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  • Open Access

    ARTICLE

    IMPACT OF THERMAL RADIATION ON DOUBLE-DIFFUSIVE CONVECTION FLOW OF CASSON FLUID OVER A STRETCHING VERTICAL SURFACE

    K. Ganesh Kumar1 , G.K. Ramesh2,*, 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 >

  • Open Access

    ARTICLE

    FLOW AND HEAT TRANSFER OF CARBON NANOFLUIDS OVER A VERTICAL PLATE

    Mahantesh M Nandeppanavara,*, S. Shakunthalab

    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 >

  • Open Access

    ARTICLE

    NON-LINEAR RADIATIVE FLOW OF NANOFLUID PAST A MOVING/STATIONARY RIGA PLATE

    G.K. Ramesha,*, B.J. Gireeshab

    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 >

  • Open Access

    ARTICLE

    NONLINEAR RADIATIVE HEAT TRANSFER TO CARREAU FLUID OVER A NONLINEAR STRETCHING SHEET IN A POROUS MEDIUM IN THE PRESENCE OF NON-UNIFORM HEAT SOURCE/SINK AND VISCOUS DISSIPATION

    M. Umeshaiah1 , M. R. Krishnamurthy2 , N.G. Rudraswamy3 , B. J. Gireesha4, B.C. Prasannakumara5,*

    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, More >

  • Open Access

    ARTICLE

    Numerical Solutions of Fractional System of Partial Differential Equations By Haar Wavelets

    F. Bulut1,2, Ö. Oruç3, A. Esen3

    CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 263-284, 2015, DOI:10.3970/cmes.2015.108.263

    Abstract In this paper, time fractional one dimensional coupled KdV and coupled modified KdV equations are solved numerically by Haar wavelet method. Proposed method is new in the sense that it doesn’t use fractional order Haar operational matrices. In the proposed method L1 discretization formula is used for time discretization where fractional derivatives are Caputo derivative and spatial discretization is made by Haar wavelets. L2 and L error norms for various initial and boundary conditions are used for testing accuracy of the proposed method when exact solutions are known. Numerical results which produced by the proposed method for More >

  • Open Access

    ARTICLE

    Numerical Solution for the Variable Order Time Fractional Diffusion Equation with Bernstein Polynomials

    Yiming Chen1, Liqing Liu1, Xuan Li1 and Yannan Sun1

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 81-100, 2014, DOI:10.3970/cmes.2014.097.081

    Abstract In this paper, Bernstein polynomials method is proposed for the numerical solution of a class of variable order time fractional diffusion equation. Coimbra variable order fractional operator is adopted, as it is the most appropriate and desirable definition for physical modeling. The Coimbra variable order fractional operator can also be regarded as a Caputo-type definition. The main characteristic behind this approach in this paper is that we derive two kinds of operational matrixes of Bernstein polynomials. With the operational matrixes, the equation is transformed into the products of several dependent matrixes which can also be More >

  • Open Access

    ARTICLE

    Operational Matrix Method for Solving Variable Order Fractional Integro-differential Equations

    Mingxu Yi1, Jun Huang1, Lifeng Wang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 361-377, 2013, DOI:10.3970/cmes.2013.096.361

    Abstract In this paper, operational matrix method based upon the Bernstein polynomials is proposed to solve the variable order fractional integro-differential equations in the Caputo derivative sense. We derive the Bernstein polynomials operational matrix of fractional order integration and introduce the product operational matrix of Bernstein polynomials. A truncated the Bernstein polynomials series together with the polynomials operational matrix are utilized to reduce the variable order fractional integro-differential equations to a system of algebraic equations. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Some examples are included to demonstrate the More >

  • Open Access

    ARTICLE

    Numerical Algorithm to Solve Fractional Integro-differential Equations Based on Operational Matrix of Generalized Block Pulse Functions

    Yunpeng Ma1, Lifeng Wang1, Zhijun Meng1

    CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.1, pp. 31-47, 2013, DOI:10.3970/cmes.2013.096.031

    Abstract In this paper, we propose a numerical algorithm for solving linear and nonlinear fractional integro-differential equations based on our constructed fractional order generalized block pulse functions operational matrix of integration. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations by the matrix and these algebraic equations are solved through known computational methods. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach. Moreover, comparing the methodology with the known technique shows that our approach is more efficient and more convenient. More >

  • Open Access

    ARTICLE

    Wavelet operational matrix method for solving fractional integral and differential equations of Bratu-type

    Lifeng Wang1, Yunpeng Ma1, Zhijun Meng1, Jun Huang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 353-368, 2013, DOI:10.3970/cmes.2013.092.353

    Abstract In this paper, a wavelet operational matrix method based on the second kind Chebyshev wavelet is proposed to solve the fractional integral and differential equations of Bratu-type. The second kind Chebyshev wavelet operational matrix of fractional order integration is derived. A truncated second kind Chebyshev wavelet series together with the wavelet operational matrix is utilized to reduce the fractional integral and differential equations of Bratu-type to a system of nonlinear algebraic equations. The convergence and the error analysis of the method are also given. Two examples are included to verify the validity and applicability of More >

  • Open Access

    ARTICLE

    Numerical solution of fractional partial differential equations using Haar wavelets

    Lifeng Wang1, Zhijun Meng1, Yunpeng Ma1, Zeyan Wu2

    CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.4, pp. 269-287, 2013, DOI:10.3970/cmes.2013.091.269

    Abstract In this paper, we present a computational method for solving a class of fractional partial differential equations which is based on Haar wavelets operational matrix of fractional order integration. We derive the Haar wavelets operational matrix of fractional order integration. Haar wavelets method is used because its computation is sample as it converts the original problem into Sylvester equation. Finally, some examples are included to show the implementation and accuracy of the approach. More >

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