differences interpolation and numerical differentiation

... Trang 1NUMERICAL DIFFERENTIATION ANDINTEGRATION Dr Lê Xuân Đại HoChiMinh City University of Technology Faculty of Applied ... a + h, b whereh = b − a 2 and replace the integrand f (x)by the second order forward Newton divided-difference , which passes through 3 points (a, f (a)), (x1, f (x1))and (b, f (b))starting from ... f (x) by the interpolating polynomial P n (x) and we Trang 11by Newton forward divided-differenceformula which passes through 2 points (a, f (a)) and (b, f (b))starting from (a, f (a)). Therefore,

Ngày tải lên: 14/05/2025, 21:37

... [W/m2K], di and do are, respectively, the inside and outside diameters of tubes 68 Two Phase Flow, Phase Change and Numerical Modeling [m], km is the thermal conductivity [W/mK], Rfi and Rfo are ... Flow, Phase Change and Numerical Modeling increasingly cold air flowing across the coil In (Fig.19) and considering a representative circuit, the temperature distribution for CO2 and R507A are compared ... configurations and frosting conditions The proposed models were validated against sets of data obtained on a dedicated refrigeration facility, and from the literature Comparison of numerical predictions and

Ngày tải lên: 19/06/2014, 12:20

... Flow, Phase Change and Numerical Modeling calculations of heat transfer coefficient for both shell- and refrigerant-side stream If the condenser's refrigerant inlet temperature and pressure, water ... calculation, size estimation, and performance rating of the shell-and-tube condenser has been developed, varified, and modified A good agreement is observed between the computed values and the experimental ... refrigerant outlet temperature, and (c) heat transfer rate 81 82 Two Phase Flow, Phase Change and Numerical Modeling 7 References Allen, B., & Gosselin, L (2008) Optimal geometry and flow arrangement for

Ngày tải lên: 19/06/2014, 12:20

... 4The liquid-wall and the vapor-wall shear stresses are expressed as 2 1 w f2 l l l e kfR v ev kfR Where kl and kv are the Poiseuille numbers, and Dhlw and Dhvw are the liquid-wall and the vapor-wall ... infinity The liquid and vapor passage sections, Al, and Av, the interfacial area, Ail, the contact areas of the phases with the wall, Alp and Avp, are expressed using the contact angle and the interface ... comparison between the numerical results and the experimental ones, and a good agreement is found between the temperature distribution along the FMHP computed from the model and the temperature

Ngày tải lên: 19/06/2014, 12:20

... lines (1) and (2) illustrate the centreline and surface temperatures of a 130 x 390 mm x mm Sovel slab; lines (3) and (4) depict the shell thickness and the distance between the solidus and liquidus ... lines (1) and (2) illustrate the centreline and surface temperatures of a 130 x 390 mm x mm Sovel slab; lines (3) and (4) depict the shell thickness and the distance between the solidus and liquidus ... 1 and 2 depict the centreline and surface temperature, respectively Lines 3 and 4 illustrate the shell growth and solid fraction, respectively The borders of the final casting segments 5, 6, and

Ngày tải lên: 19/06/2014, 12:20

... effective diffusivity of k and ω, respectively; G k and G ω are the generation of k and ω, respectively, due to mean velocity gradients; and Y k and Y ωare the dissipation of k and ω, respectively To ... discretization, the numericalmethods and boundary conditions used and the grid convergence study After that, inSection 4 the different results obtained from the numerical simulations will be presented anddiscussed ... both numericallyand experimentally to obtain an average Nusselt number correlation as a function of 4non-dimensional parameters And, what is most important from a numerical point of view,their numerical

Ngày tải lên: 19/06/2014, 12:20

... 1974; Goldstein and Behbahani, 1982; Kamotani and Greber, 1974; Kavsaoglu and Schetz, 1989; Kawai and Lele, 2007; Kiel et al., 2003; Patankar, Basu, and Alpay, 1977; Rivero, Ferre, and Giralt, 2001; ... Giralt, 2001; Sucec and Bowley, 1976; Nirmolo, 1970; Pratte and Baines, 1967), and swirling jets in crossflow (Denev, Frohlich, and Bockhorn, 2009; Kamal, 2009; Kavsaoglu and Schetz, 1989): the ... 50, 67, and 75º (S =0.18, 0.31, 0.79, 1.57, and 2.49, respectively) Re was 5,000, 10,000, 20,000, and 50,000 For fixed S, as Re increases the azimuthal velocity turbulence increases, and the

Ngày tải lên: 19/06/2014, 12:20

... between models and experiments have been proposed and allow: (i) to obtain some main information on precursor defects and their link to the physical mechanisms involved in laser damage and (ii) to ... Change and Numerical Modeling 240 For pulsed laser ablation of metals, the ultrafast heating mechanisms perform great disparity for femtosecond and nanosecond pulse duration In fact, the electron and ... where subscripts e and p stands for electron and phonon, respectively T denotes temperature, C the heat capacity, q the heat flux, G the electron-phonon coupling strength, and Q is the laser

Ngày tải lên: 19/06/2014, 12:20

... two-phase region as quality and void fraction perturbations and will travel with the flow along the channel The combined effects of flow and void fraction perturbations and the variation of the ... Oscillations) and DWOs for a typical NASA type phase change system for space exploration applications 3.2 Numerical code simulations on density wave oscillations On the other hands, qualified numerical ... domain, linear and non-linear models In frequency domain (Lahey Jr & Moody, 1977), governing equations and necessary constitutive laws are linearized about an operating point and then Laplace-transformed

Ngày tải lên: 19/06/2014, 12:20

... of low heat flux and surface superheat Pautsch and Shedd (2005) and Shedd and Pautsch (2005) conducted a series of spray cooling experiments with single and multiple nozzles and developed an ... ρv (9) where c and n were unknown beforehand, and then obtained using the experimental CHF data that c=0.386 and n=0.549, with the standard errors of 0.039 for c, 0.0154 for n, and 0.937 for the ... mechanisms and factors present in spray cooling make it favourable for evaporation to take place and make full use of latent heat to cool the heat source 292 Two Phase Flow, Phase Change and Numerical

Ngày tải lên: 19/06/2014, 12:20

... Phase Change and Numerical Modeling ′ sin θ w nf = , sin θ f′ nw (8) where θ’w and θ’f are the angles of incidence and refraction, and x0 and y0 are the intersection points between laser and inner ... are treated with two fluoroalkylsilanes (FAS3 and FAS17) Static contact angles of FAS3 and FAS17 are 146 º and 160 º for rough surface and 78 º and 104 º, respectively From this study, the contact ... used as test tubes Table 1 and Fig 2 show the dimensions and the photographs of the test tubes Tube diameter was measured with a microscope, and the differences of inlet and outlet inner diameters

Ngày tải lên: 19/06/2014, 12:20

... identical to Rcorner, and the interface shape becomes axisymmetric In Fig 12, measured bubble radii in Dh = 0.3 and 0.5 mm channels are almost identical, and they are larger than the numerical simulation ... force makes the bubble nose slender and increases the bubble nose curvature at finite Reynolds numbers It is also reported in Edvinsson & Irandoust (1996) and Kreutzer et al (2005) that the ... 30.6432 Aussillous and Quere (2000) modified Bretherton’s analysis, and replaced the bubble nose curvature κ = 1/(Dh/2) with κ = 1/{(Dh/2)-δ0} In their analysis, the momentum balance and the curvature

Ngày tải lên: 19/06/2014, 12:20

... respectively Ue (s) and UVW (s), is sufficient to explain any tendency to the aggregation of the suspension This concept was developed by Derjaguin and Landau and also by Vervey and Overbeck In the ... heated from horizontal and vertical sides and cooled from vertical side., Archives of Thermodynamics, Vol 31(2010), No 4, pp 51-59 386 Two Phase Flow, Phase Change and Numerical Modeling Bieliński, ... heat flux approaches a maximum and then slowly decreases for minichannels The effect of geometrical and thermal parameters on the mass flux distributions was obtained numerically for the steady-state

Ngày tải lên: 19/06/2014, 12:20

... the dispersion of results and numerical models proposeduntil now Systematic comparative studies and use of molecular dynamic simulations fortransport coefficients modeling and Monte-Carlo simulations ... have a wide range of industrial and medical applications such as transportation, micromechanics and instrumentation, heating-ventilating and conditioning systems, and drug delivery systems Details ... Effects of Reynolds number and concentration of nanoparticles on the heat transfer performance are also reported and discussed Trang 14Two Phase Flow, Phase Change and Numerical Modeling 422 2

Ngày tải lên: 19/06/2014, 12:20

... density of a fluid (Landau&Lifshitz, 1987), ε=e+(p/ρ)+v 2 /2 , the “classical” form of the energy conservation law results (the physical significances of e and p are given in (Landau&Lifshitz, ... regime, temperature and nanofluids concentrations Figures 9-11 highlights the results of values of water and three types of nanofluids used depending on the Reynolds number and the primary agent ... nanoparticles suspension, International Journal of Numerical Methods for Heat and Fluid Flow, Vol 16, No 3, pp 275 - 292 Nottale L (1992), Fractal Space-Time and Microphysics: Towards a Theory of Scale

Ngày tải lên: 19/06/2014, 12:20

... b, and α are also parameters which need to be specified 8 Numerical solution and concluding remarks The volume fraction equation, Eqn (40) and the velocity equation, Eqn (41) are coupled and ... stress-differences and is properly frame invariant (Cowin, 1974; Trang 7where β are material properties, and 's 1 ( )TD u u In what follows we will use the concept of volume fraction4ν , and use ... avalanches and mudslides; it is also used for transporting and drying of bulk solids (such as agricultural and pharmaceutical products) It is a viscometric flow (Truesdell, 1974) and one which

Ngày tải lên: 19/06/2014, 12:20

... continuity and Navier-Stokes equations are solved with the Enthalpy- Porosity and the VOF methods in order to simulate a melting and falls-off PCM and we can safely said that our model and code ... Phase Flow, Phase Change and Numerical Modeling Lamberg, P.; Lehtiniemi, R & Henell, A (2004) Numerical and Experimental Investigation of Melting and Freezing Processes in Phase ... copper and the solid PCM, and the heat balance equation between the PCM and air. The boundary conditions are expressed as follows: at x = 0 300 ;TK= at interface between the PCM and air

Ngày tải lên: 19/06/2014, 12:20

... closed form, and the last example cannot be solved by int at all It can only be computed numerically, with quad 121 The function f provided to quad and quadl must operate on a vector x and return ... of the function better than spline Polynomial multiplication and division (convolution and deconvolution) are performed by the conv and deconv functions MATLAB also has a built-in fast Fourier ... of the vector An optional fourth argument to quad and quadl modifies the error tolerance Double and triple integrals are evaluated by dblquad and triplequad Arrayvalued functions are integrated...

Ngày tải lên: 29/09/2013, 22:20

... SIMILARITIES AND DIFFERENCES: COMPARE AND CONTRAST – How Comparison and Contrast Work Finding the Facts What two things are being compared and contrasted here? When writers compare and contrast, ... like manner and also These words and phrases show difference: but on the other hand however conversely 69 yet on the contrary nevertheless – SIMILARITIES AND DIFFERENCES: COMPARE AND CONTRAST ... mandatory school uniforms and offer several possible effects Often, authors will use the cause and effect structure to make arguments like the ones we’ve just seen: one for and one against mandatory...

Ngày tải lên: 25/10/2013, 17:20

... and ubiquitin C-terminal hydrolase (specific markers for neural and neuroendocrine tissues) were found in rat long bones at embryonic day 15, in the diaphyseal and metaphyseal perichondrium, and ... adrenergic and cholinergic in nature, and originate from paravertebral sympathetic ganglia [16] Experimental nerve deletion and immunohistochemistry analysis have shown that both myelinated and unmyelinated ... Increased TBV Increased TBV and CBV Normal Normal 25 45,51 Y2) ⁄ )ob) ⁄ ) Leptin and Y2 Increased Increased Y1) ⁄ ) Y1 Decreased TBV and CBV in relation to Y2) ⁄ ) Increased TBV and CBV ND Increased...

Ngày tải lên: 18/02/2014, 04:20