Mahdi Saedshoar Heris¹, Mohammad Javidi¹, Bashir Ahmad^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.1, pp. 249-272, 2019, DOI:10.32604/cmes.2019.08080

Abstract In this paper, we propose numerical methods for the Riesz space fractional advection-dispersion equations with delay (RFADED). We utilize the fractional backward differential formulas method of second order (FBDF2) and weighted shifted Grünwald difference (WSGD) operators to approximate the Riesz fractional derivative and present the finite difference method for the RFADED. Firstly, the FBDF2 and the shifted Grünwald methods are introduced. Secondly, based on the FBDF2 method and the WSGD operators, the finite difference method is applied to the problem. We also show that our numerical schemes are conditionally stable and convergent with the accuracy More >

Hamzeh T. Alkasasbeh^*

Frontiers in Heat and Mass Transfer, Vol.10, pp. 1-8, 2018, DOI:10.5098/hmt.10.32

Abstract This paper focuses on the numerical solution for magnetohydrodynamic (MHD) flow of micropolar Casson fluid with thermal radiation over a horizontal circular cylinder. The nonlinear partial differential equations of the boundary layer are first transformed into a non-dimensional form and then solved numerically using an implicit finite difference scheme known as Keller-box method. The The effects of the emerging parameters, namely Casson fluid parameter, magnetic parameter, radiation parameter and micropolar parameter on the local Nusselt number and the local skin friction coefficient, as well as the temperature, velocity and angular velocity profiles are shown graphically More >

Somayeh Ezadi^a, Tofigh Allahviranloo^b

Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 193-204, 2018, DOI:10.1080/10798587.2017.1328812

Abstract In this article, the researcher at first focuses on introducing a linear regression based on the Z-number. In this regression, observations are real, but the coefficients and results of observations are unknown and in the form of Z-rating. Therefore, to estimate this type of regression, we have three distinct ways depending on different conditions dominating the problem. The three methods are a combination of artificial neural networks and fuzzy generalized improvements of the technique. Moreover the method of calculating the weights of the Z-number neural network has been mentioned and the stability of neural network More >

Raheleh Jafari^a, Wen Yu^a, Xiaoou Li^b

Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 151-158, 2018, DOI:10.1080/10798587.2017.1327154

Abstract In this paper, the uncertainty property is represented by the Z-number as the coefficients of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. We also extend the fuzzy equation into dual type, which is natural for linearin-parameter nonlinear systems. The solutions of these fuzzy equations are the controllers when the desired references are regarded as the outputs. The existence conditions of the solutions (controllability) are proposed. Two types of neural networks are implemented to approximate solutions of the fuzzy equations with Z-number coefficients. More >

Jiaquan Xie^1,3,*, Fuqiang Zhao^1,3, Zhibin Yao^1,3, Jun Zhang^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.115, No.1, pp. 67-84, 2018, DOI:10.3970/cmes.2018.115.067

Abstract In this paper, the three-variable shifted Jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of three-dimensional multi-term fractional-order PDEs with variable coefficients. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. The approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by three-variable shifted Jacobi polynomials are compared with the exact solutions. Furthermore some theorems and lemmas are introduced to verify the convergence results of our algorithm. Lastly, More >

G. Venkata Ramana Reddy^1,*, Y. Hari Krishna¹

FDMP-Fluid Dynamics & Materials Processing, Vol.14, No.3, pp. 213-222, 2018, DOI:10.3970/fdmp.2018.00411

Abstract The objective of the present problem is to investigate a two-dimensional unsteady flow of a viscous incompressible electrically conducting fluid over a stretching surface taking into account a transverse magnetic field of constant strength. Applying the similarity transformation, the governing boundary layer equations of the problem converted into nonlinear ordinary differential equations and then solved numerically using fourth order Runge-Kutta method with shooting technique. The effects of various parameters on the velocity and temperature fields as well as the skin-friction coefficient and Nusselt number are presented graphically and discussed qualitatively. More >

Noraihan Afiqah Rawi^a , Abdul Rahman Mohd Kasim^b , Zaiton Mat Isa^a , Aurangzaib Mangi^c , Sharidan Shafie^a,*

Frontiers in Heat and Mass Transfer, Vol.8, pp. 1-7, 2017, DOI:10.5098/hmt.8.12

Abstract Mixed convection flows of nanofluid past an inclined stretching sheet with g-jitter effect is studied in this paper. Water based nanofluid containing copper, copper oxide, aluminium oxide and silver nanoparticles are concerned. Coupled nonlinear partial differential equations are solved using Kellerbox method. The effect of solid nanoparticles volume fraction parameter, frequency of oscillation and inclination angle parameter is observed to reduce the skin friction and heat transfer coefficients whereas mixed convection parameter increases both skin friction and heat transfer coefficients. Present study also shows that, the heat transfer coefficient is highest for silver nanofluid. More >

K. Ganesh Kumar¹ , G.K. Ramesh^2,*, B.J. Gireesha¹

Frontiers in Heat and Mass Transfer, Vol.9, pp. 1-8, 2017, DOI:10.5098/hmt.9.32

Abstract The present article addresses the double-diffusive convection flow of the Casson fluid with thermal radiation. With suitable independent transformations, the governing partial differential equations are first transformed into ordinary differential equations. The converted equations are solved numerically by using Runge-Kutta-Fehlberg forth-fifth technique (RKF45 Method) via shooting technique. The eects of the emerging parameters, the skin friction coecient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields. Outcome shows that buoyancy forces due to temperature difference suppress the skin friction whereas it will enhance the local Nusselt and More >

Mahantesh M Nandeppanavar^a,*, S. Shakunthala^b

Frontiers in Heat and Mass Transfer, Vol.9, pp. 1-10, 2017, DOI:10.5098/hmt.9.27

Abstract In this paper, the buoyancy effect on flow and heat transfer characteristics of nanofluid in presence of carbon nanotubes due to a vertical plate is investigated. The obtained nonlinear PDE’s are converted to the non-linear ordinary differential equations by applying the similarity transformations corresponding to the boundary conditions. These boundary value problems are solved numerically using fourth order Runge-kutta method together with the efficient shooting iteration scheme. The nature of the flow and heat transfer are plotted and discussed in detail. It is noticed that buoyancy effect is very useful in cooling the system and More >

G.K. Ramesh^a,*, B.J. Gireesha^b

Frontiers in Heat and Mass Transfer, Vol.9, pp. 1-7, 2017, DOI:10.5098/hmt.9.3

Abstract The effect of non-linear thermal radiation on nanofluid flow over a riga plate is studied. Under some conditions, our problem reduces to the Blasius problem and Sakiadis problem. Similarity transformation is used to convert the governing steady Navier-Stokes equations into a system of coupled nonlinear differential equations, which are then solved numerically via Runge-Kutta-Fehlberg 45 order method along with a shooting method. Influence of parameters involved on velocity, temperature and concentration profiles is discussed with the help of graphical aid. Numerical results have been presented on the skin-friction coefficients, local Nusselt number and Sherwood number. More >