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The effect of variable viscosity on the flow and heat transfer of a viscous Agwater and Cu-water nanofluids

Journal of Hydrodynamics 2013年第1期25卷 1-9页

作者： VAJRAVELU Kuppalapalle PRASAD Kerehalli Vinayaka NG Chiu-On Department of Mathematics University of Central Florida Department of Mathematics VSK University Department of Mechanical Engineering The University of Hong Kong

A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, and are solved numerically by the keller-box method. The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness. This is true even in the presence of variable viscosity and the viscous dissipation. Furthermore, the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the ＂nano-solid-particles＂.

关键词： nanofluid particles variable viscosity boundary layers viscous dissipation keller-box method

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MHD flow and mass transfer of chemically reactive upper convected Maxwell fluid past porous surface

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Applied Mathematics and Mechanics(English Edition) 2012年第7期33卷 899-910页

作者： K. VAJRAVELU K. V. PRASAD A. SUJATHA 吴朝安 Department of Mathematics University of Central Florida Department of Mathematics Bangalore University Department of Mechanical Engineering The University of Hong Kong

The magnetohydrodynamic （MHD） flow and mass transfer of an electrically conducting upper convected Maxwell （UCM） fluid at a porous surface are studied in the presence of a chemically reactive species. The governing nonlinear partial differential equations along with the appropriate boundary conditions are transformed into nonlinear ordinary differential equations and numerically solved by the keller-box method. The effects of various physical parameters on the flow and mass transfer characteristics are graphically presented and discussed. It is observed that the order of the chemical reaction is to increase the thickness of the diffusion boundary layer. Also, the mass transfer rate strongly depends on the Schmidt number and the reaction rate parameter. Furthermore, available results in the literature are obtained as a special case.

关键词： chemically reactive species upper convected Maxwell (UCM) fluid mag-netohydrodynamic (MHD) flow mass transfer keller-box method

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A Finite Difference Approximation for Dynamic Calculation of Vertical Free Hanging Slender Risers in Re-Entry Application

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China Ocean Engineering 2012年第4期26卷 637-652页

作者：王盛炜徐雪松姚宝恒连琏 School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong University

The dynamic calculations of slender marine risers, such as Finite Element method （FEM） or Modal Expansion Solution method （MESM）, are mainly for the slender structures with their both ends hinged to the surface and bottom. However, for the re-entry operation, risers held by vessels are in vertical free hanging state, so the displacement and velocity of lower joint would not be zero. For the model of free hanging flexible marine risers, the paper proposed a Finite Difference Approximation （FDA） method for its dynamic calculation. The riser is divided into a reasonable number of rigid discrete segments. And the dynamic model is established based on simple Euler-Bemoulli Beam Theory concerning tension, shear forces and bending moments at each node along the cylindrical structures, which is extendible for different boundary conditions. The governing equations with specific boundary conditions for riser＇s free hanging state are simplified by keller-box method and solved with Newton iteration algorithm for a stable dynamic solution. The calculation starts when the riser is vertical and still in calm water, and its behavior is obtained along time responding to the lateral forward motion at the top. The dynamic behavior in response to the lateral parametric excitation at the top is also proposed and discussed in this paper.

关键词： finite difference approximation free hanging slender risers keller-box method Newton iteration re-entryapplication

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MHD BOUNDARY-LAYER FLOW AND HEAT TRANSFER OVER PERMEABLE PLATE WITH CONVECTIVE SURFACE BOUNDARY CONDITION

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International Journal of Modeling, Simulation, and Scientific Computing 2014年第1期5卷 170-185页

作者： WUBSHET IBRAHIM BANDARI SHANKER Department of Mathematics Ambo University Ambo Ethiopia Department of Mathematics Osmania University Hyderabad 7 Andhra PradeshIndia

A numerical analysis has been carried out to investigate the problem of magnetohydrodynamic(MHD)boundary-layer flow and heat transfer of a viscous incompressible fluid over a fixed *** surface boundary condition is taken into account for thermal boundary condition.A problem formulation is developed in the presence of thermal radiation,magnetic field and heat source/sink parameters.A similarity transformation is used to reduce the governing boundary-layer equations to couple higher-order nonlinear ordinary differential *** equations are numerically solved using keller–box *** effect of the governing parameters such as radiation,Prandtl number,Hartman number,heat source/sink parameter on velocity and temperature profile is discussed and shown by plotting *** is found that the temperature is an increasing function of convective parameter A,radiation and heat source ***,the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular *** a comparison with a previously published results on a special case of the problem has done and shows excellent agreement.

关键词： keller-box method boundary-layer flow heat transfer MHD heat source or sink

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A comprehensive physical insight about thermo physical aspects of Carreau fluid flow over a rotated disk of variable thickness by implementing finite difference approach

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Propulsion and Power Research 2022年第1期11卷 143-153页

作者： Sardar Bilal Imtiaz Ali Shah Department of Mathematics AIR UniversityP.A.F ComplexSector E-9P.O.44000IslamabadPakistan

Present communication is devoted to analyze thermal characteristics of Carreau liquid flowing on variably thickened non-uniformly rotating *** formulation is constructed in view of complex coupled partial differential ***,boundary layer approach is executed for comprehensive examination of under consideration phenomenon with in boundary layer ***’s transformation is capitalized to convert the attained PDE’s into ordinary differential equations *** of attained ODE’s system is solved numerically by implementing keller-box *** of protuberant involved parameters on momentum and thermal distributions is illustrated through *** addition,impact of flow concerning parameters on wall shear stress and thermal flux is also *** assurance of present finding is done by making agreement with published results and by restricting considered problem to Newtonian ***,we observed that radially and tangentially directed wall drag lessen with growing magnitude of power law exponent ***,the consequence of disk thickness parameter grows stresses along radial direction whereas opposite behavior is depicted in case of tangentially directed friction and heat flux factors.

关键词： Carreau viscosity model Rotating disk Non-uniform thickness keller-box method

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Effect of Nonlinear Thermal Radiation on Boundary Layer Flow of Viscous Fluid over Nonlinear Stretching Sheet with Injection/Suction

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Journal of Applied Mathematics and Physics 2016年第2期4卷 307-319页

作者： T. Vijaya Laxmi Bandari Shankar Department of Mathematics Osmania University Hyderabad India Department of Mathematics M.V.S. Govt. Arts & Science College Mahabubnagar India

The present study reveals the effect of nonlinear thermal radiation and magnetic field on a boundary layer flow of a viscous fluid over a nonlinear stretching sheet with suction or an injection. Using suitable similarity transformations, governing partial differential equations were reduced to higher order ordinary differential equations and further these are solved numerically using of keller-box method. Effect of flow controlling parameter on velocity, temperature and nanoparticle fluid concentration, local skin friction coefficient, local Nusselt number and local Sherwood numbers are discussed. It is found that the dimensionless velocity decreases and temperature, concentration are increased with the increasing of magnetic parameter. The temperature profile is an increasing function of thermal radiation when it is increasing.

关键词： Nonlinear Thermal Radiation Stretching Sheet Boundary Layer keller-box method Suction/Injection

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