Asad Ejaz¹, Imran Abbas¹, Yasir Nawaz¹, Muhammad Shoaib Arif¹, Wasfi Shatanawi^2,3,4,*, Javeria Nawaz Abbasi⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.125, No.3, pp. 1119-1134, 2020, DOI:10.32604/cmes.2020.012091

Abstract In the present research, Tiwari and Das model are used for the impact of a magnetic field on non-Newtonian nanofluid flow in the presence of injection and suction. The PDEs are converted into ordinary differential equations (ODEs) using the similarity method. The obtained ordinary differential equations are solved numerically using shooting method along with RK-4. Part of the present study uses nanoparticles (NPs) like TiO₂ and Al₂O₃ and sodium carboxymethyl cellulose (CMC/water) is considered as a base fluid (BF). This study is conducted to find the influence of nanoparticles, Prandtl number, and magnetic field on velocity and temperature profile, however,… More >

F. Mabood¹, T. A. Yusuf², A. M. Rashad³, W. A. Khan^4,*, Hossam A. Nabwey^5,6

CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 575-587, 2021, DOI:10.32604/cmc.2020.012505

Abstract The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration,… More >

Hammad Alotaibi^1,*, Saeed Althubiti¹, Mohamed R. Eid^2,3, K. L. Mahny⁴

CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 229-245, 2021, DOI:10.32604/cmc.2020.012234

Abstract This paper introduces the effect of heat absorption (generation) and suction (injection) on magnetohydrodynamic (MHD) boundary-layer flow of Casson nanofluid (CNF) via a non-linear stretching surface with the viscous dissipation in two dimensions. By utilizing the similarity transformations, the leading PDEs are transformed into a set of ODEs with adequate boundary conditions and then resolved numerically by (4–5)^th-order Runge-Kutta Fehlberg procedure based on the shooting technique. Numerical computations are carried out by Maple 15 software. With the support of graphs, the impact of dimensionless control parameters on the nanoparticle concentration profiles, the temperature, and the flow velocity are studied. Other… More >

Liaquat Ali Lund^1,2,*, Zurni Omar¹, Ilyas Khan³, El-Sayed M. Sherif^4,5

CMC-Computers, Materials & Continua, Vol.66, No.1, pp. 127-139, 2021, DOI:10.32604/cmc.2020.013120

Abstract In this study, magnetohydrodynamic (MHD) three-dimensional (3D) flow of alumina (Al₂O₃) and copper (Cu) nanoparticles of an electrically conducting incompressible fluid in a rotating frame has been investigated. The shrinking surface generates the flow that also has been examined. The single-phase (i.e., Tiwari and Das) model is implemented for the hybrid nanofluid transport phenomena. Results for alumina and copper nanomaterials in the water base fluid are achieved. Boundary layer approximations are used to reduce governing partial differential (PDEs) system into the system of the ordinary differential equations (ODEs). The three-stage Lobatto IIIa method in bvp4c solver is applied for solutions… More >

Muhammad Saqib¹, Hanifa Hanif^{1, 2}, T. Abdeljawad^{3, 4, 5}, Ilyas Khan^{6, *}, Sharidan Shafie¹, Kottakkaran Sooppy Nisar⁷

CMC-Computers, Materials & Continua, Vol.65, No.3, pp. 1959-1973, 2020, DOI:10.32604/cmc.2020.011339

Abstract The idea of fractional derivatives is applied to several problems of viscoelastic fluid. However, most of these problems (fluid problems), were studied analytically using different integral transform techniques, as most of these problems are linear. The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations. Most importantly, in the nonlinear problems, either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems (without developing the fractional model even using artificial replacement) are solved. These problems were mostly solved for steady-state fluid problems.… More >

K. Ganesh Kumar^{1, *}, S. Manjunatha², N. G. Rudraswamy³

FDMP-Fluid Dynamics & Materials Processing, Vol.16, No.2, pp. 131-146, 2020, DOI:10.32604/fdmp.2020.0152

Abstract Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated. The converted set of boundary layer equations are solved numerically by RKF-45 method. Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters. Furthermore, the skin friction coefficient and Nusselt number are also presented in Tabs. 2 and 3. It is found that the heat transfer rates are advanced in occurrence of nonlinear radiation compered to linear radiation. Also, it is noticed that velocity and temperature profile increases by increasing… More >

Naeem Faraz^{1, *}, Yasir Khan², Amna Anjum¹, Anwar Hussain³

CMES-Computer Modeling in Engineering & Sciences, Vol.122, No.3, pp. 1099-1118, 2020, DOI:10.32604/cmes.2020.08389

Abstract Current research is about the injection of a viscous fluid in the presence of a transverse uniform magnetic field to reduce the sliding drag. There is a slip-on both the slider and the ground in the two cases, for example, a long porous slider and a circular porous slider. By utilizing similarity transformation Navier-Stokes equations are converted into coupled equations which are tackled by Integral Transform Method. Solutions are obtained for different values of Reynolds numbers, velocity slip, and magnetic field. We found that surface slip and Reynolds number has a substantial influence on the lift and drag of long… More >

Yasir Nawaz¹, Muhammad Shoaib Arif ¹, Mairaj Bibi^{2, *}, Javeria Nawaz Abbasi², Umer Javed³, Amna Nazeer²

CMC-Computers, Materials & Continua, Vol.62, No.2, pp. 657-677, 2020, DOI:10.32604/cmc.2020.08584

Abstract Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent Algorithm to solve the resulted difference equation. The flow problem is constructed using continuity, and Navier Stoke equations and these PDEs are further converted into boundary value problem by applying suitable similarity transformations. A central finite difference method is proposed that gives third-order accuracy using three grid points. The stability conditions of the present proposed method using a Gauss-Seidel iterative procedure is found using VonNeumann stability criteria and order of… More >

Mohamed Abd El-Aziz^{1, 2}, A. M. Aly^{1, 3, *}

CMC-Computers, Materials & Continua, Vol.62, No.2, pp. 525-549, 2020, DOI:10.32604/cmc.2020.08576

Abstract This study focusses on the numerical investigations of boundary layer flow for magnetohydrodynamic (MHD) and a power-law nanofluid containing gyrotactic microorganisms on an exponentially stretching surface with zero nanoparticle mass flux and convective heating. The nonlinear system of the governing equations is transformed and solved by Runge-Kutta-Fehlberg method. The impacts of the transverse magnetic field, bioconvection parameters, Lewis number, nanofluid parameters, Prandtl number and power-law index on the velocity, temperature, nanoparticle volume fraction, density of motile microorganism profiles is explored. In addition, the impacts of these parameters on local skin-friction coefficient, local Nusselt, local Sherwood numbers and local density number… More >

S . Samantha Kumari^1,*, G. Sankara Sekhar Raju²

FDMP-Fluid Dynamics & Materials Processing, Vol.15, No.5, pp. 471-489, 2019, DOI:10.32604/fdmp.2019.04222

Abstract This paper investigates the chemical reaction and thermal radiation effects on unsteady MHD free convective flow past a vertical porous plate in the presence of heat absorption/generation. The novelty of present investigation is that the temperature and concentration of the plate are span wise cosinusoidally unsteady with time. The second order perturbation technique is employed to study the non-linear partial differential equations which govern the fluid flow. The effects of magnetic parameter, radiation, Eckert number, Schmidt number and chemical reaction parameters on velocity, temperature and concentration distributions as well as skin friction coefficients, the rate of heat transfer and the… More >