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A boundary-layer model is described for the two-dimensional nonlinear transient thermal convection heat and mass transfer in an optically-thick fluid in a Darcian porous medium adjacent to an impulsively started vertical surface, in the presence of significant thermal radiation and buoyancy forces in an (X1,Y1,t1) coordinate system. An algebraic approximation is employed to simplify the integro-differential equation of radiative transfer for unidirectional flux normal to the plate into the boundary-layer regime, by incorporating this flux term in the energy conservation equation. The conservation equations are non-dimensionalized into an (X,Y,T) coordinate system and solved using the Network Simulation Method (NSM), a robust numerical technique which demonstrates high efficiency and accuracy. The transient variation of non-dimensional streamwise velocity component (u) and temperature (T) and concentration (C) functions is computed for various selected values of Stark number (radiation–conduction interaction parameter) and Darcy number. Transient velocity (u) and steady-state local skin friction (τX) are also studied for various thermal Grashof number (Gr), species Grashof number (Gm), Schmidt number (Sc) and Stark number (N) values. These computations for the infinite permeability case (Da  ∞) are compared with previous finite difference solutions [Prasad et al. Int J Therm Sci 2007;46(12):1251–8] and shown to be in excellent agreement. An increase in Darcy number is seen to accelerate the flow and boost velocity. A decrease in Stark number (corresponding to an increase in thermal radiation heat transfer contribution) is shown to increase the velocity values. Temperature function is observed to fall in value with a rise in Da and increase with decrease in N (corresponding to an increase in thermal radiation heat transfer contribution). Applications of the study include rocket combustion chambers, astrophysical flows, spacecraft thermal fluid dynamics in debris-laden environments (cosmic dust), heat transfer in forest fire spread, geochemical contamination and ceramic materials processing.  相似文献   
2.
A mathematical model for two dimensional steady laminar natural convective anisotropic slip boundary layer flows from a rotating vertical cone embedded in ethylene glycol bionanofluid is presented. The influence of Stefan blowing is also taken into account. Four different non-particles namely Copper (Cu), Alumina (Al2O3), Copper Oxide (Cuo), Titanium Oxide (TiO2) are explored. Suitable similarity transformations are used to convert the governing equations into non-linear ordinary differential equations. These are then solved numerically, with appropriate boundary conditions, utilizing an implicit finite difference method (the BVP5C code in MATLAB). During computation Sc, Lb, Le and Lb are presented as unity, whilst Pr is taken as 151. The effects of the governing parameters on the dimensionless velocities, temperature, nanoparticle volume fraction, density of motile microorganisms as well as on the local skin friction, local Nusselt, Sherwood number and motile micro-organism number density are thoroughly examined via tables and graphs. It is found that the skin friction factor increases with tangential slip, magnetic field and Schmidt number whilst it decreases with blowing parameter and spin parameters. It is further observed that both the friction and heat transfer rates are highest for copper nanoparticles and lowest for TiO2nanoparticles. Validation of the BVP5C numerical solutions with published results for several special cases of the general model is included. The study is relevant to electro-conductive bio-nano-materials processing.  相似文献   
3.
This article presents a numerical study on oscillating peristaltic flow of generalized Maxwell fluids through a porous medium. A sinusoidal model is employed for the oscillating flow regime. A modified Darcy-Brinkman model is utilized to simulate the flow of a generalized Maxwell fluid in a homogenous, isotropic porous medium. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. The numerical and approximate analytical solutions of the problem are obtained by a semi-numerical technique, namely the homotopy perturbation method. The influence of the dominating physical parameters such as fractional Maxwell parameter, relaxation time, amplitude ratio, and permeability parameter on the flow characteristics are depicted graphically. The size of the trapped bolus is slightly enhanced by increasing the magnitude of permeability parameter whereas it is decreased with increasing amplitude ratio. Furthermore, it is shown that in the entire pumping region and the free pumping region, both volumetric flow rate and pressure decrease with increasing relaxation time, whereas in the co-pumping region, the volumetric flow rate is elevated with rising magnitude of relaxation time.  相似文献   
4.
A numerical study of pulsatile flow and mass transfer of an electrically conducting Newtonian biofluid via a channel containing porous medium is considered. The conservation equations are transformed and solved under boundary conditions prescribed at both walls of the channel, using a finite element method with two-noded line elements. The influence of magnetic field on the flow is studied using the dimensionless hydromagnetic number, Nm, which defines the ratio of magnetic (Lorentz) retarding force to the viscous hydrodynamic force. A Darcian linear impedance for low Reynolds numbers is incorporated in the transformed momentum equation and a second order drag force term for inertial (Forchheimer) effects. Velocity and concentration profiles across the channel width are plotted for various values of the Reynolds number (Re), Darcy parameter (λ), Forchheimer parameter (Nf), hydro-magnetic number (Nm), Schmidt number (Sc) and also with dimensionless time (T). Profiles of velocity varying in space and time are also provided. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. Increasing the hydromagnetic number (Nm) from 1 to 15 considerably depresses biofluid velocity (U) indicating that a magnetic field can be used as a flow control mechanism in, for example, medical applications. A rise in Nf from 1 to 20 strongly retards the flow development and decreases the velocity, U, across the width of the channel. The effects of other parameters on the flowfield are also discussed at length. The flow model also has applications in the analysis of electrically conducting haemotological fluids flowing through filtration media, diffusion of drug species in pharmaceutical hydromechanics, and also in general fluid dynamics of pulsatile systems.  相似文献   
5.
Many empirical potential energy functions have been modeled to represent the potential energy function of a diatomic molecule along whole range of internuclear distance coordinate, whereby one can determine certain molecular constants. Here we employ various potential functions such as Morse, Rydberg, Varshni(II), Varshni(III), Varshni(VI), Pöschl-Teller, Hulburt-Hirschfelder, Lippincott, Frost-Musulin, Linnet, and Rosen-Morse, and the Numerov method to solve the nuclear Schrödinger equation for F2, as an example of a homonuclear diatomic molecule. Herewith, the vibrational and vibration-rotation energy levels are obtained and excellent accuracy is achieved. The potential of employing the Numerov method in engineering physics computations is emphasized.  相似文献   
6.
A theoretical study of unsteady magnetohydrodynamic viscous Hartmann–Couette laminar flow and heat transfer in a Darcian porous medium intercalated between parallel plates, under a constant pressure gradient is presented. Viscous dissipation, Joule heating, Hall current and ionslip current effects are included as is lateral mass flux at both plates. The dimensionless conservation equations for the primary (x1-direction), secondary (z1-direction) momentum and also energy conservation equation are derived and solved using a computational technique known as Network Simulation Methodology (NSM). Velocity distributions (u1, w1) and temperature distribution (T1) at the channel centre (y1 = 0) over time (t1) are studied graphically for the effects of Darcy number (Da), Hartmann number (Ha), transpiration (Nt), Hall current parameter (Be), ionslip parameter (Bi), pressure gradient parameter (dP/dx1) with Prandtl number prescribed at 7.0 (electrically conducting water), Eckert number held constant at 0.25 (heat convection from the plates to the fluid) and Reynolds number (Re) fixed at 5.0 (for Re < 10, Darcian model is generally valid). Increasing Darcy number causes an increase in temperature, T1; values are however significantly reduced for the higher Hartmann number case (Ha = 10). For the case of low transpiration (i.e. Nt = 1 which corresponds to weak suction at the upper plate and weak injection at the lower plate), both primary velocity (u1) and secondary velocity (w1) are increased with a rise in Darcy number (owing to a simultaneous decrease in Darcian porous drag); temperature T1 is also increased considerably with increasing Da. However, for stronger transpiration (Nt = 10), magnitudes of u1, w1 and T1 are significantly reduced and also significant overshoots are detected prior to the establishment of steady state flow. With increasing Hall current parameter, Be, (for the purely fluid regime i.e. Da  ∞), primary velocity is considerably increased, whereas secondary velocity is reduced; temperatures are decreased in the early stages of flow but effectively increased in the steady state with increasing Be. With strong Darcian drag present (Da = 0.01 i.e. very low permeability), magnitudes of u1, w1 and T1 are considerably reduced and temperatures are found to be reduced for all t1, with increasing Hall current effect (Be). Increasing ionslip current parameter (Bi) increases primary velocity (u1), decreases secondary velocity (w1) and also temperature (T1) for all time (t1), in the infinite permeability case (Da  ∞). For weakly Darcian flow, ionslip parameter (Bi) has a much reduced effect on the velocity distributions. Temperature, T1 is strongly increased with a rise in pressure gradient parameter, dP1/dx1, as is primary velocity (u1); however, secondary velocity (w1) is reduced. The present study has applications in hybrid magnetohydrodynamic (MHD) energy generators, materials processing, geophysical hydromagnetics, etc.  相似文献   
7.
In this article we derive semi-analytical/numerical solutions for transport phenomena (momentum, heat and mass transfer) in a nanofluid regime adjacent to a nonlinearly porous stretching sheet by means of the Homotopy analysis method (HAM). The governing equations are reduced to a nonlinear, coupled, non-similar, ordinary differential equation system via appropriate similarity transformations. This system is solved under physically realistic boundary conditions to compute stream function, velocity, temperature and concentration function distributions. The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation. Furthermore the current HAM solutions demonstrate very good correlation with the non-transpiring finite element solutions of Rana and Bhargava (Commun. Nonlinear Sci. Numer. Simul. 17:212–226, 2012). The influence of stretching parameter, transpiration (wall suction/injection) Prandtl number, Brownian motion parameter, thermophoresis parameter and Lewis number on velocity, temperature and concentration functions is illustrated graphically. Transpiration is shown to exert a substantial influence on flow characteristics. Applications of the study include industrial nanotechnological fabrication processes.  相似文献   
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