtl number, and inclination angle of cavity. The average Nusselt number is substantially higher for the uniform heated case in comparison to the sinusoidal heated case regardless of the choice of other physical parameters. Further, the average Nusselt numbers decrease by increasing micropolar parameter (R0) and Hartmann number (Ha) while an opposite trend prevails with increasing rest of the parameters (ω, Da, Pr) for both cases. It is noted that when the cavity is inclined at 45° or 90° and magnetic field is applied either along the x-axis (φ = 0°) or inclined at 45° or 90°, only clockwise circulation exists inside the conduit. The presence of counterclockwise circulating roll in the top corner of the cavity is linked with the choice of heating mode adopted at the side walls. In fact, such circulations are more likely to appear for the case of nonuniform heated side walls. The solution is benchmarked with the previous available data. The analysis presented here has potential application in solar collectors and porous heat exchanges.