Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field

The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant velocity which is in the same or opposite direction to that of free stream velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free stream velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.

An inverse problem for the Helmholtz equation involving two semi-infinite fluids

An analytical method is developed for solving an inverse problem for Helmholtz's equation associated with two semi-infinite incompressible fluids of different variable refractive indices, separated by a plane interface. The unknowns of the inverse problem are: (i) the refractive indices of the two fluids, (ii) the ratio of the densities of the two fluids, and (iii) the strength of an acoustic source assumed to be situated at the interface of the two fluids. These are determined from the pressure on the interface produced by the acoustic source. The effect of the surface tension force at the interface is taken into account in this paper. The application of the proposed analytical method to solve the inverse problem is also illustrated with several examples. In particular, exact solutions of two direct problems are first derived using standard classical methods which are then used in our proposed inverse method to recover the unknowns of the corresponding inverse problems. The results are found to be in excellent agreement.

Numerical modeling of heat and mass transfer in laser surface alloying: Non-equilibrium solidification effects

A transient macroscopic model is developed for studying heat and mass transfer in a single-pass laser surface alloying process, with particular emphasis on non-equilibrium solidification considerations. The solution for species concentration distribution requires suitable treatment of non-equilibrium mass transfer conditions. In this context, microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition-coefficient. The effective partition-coefficient is numerically modeled by Means of a number of macroscopically observable parameters related to the solidifying domain. The numerical model is so developed that the modifications on account of non-equilibrium solidification considerations can be conveniently implemented in existing numerical codes based on equilibrium solidification considerations.

Role of in situ generated tribofilm on the tribological characteristics of monolith and TiB2 reinforced MoSi2 intermetallic

Wear experiments performed on steel disc with increasing load for monolithic MoSi2 of different densities and its composite with TiB2 showed three distinct wear regimes. The specimens exhibited severe wear rate below the lower and above the upper critical loads and mild wear in between the two critical loads. The increase in density of the monolith and the reinforcement of TiB2 were effective in reducing the coefficient of friction and the specific wear rate. The wear experiments have been performed in these three regimes (15, 50 and 75 N). The tribofilm formed on the pin surface was found to contain both pin and disc materials. The temperature of the pins during the sliding against EN-24 disc was calculated using one dimensional heat transfer equation at different loads for each composition. The composite experiences lower temperatures compared to the monoliths. (C) 2002 Elsevier Science B.V. All rights reserved.

Scaling analysis of momentum and heat transport in gas tungsten arc weld pools

A systematic procedure is outlined for scaling analysis of momentum and heat transfer in gas tungsten arc weld pools. With suitable selections of non-dimentionalised parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them is analysed accordingly. The analysis is then used to predict the orders of magnitude of some important quantities, such as the velocity scene lit the top surface, velocity boundary layer thickness, maximum temperature increase in the pool, and time required for initiation of melting. Some of the quantities predicted from the scaling analysis can also be used for optimised selection of appropriate grid size and time steps for full numerical simulation of the process. The scaling predictions are finally assessed by comparison with numerical results quoted in the literature, and a good qualitative agreement is observed.

A scaling analysis of momentum and heat transport in laser surface melting

In this paper, we outline a systematic procedure for scaling analysis of momentum and heat transfer in laser melted pools. With suitable choices of non-dimensionalising parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them are accordingly analysed. The analysis is then utilised to predict the orders of magnitude of some important quantities, such as the velocity scale at the top surface, velocity boundary layer thickness, maximum temperature rise in the pool, fully developed pool-depth, and time required for initiation of melting. Using the scaling predictions, the influence of various processing parameters on the system variables can be well recognised, which enables us to develop a deeper insight into the physical problem of interest. Moreover, some of the quantities predicted from the scaling analysis can be utilised for optimised selection of appropriate grid-size and time-steps for full numerical simulation of the process. The scaling predictions are finally assessed by comparison with experimental and numerical results quoted in the literature, and an excellent qualitative agreement is observed.

Thermodynamic analysis of enzyme catalysed reactions: new insights into the Michaelis-Menten equation

A simple thermodynamic analysis of the well-known Michaelis-Menten equation (MME) of enzyme catalysis is proposed that employs the chemical potential mu to follow the Gibbs free energy changes attending the formation of the enzyme-substrate complex and its turnover to the product. The main conclusion from the above analysis is that low values of the Michaelis constant KM and high values of the turnover number k(cat) are advantageous: this supports a simple algebraic analysis of the MME, although at variance with current thinking. Available data apparently support the above findings. It is argued that transition state stabilisation - rather than substrate distortion or proximity - is the key to enzyme catalysis.

Thermodynamic studies on NdFeO3(s)

The enthalpy increments and the standard molar Gibbs energy of formation of NdFeO3(s) have been measured using a hightemperature Calvet microcalorimeter and a solid oxide galvanic cell, respectively. A lambda-type transition, related to magnetic order-disorder transformation (antiferromagnetic to paramagnetic), is apparent from the heat capacity data at similar to 687 K. Enthalpy increments, except in the vicinity of transition, can be represented by a polynomial expression: {Hdegrees(m)(T)-Hdegrees(m) (298.15 K)} /J(.)mol(-1) (+/- 0.7%)=-53625.6+146.0(T/K) +1.150 X 10(-4)(T/K)(2) +3.007 x 10(6)(T/K)(-1); (298.15 less than or equal to T/K less than or equal to 1000). The heat capacity, the first differential of {Hdegrees(m)(T)-Hdegrees(m)(298.15 K)}with respect to temperature, is given by Cdegrees(pm)/J(.)K(-1.)mol(-1)=146.0+ 2.30x10(-4) (T/K) - 3.007 X 10(6)(T/K)(-2). The reversible emf's of the cell, (-) Pt/{NdFeO3(s) +Nd2O3(s)+Fe(s)}//YDT/CSZ// Fe(s)+'FeO'(s)}/Pt(+), were measured in the temperature range from 1004 to 1208 K. It can be represented within experimental error by a linear equation: E/V=(0.1418 +/- 0.0003)-(3.890 +/- 0.023) x 10(-5)(T/K). The Gibbs energy of formation of solid NdFeO, calculated by the least-squares regression analysis of the data obtained in the present study, and data for Fe0.95O and Nd2O3 from the literature, is given by Delta(f)Gdegrees(m)(NdFeO3 s)/kJ (.) mol(-1)( +/- 2.0)=1345.9+0.2542(T/K); (1000 less than or equal to T/K less than or equal to 1650). The error in Delta(f)Gdegrees(m)(NdFeO3, s, T) includes the standard deviation in emf and the uncertainty in the data taken from the literature. Values of Delta(f)Hdegrees(m)(NdFeO3, s, 298.15 K) and Sdegrees(m) (NdFeO3 s, 298.15 K) calculated by the second law method are - 1362.5 (+/-6) kJ (.) mol(-1) and 123.9 (+/-2.5) J (.) K-1 (.) mol(-1), respectively. Based on the thermodynamic information, an oxygen potential diagram for the system Nd-Fe-O was developed at 1350 K. (C) 2002 Elsevier Science (USA).

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.

Roy equation analysis of ππ scattering

We analyse the Roy equations for the lowest partial waves of elastic ππ scattering. In the first part of the paper, we review the mathematical properties of these equations as well as their phenomenological applications. In particular, the experimental situation concerning the contributions from intermediate energies and the evaluation of the driving terms are discussed in detail. We then demonstrate that the two S-wave scattering lengths a00 and a02 are the essential parameters in the low energy region: Once these are known, the available experimental information determines the behaviour near threshold to within remarkably small uncertainties. An explicit numerical representation for the energy dependence of the S- and P-waves is given and it is shown that the threshold parameters of the D- and F-waves are also fixed very sharply in terms of a00 and a20. In agreement with earlier work, which is reviewed in some detail, we find that the Roy equations admit physically acceptable solutions only within a band of the (a00,a02) plane. We show that the data on the reactions e+e−→ππ and τ→ππν reduce the width of this band quite significantly. Furthermore, we discuss the relevance of the decay K→ππeν in restricting the allowed range of a00, preparing the grounds for an analysis of the forthcoming precision data on this decay and on pionic atoms. We expect these to reduce the uncertainties in the two basic low energy parameters very substantially, so that a meaningful test of the chiral perturbation theory predictions will become possible.

Thermal instability in a three-dimensional rigid container with prescribed heat flux at lower boundary

The Bénard–Marangoni convection is studied in a three-dimensional container with thermally insulated lateral walls and prescribed heat flux at lower boundary. The upper surface of the incompressible, viscous fluid is assumed to be flat with temperature dependent surface tension. A Galerkin–Tau method with odd and even trial functions satisfying all the essential boundary conditions except the natural boundary conditions at the free surface has been used to solve the problem. The critical Marangoni and Rayleigh numbers are determined for the onset of steady convection as a function of aspect ratios x0 and y0 for the cases of Bénard–Marangoni, pure Marangoni and pure Bénard convections. It is observed that critical parameters are decreasing with an increase in aspect ratios. The flow structures corresponding to the values of the critical parameters are presented in all the cases. It is observed that the critical parameters are higher for case with heat flux prescribed than those corresponding to the case with prescribed temperature. The critical Marangoni number for pure Marangoni convection is higher than critical Rayleigh number corresponding to pure Bénard convection for a given aspect ratio whereas the reverse was observed for two-dimensional infinite layer.

Unsteady mhd flow and heat transfer on a rotating disk in an ambient fluid

An unsteady flow and heat transfer of a viscous incompressible electrically conducting fluid over a rotating infinite disk in an otherwise ambient fluid are studied. The unsteadiness in the flow field is caused by the angular velocity of the disk which varies with time. The magnetic field is applied normal to the disk surface. The new self-similar solution of the Navier-Stokes and energy equations is obtained numerically. The solution obtained here is not only the solution of the Navier-Stokes equations, but also of the boundary layer equations. Also, for a simple scaling factor, it represents the solution of the flow and heat transfer in the forward stagnation-point region of a rotating sphere or over a rotating cone. The asymptotic behaviour of the solution for a large magnetic field or for a large independent variable is also examined. The surface shear stresses in the radial and tangential directions and the surface heat transfer increase as the acceleration parameter increases. Also the surface shear stress in the radial direction and the surface heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction increases. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Analytical solutions for heat transfer during cyclic melting and freezing of a phase change material used in electronic or electrical packaging

In this paper we develop an analytical heat transfer model, which is capable of analyzing cyclic melting and solidification processes of a phase change material used in the context of electronics cooling systems. The model is essentially based on conduction heat transfer, with treatments for convection and radiation embedded inside. The whole solution domain is first divided into two main sub-domains, namely, the melting sub-domain and the solidification sub-domain. Each sub-domain is then analyzed for a number of temporal regimes. Accordingly, analytical solutions for temperature distribution within each subdomain are formulated either using a semi-infinity consideration, or employing a method of quasi-steady state, depending on the applicability. The solution modules are subsequently united, leading to a closed-form solution for the entire problem. The analytical solutions are then compared with experimental and numerical solutions for a benchmark problem quoted in the literature, and excellent agreements can be observed.