A. Rasekh^a,*, D.D. Ganji^b, S. Tavakoli^b

Frontiers in Heat and Mass Transfer, Vol.3, No.4, pp. 1-6, 2012, DOI:10.5098/hmt.v3.4.3003

Abstract The present paper deals with the analysis of boundary layer flow and heat transfer of a nanofluid over a stretching circular cylinder in the presence of non-uniform heat source/sink. The governing system of partial differential equations is converted to ordinary differential equations by using similarity transformations, which are then solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The solutions for the temperature and nanoparticle concentration distributions depend on six parameters, Prandtl number Pr, Lewis number Le, the Brownian motion parameter Nb, the thermophoresis parameter Nt, and non-uniform heat generation/absorption parameters A*, B*. Numerical results are presented both in tabular… More >

Sergiy Reutskiy¹, Yuhui Zhang^2,*, Jun Lu^3,*, Ciren Pubu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.2, pp. 1583-1612, 2024, DOI:10.32604/cmes.2023.044878

Abstract This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations (FODEs) which have been widely used in modeling various phenomena in engineering and science. An approximate solution of the system is sought in the form of the finite series over the Müntz polynomials. By using the collocation procedure in the time interval, one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure. This technique also serves as the basis for solving the time-fractional partial differential equations (PDEs). The modified radial basis… More >

Greg Ball, John Polansky, Tarik Kaya^*

Frontiers in Heat and Mass Transfer, Vol.4, No.1, pp. 1-9, 2013, DOI:10.5098/hmt.v4.1.3002

Abstract The fluid flow and heat transfer in an evaporating extended meniscus are numerically studied. Continuity, momentum, energy equations and the Kelvin-Clapeyron model are used to develop a third order, non-linear ordinary differential equation which governs the evaporating thin film. It is shown that the numerical results strongly depend on the choice of the accommodation coefficient and Hamaker constant as well as the initial perturbations. Therefore, in the absence of experimentally verified values, the numerical solutions should be considered as qualitative at best. It is found that the numerical results produce negative liquid pressures under certain specific conditions. This result may… 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 Sherwood numbers. 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 present results compared with previously… 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. It is found that in… More >

M. Umeshaiah¹ , M. R. Krishnamurthy² , N.G. Rudraswamy³ , B. J. Gireesha⁴, B.C. Prasannakumara^5,*

Frontiers in Heat and Mass Transfer, Vol.9, pp. 1-8, 2017, DOI:10.5098/hmt.9.4

Abstract This article presents the effect of nonlinear thermal radiation on boundary layer flow and heat transfer of Carreau fluid model over a nonlinear stretching sheet embedded in a porous medium in the presence of non-uniform heat source/sink and viscous dissipation with convective boundary condition. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations using similarity transformation, which is then solved numerically by the fourth-fifth order Runge–Kutta-Fehlberg integration scheme featuring a shooting technique. The influence of significant parameters such as power law index parameter, Stretching parameter, Weissenberg number, permeability parameter, temperature… 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 and discussed. The present results… More >

Elyazid Flilihi, Mohammed Sriti, Driss Achemlal

Frontiers in Heat and Mass Transfer, Vol.12, pp. 1-10, 2019, DOI:10.5098/hmt.12.12

Abstract A numerical investigation is performed to analyze the transient laminar free convection over an isothermal inclined plate embedded in a saturated porous medium with the viscous dissipation effects. The flow in the porous medium is modeled with the Darcy-Brinkman- Forchheimer model, taking into account the convective term. The dimensionless nonlinear partial differential equations are solved numerically using an explicit finite difference method. The effects of different parameters: (1 ≤ Re ≤ 10 ; 10⁻² ≤ Da ≤ 10 ; 0 ≤ Gr ≤ 50 ; 0 ≤ F r ≤ 3 ; 0 ≤ Ec ≤ 1 ; 0 ≤… More >