Browsing by Author "Khan, Ilyas"

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Citation - WoS: 9
Citation - Scopus: 14
Finite Element Least Square Technique for Newtonian Fluid Flow Through a Semicircular Cylinder of Recirculating Region Via Comsol Multiphysics
(Hindawi Ltd, 2020) Memon, Abid A.; Memon, M. Asif; Bhatti, Kaleemullah; Shaikh, Gul M.; Baleanu, Dumitru; Alhussain, Ziyad A.; Khan, Ilyas
This article aims to study Newtonian fluid flow modeling and simulation through a rectangular channel embedded in a semicircular cylinder with the range of Reynolds number from 100 to 1500. The fluid is considered as laminar and Newtonian, and the problem is time independent. A numerical procedure of finite element's least Square technique is implemented through COMSOL multiphysics 5.4. The problem is validated through asymptotic solution governed through the screen boundary condition. The vortex length of the recirculating region formed at the back of the cylinder and orientation of velocity field and pressure will be discussed by three horizontal and four vertical lines along the recirculating region in terms of Reynolds number. It was found that the two vortices of unequal size have appeared and the lengths of these vortices are increased with the increase Reynolds number. Also, the empirical equations through the linear regression procedure were determined for those vortices. The orientation of the velocity magnitude as well as pressure along the lines passing through the center of upper and lower vortices are the same.
Citation - WoS: 16
Citation - Scopus: 17
Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (Seiqv) Reaction-Diffusion Epidemic Model
(Frontiers Media Sa, 2020) Fatima, Mehreen; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Ahmed, Nauman
In this paper, two structure-preserving nonstandard finite difference (NSFD) operator splitting schemes are designed for the solution of reaction diffusion epidemic models. The proposed schemes preserve all the essential properties possessed by the continuous systems. These schemes are applied on a diffusive SEIQV epidemic model with a saturated incidence rate to validate the results. Furthermore, the stability of the continuous system is proved, and the bifurcation value is evaluated. A comparison is also made with the existing operator splitting numerical scheme. Simulations are also performed for numerical experiments.
Citation - WoS: 80
Citation - Scopus: 94
Entropy Generation and Consequences of Mhd in Darcy-Forchheimer Nanofluid Flow Bounded by Non-Linearly Stretching Surface
(Mdpi, 2020) Shafiq, Anum; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Shahzadi, Gullnaz; Rasool, Ghulam
Present communication aims to inspect the entropy optimization, heat and mass transport in Darcy-Forchheimer nanofluid flow surrounded by a non-linearly stretching surface. Navier-Stokes model based governing equations for non-Newtonian nanofluids having symmetric components in various terms are considered. Non-linear stretching is assumed to be the driving force whereas influence of thermal radiation, Brownian diffusion, dissipation and thermophoresis is considered. Importantly, entropy optimization is performed using second law of thermodynamics. Governing problems are converted into nonlinear ordinary problems (ODEs) using suitably adjusted transformations. RK-45 based built-in shooting mechanism is used to solve the problems. Final outcomes are plotted graphically. In addition to velocity, temperature, concentration and Bejan number, the stream lines, contour graphs and density graphs have been prepared. For their industrial and engineering importance, results for wall-drag force, heat flux (Nusselt) rate and mass flux (Sherwood) rate are also given in tabular data form. Outputs indicate that velocity reduces for Forchheimer number as well as for the porosity factor. However, a rise is noted in temperature distribution for elevated values of thermal radiation. Entropy optimization shows enhancement for larger values of temperature difference ratio. Skin-friction enhances for all relevant parameters involved in momentum equation.
Citation - WoS: 26
Citation - Scopus: 36
Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of a Spatially Two-Dimensional Burgers-Huxley Equation
(Mdpi, 2020) Bano, Shahida; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Hussain, Amjad
In this paper, we investigate a spatially two-dimensional Burgers-Huxley equation that depicts the interaction between convection effects, diffusion transport, reaction gadget, nerve proliferation in neurophysics, as well as motion in liquid crystals. We have used the Lie symmetry method to study the vector fields, optimal systems of first order, symmetry reductions, and exact solutions. Furthermore, using the power series method, a set of series solutions are obtained. Finally, conservation laws are derived using optimal systems.
Citation - WoS: 37
Citation - Scopus: 39
Enhanced Heat Transfer in Moderately Ionized Liquid Due To Hybrid Mos2/Sio2 Nanofluids Exposed by Nonlinear Radiation: Stability Analysis
(Mdpi, 2020) Zaib, A.; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Umair
This study considers ethylene-glycol as a moderate ionized regular liquid whose rheological behavior can be analyzed through the relations of the Carreau stress-strain tensor. Hybrid nanoliquids are potent liquids that give better performance for heat transfer and the properties of thermo physical than regular heat transfer liquids (water, ethylene glycol, and oil) and nanoliquids by single nanomaterials. Here, a type of hybrid nanoliquid involving silicon oxide (SiO2) and Molybdenum disulfide (MoS2) nanoparticles with ethylene glycol as a base liquid are considered. In addition, the impact of nonlinear radiation along with Lorentz force is invoked. Similarity variables are utilized to acquire the numerical findings and their solutions for transmuting ordinary differential equations (ODEs). Using bvp4c from MATLAB, we can obtain these quantitative and numerical results of the converted nonlinear equations. The impacts of the pertinent constraints on the temperature distribution, velocity, Nusselt number, and skin friction are estimated. The outcomes indicate that the double-edged methods for the results originate from the precise values of the permeable parameters. Further, the critical values (S-c = 1.9699, 2.0700 and 2.2370) are enhanced due to the influence of the local Weissenberg number. This implies that the increasing value of the local Weissenberg number accelerate the boundary layer separation. Furthermore, a stability investigation is performed and confirms that the first solution is a physically reliable solution.
Citation - WoS: 86
Citation - Scopus: 120
Analysis and Dynamics of Fractional Order Mathematical Model of Covid-19 in Nigeria Using Atangana-Baleanu Operator
(Tech Science Press, 2021) Shaikh, Amjad S.; Ibrahim, Mohammed O.; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khan, Ilyas; Abioye, Adesoye I.; Peter, Olumuyiwa J.
We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R-0 is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana-Baleanu fractional derivative operator and existence criteria of solution for the operator is established. We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model. We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations. The impacts of various biological parameters on transmission dynamics of COVID-19 is examined. These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease. In the end, the obtained results are demonstrated graphically to justify our theoretical findings.
Citation - WoS: 9
Citation - Scopus: 9
Insights Into the Stability of Mixed Convective Darcy-Forchheimer Flows of Cross Liquids From a Vertical Plate With Consideration of the Significant Impact of Velocity and Thermal Slip Conditions
(Mdpi, 2020) Zaib, Aurang; Khan, Ilyas; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khan, Umair
This paper reflects the effects of velocity and thermal slip conditions on the stagnation-point mixed convective flow of Cross liquid moving over a vertical plate entrenched in a Darcy-Forchheimer porous medium. A Cross liquid is a type of non-Newtonian liquid whose viscosity depends on the shear rate. The leading partial differential equations (PDEs) are altered to nonlinear ordinary differential equations (ODEs) via feasible similarity transformations. These transmuted equations are computed numerically through the bvp4c solver. The authority of sundry parameters on the temperature and velocity distributions is examined graphically. In addition, the characteristics of heat transfer are analyzed in the presence of the impact of drag forces. The outcomes reveal that the permeability parameter decelerates the drag forces and declines the rate of heat transfer in both forms of solutions. Moreover, it is found that the drag forces decline with the growing value of the Weissenberg parameter in the upper branch solutions, while a reverse trend is revealed in the lower branch solutions. However, the rate of heat transfer shows a diminishing behavior with an increasing value of the Weissenberg parameter.
Citation - WoS: 2
Citation - Scopus: 2
Standard Routine Techniques of Modeling of Tick-Borne Encephalitis
(de Gruyter Poland Sp Z O O, 2020) Arooj, Aroosa; Yasmin, Nusrat; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Akram, Saima
Tick-borne encephalitis (TBE) is a flaviviral vector-borne disease, which is spread by a tick named Ixodes persulcatus in domestic animals as well as in humans. In this article, susceptible, exposed, infected, recovered model; with no immunity after getting recovered is taken. The only possible immunity is before getting the disease (in our model). The vaccination details are also discussed in the article. Hence, SEIS (susceptible, exposed, infected and again susceptible with zero removal from the specie compartment) is used to construct a mathematical model of TBE. TBE is acute inflammation of the brain parenchyma. After becoming viral in European states and some Asian countries, especially in China, this is an emerging viral disease in Pakistan. After constructing a model, formula for the basic reproduction number R-0-like threshold has been derived by using the next-generation matrix method. The formula for R-0-like threshold is used to evaluate whether the disease is going to be outbroken in the respective area from which the specific data are taken into consideration. The main motivation behind selection of this topic is to address the unawareness of this disease specifically in Pakistan and in its neighboring countries when there persists probability for the outbreak of this disease. Some equilibrium points and their local stability is also discussed. Numerical computations and graphs are also presented to validate the results.
Citation - WoS: 49
Citation - Scopus: 57
Dual Similarity Solutions of Mhd Stagnation Point Flow of Casson Fluid With Effect of Thermal Radiation and Viscous Dissipation: Stability Analysis
(Nature Portfolio, 2020) Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat Ali
In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.
Citation - WoS: 18
Citation - Scopus: 24
Rotating 3d Flow of Hybrid Nanofluid on Exponentially Shrinking Sheet: Symmetrical Solution and Duality
(Mdpi, 2020) Omar, Zurni; Dero, Sumera; Baleanu, Dumitru; Khan, Ilyas; Lund, Liaquat Ali
This article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina (Al2O3), and copper (Cu) as solid nanoparticles. The system of governing partial differential equations (PDEs) was transformed by an exponential similarity variable into the equivalent system of ordinary differential equations (ODEs). By applying a three-stage Labatto III-A method that is available in bvp4c solver in the Matlab software, the resultant system of ODEs was solved numerically. In the case of the hybrid nanofluid, the heat transfer rate improves relative to the viscous fluid and regular nanofluid. Two branches were obtained in certain ranges of the involved parameters. The results of the stability analysis revealed that the upper branch is stable. Moreover, the results also indicated that the equations of the hybrid nanofluid have a symmetrical solution for different values of the rotation parameter (Omega).
Citation - WoS: 1
Citation - Scopus: 1
Analysis of Positive Measure Reducibility for Quasi-Periodic Linear Systems Under Brjuno-Russmann Condition
(Amer inst Mathematical Sciences-aims, 2022) Ismaeel, Tariq; Ahmad, Riaz; Khan, Ilyas; Baleanu, Dumitru; Afzal, Muhammad
In this article, we discuss the positive measure reducibility for quasi-periodic linear systems close to a constant which is defined as: dx/dt = (A(lambda) + Q(phi, lambda))x, (phi) over dot = omega, where omega is a Brjuno vector and parameter lambda is an element of (a, b). The result is proved by using the KAM method, Brjuno-Russmann condition, and non-degeneracy condition.
Citation - WoS: 13
Citation - Scopus: 13
Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface
(Mdpi, 2020) Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat Ali
In this article, we reconsidered the problem of Aurangzaib et al., and reproduced the results for triple solutions. The system of governing equations has been transformed into the system of non-linear ordinary differential equations (ODEs) by using exponential similarity transformation. The system of ODEs is reduced to initial value problems (IVPs) by employing the shooting method before solving IVPs by the Runge Kutta method. The results reveal that there are ranges of multiple solutions, triple solutions, and a single solution. However, Aurangzaib et al., only found dual solutions. The effect of the micropolar parameter, suction parameter, and Prandtl number on velocity, angular velocity, and temperature profiles have been taken into account. Stability analysis of triple solutions is performed and found that a physically possible stable solution is the first one, while all leftover solutions are not stable and cannot be experimentally seen.
Citation - WoS: 20
Citation - Scopus: 19
Hydromagnetic Flow of Micropolar Nanofluid
(Mdpi, 2020) Anwar, Muhammad Imran; Misiran, Masnita; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Seikh, Asiful H.; Rafique, Khuram
Similar to other fluids (Newtonian and non-Newtonian), micropolar fluid also exhibits symmetric flow and exact symmetric solution similar to the Navier-Stokes equation; however, it is not always realizable. In this article, the Buongiorno mathematical model of hydromagnetic micropolar nanofluid is considered. A joint phenomenon of heat and mass transfer is studied in this work. This model indeed incorporates two important effects, namely, the Brownian motion and the thermophoretic. In addition, the effects of magnetohydrodynamic (MHD) and chemical reaction are considered. The fluid is taken over a slanted, stretching surface making an inclination with the vertical one. Suitable similarity transformations are applied to develop a nonlinear transformed model in terms of ODEs (ordinary differential equations). For the numerical simulations, an efficient, stable, and reliable scheme of Keller-box is applied to the transformed model. More exactly, the governing system of equations is written in the first order system and then arranged in the forms of a matrix system using the block-tridiagonal factorization. These numerical simulations are then arranged in graphs for various parameters of interest. The physical quantities including skin friction, Nusselt number, and Sherwood number along with different effects involved in the governing equations are also justified through graphs. The consequences reveal that concentration profile increases by increasing chemical reaction parameters. In addition, the Nusselt number and Sherwood number decreases by decreasing the inclination.
Citation - WoS: 37
Citation - Scopus: 38
Comparative Investigation on Mhd Nonlinear Radiative Flow Through a Moving Thin Needle Comprising Two Hybridized Aa7075 and Aa7072 Alloys Nanomaterials Through Binary Chemical Reaction With Activation Energy
(Elsevier, 2020) Zaib, A.; Khan, Ilyas; Baleanu, Dumitru; Sherif, El-Sayed M.; Khan, Umair
The intention of the current study is analyzing the significance of nonlinear radiation on magnetic field involving hybrid AA7075 and AA7072 alloys nanomaterials through thin needle. The scenario has been modeled mathematically by captivating the binary chemical reaction and activation energy. Similarity variables are deployed to change the system of PDE's into nonlinear ODE's and subsequently solved these equations through bvp4c solver. Influence of distinct material parameters on the velocity, concentration and temperature along with the correlated engineering features quantities such as drag force, heat and mass transfer rate are obtained and demonstrated via plots. The velocity of the liquid is declining function of magnetic field, while the temperature augments. In addition, obtained numerical results are contrasted through the available literature and appeared to be in admirable harmony. The current investigation shows the important features in solar hybrid alloy nano materials systems and aircraft technology. (C) 2020 The Authors. Published by Elsevier B.V.
Citation - WoS: 10
Citation - Scopus: 10
Comparative Thermal Performance in Sio2-H2o and (mos2-Sio2) Over a Curved Stretching Semi-Infinite Region: a Numerical Investigation
(Tech Science Press, 2021) Khan, Umar; Wahab, Hafiz Abdul; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ullah, Basharat
The investigation of Thermal performance in nanofluids and hybrid nanofluids over a curved stretching infinite region strengthens its roots in engineering and industry. Therefore, the comparative thermal analysis in SiO2-H2O and (MoS2-SiO2)-H2O is conducted over curved stretching surface. The model is reduced in the dimensional version via similarity transformation and then treated numerically. The velocity and thermal behavior for both the fluids is decorated against the preeminent parameters. From the analysis, it is examined that the motion of under consideration fluids declines against Fr and lambda. The thermal performance enhances for higher volumetric fraction and lambda. Further, it is noticed that thermal performance prevailed in (MoS2-SiO2)-H2O throughout the analysis. Therefore, (MoS2-SiO2)-H2O is better for industrial and engineering uses where high heat transfer is required to accomplished different processes of production.
Citation - WoS: 5
Citation - Scopus: 6
Influence of Interfacial Electrokinetic on Mhd Radiative Nanofluid Flow in a Permeable Microchannel With Brownian Motion and Thermophoresis Effects
(de Gruyter Poland Sp Z O O, 2020) Nie, Yufeng; Shah, Zahir; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Raees; Khan, Abdul Samad
In this study, the behavior of a microchannel flow is examined. The fluid is considered to be a nanofluid, which moves between two parallel flat plates in the presence of an electrical double layer. The Buongiorno nanofluid is considered with body force. In this study, the unphysical supposition presented in the preceding work to the discontinuity of the flow fled where the electrostatic potential in the central of the canal must be equal to zero is removed. The incorrect supposition that the pressure constant is preserved, which is considered a known form, is corrected. The current fresh model equation is modified by using dimensionless parameters to convert partial differential equations into ordinary differential equations. The transformed nonlinear equations are solved by the homotopy analysis method. The physical parameters, magnetic parameters, Eckert number, Lewis number, Brownian motion parameters, thermophoresis parameters, and Prandtl number are analyzed. The influence of both the viscous and Joule dissipation in the presence of magneto-hydrodynamic effect is examined.
Citation - WoS: 34
Citation - Scopus: 36
Mathematical Analysis of Entropy Generation in the Flow of Viscoelastic Nanofluid Through an Annular Region of Two Asymmetric Annuli Having Flexible Surfaces
(Mdpi, 2020) Gul, Ayesha; Khan, Ilyas; Ramesh, Katta; Khan, Sami Ullah; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Riaz, Arshad
In this manuscript, the authors developed the mathematical model for entropy generation analysis during the peristaltic propulsion of Jeffrey nanofluids passing in a midst of two eccentric asymmetric annuli. The model was structured by implementation of lubrication perspective and dimensionless strategy. Entropy generation caused by the irreversible influence of heat and mass transfer of nanofluid and viscous dissipation of the considered liquid was taken into consideration. The governing equations were handled by a powerful analytical technique (HPM). The comparison of total entropy with the partial entropy was also invoked by discussing Bejan number results. The influence of various associated variables on the profiles of velocity, temperature, nanoparticle concentration, entropy generation and Bejan number was formulated by portraying the figures. Mainly from graphical observations, we analyzed that, in the matter of thermophoresis parameter and Brownian motion parameter, entropy generation is thoroughly enhanced while inverse readings were reported for the temperature difference parameter and the ratio of temperature to concentration parameters.
Citation - WoS: 29
Citation - Scopus: 34
Magnetized Flow of Cu + Al2o3 + H2o Hybrid Nanofluid in Porous Medium: Analysis of Duality and Stability
(Mdpi, 2020) Omar, Zurni; Dero, Sumera; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat Ali
In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of S-c <= S and M-c <= M (S-c > S and M-c > M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised.
Citation - WoS: 51
Citation - Scopus: 53
Numerical Simulation of Mixed Convection Squeezing Flow of a Hybrid Nanofluid Containing Magnetized Ferroparticles in 50%:50% of Ethylene Glycol-Water Mixture Base Fluids Between Two Disks With the Presence of a Non-Linear Thermal Radiation Heat Flux
(Frontiers Media Sa, 2020) Khan, Umair; Zaib, A.; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy
Ferroliquids are an example of a colloidal suspension of magnetic nanomaterials and regular liquids. These fluids have numerous applications in medical science such as cell separation, targeting of drugs, magnetic resonance imaging, etc. The hybrid nanofluid is composed by scattering the magnetic nanomaterial of more than one type nanoparticles suspended into the base fluid. It has different scientific applications such as heat dissipation, dynamic sealing, damping, etc. Owing to the vast ferrofluid applications, the time-dependent squeezed flow of hybrid ferroliquids under the impact of non-linear radiation and mixed convection within two disks was explored for the first time in this analysis. Here, the cobalt and magnetite ferrofluids are considered and scattered in a 50%:50% mixture of water-EG (ethylene glycol). The similarity technique is used to reduce the leading PDEs into coupled non-linear ODEs. The transmuted equations together with recommended boundary restrictions are numerically solved via Matlab solver bvp4c. The opposing and assisting flows are considered. The impacts of an emerging parameter on fluid velocity and temperature field of hybrid ferroliquids are examined through the different graphical aids. The results showed that the opposite trend is scrutinized due to the magnetic influence on the temperature and velocity in the case of assisting and opposing flows. The velocity augments due to the volume fraction of nanoparticles in the assisting flow and declines in the opposing flow, while the opposite direction is noticed in the temperature field.
Citation - WoS: 10
Citation - Scopus: 13
Numerical Simulation of Drag Reduction on a Square Rod Detached With Two Control Rods at Various Gap Spacing Via Lattice Boltzmann Method
(Mdpi, 2020) Khalid, Asma; Khan, Ilyas; Shams-Ul-Islam; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Manzoor, Raheela
Numerical simulations are performed to examine the effect of size of control rods (d1) and spacing ratio (g) on flow around a square rod with upstream and downstream control rods aligned in-line using the lattice Boltzmann method (LBM). The Reynolds number (Re) is fixed at Re = 160, while the spacing between the main rod and control rods is taken in the range 1 <= g <= 5 and the size of the control rod is varied between 4 and 20. Seven different types of flow mods are observed in this study at different values of g and d1. Variation in force statistics, like mean drag coefficient (C-dmean), Strouhal number (St), root mean square values of drag (C-drms) and lift coe fficients (C-lrms), and percentage reduction in mean drag coefficient is discussed in detail. It was examined that vortex shedding completely suppressed at (g, d1) = (1, 12), (2, 12), and (2, 16) where steady flow mode exists. Moreover, it was found that at large gap spacing, where g = 5, the effect of control rods on the main rod vanishes. Due to this strong vortex shedding produced and as a result, maximum value of C-dmean is found at (g, d1) = (5, 8). The negative values of mean drag force are also observed at some gap spacing and size of control rods are due to the effect of thrust. Furthermore, the maximum percentage reduction in C-dmean is 121%, found at (g, d1) = (2, 20).