Search results

The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

The purpose of this paper is to determine both analytically and numerically the solution to a new one-dimensional equation for the propagation of small-amplitude waves in shallow waters that accounts for linear and nonlinear drift, diffusive attenuation, viscosity and dispersion, its dependence on the initial conditions, and its linear stability.

An implicit, finite difference method valid for both parabolic and second-order hyperbolic equations has been used to solve the equation in a truncated domain for five different initial conditions, a nil initial first-order time derivative and relaxation times linearly proportional to the viscosity coefficient.

A fast transition that depends on the coefficient of the linear drift, the diffusive attenuation and the power of the nonlinear drift are found for initial conditions corresponding to the exact solution of the generalized regularized long-wave equation. For initial Gaussian, rectangular and triangular conditions, the wave’s amplitude and speed increase as both the amplitude and the width of these conditions increase and decrease, respectively; wide initial conditions evolve into a narrow leading traveling wave of the pulse type and a train of slower oscillatory secondary ones. For the same initial mass and amplitude, rectangular initial conditions result in larger amplitude and velocity waves of the pulse type than Gaussian and triangular ones. The wave’s kinetic, potential and stretching energies undergo large changes in an initial layer whose thickness is on the order of the diffusive attenuation coefficient.

A new, one-dimensional equation for the propagation of small-amplitude waves in shallow waters is proposed and studied analytically and numerically. The equation may also be used to study the displacement of porous media subject to seismic effects, the dispersion of sound in tunnels, the attenuation of sound because of viscosity and/or heat and mass diffusion, the dynamics of second-order, viscoelastic fluids, etc., by appropriate choices of the parameters that appear in it.

This paper aims to report the results of numerical analysis of turbulent fluid flow and forced-convection heat transfer in solar air channels with baffle-type attachments of various shapes. The effect of reconfiguring baffle geometry on the local and average heat transfer coefficients and pressure drop measurements in the whole domain investigated at constant surface temperature condition along the top and bottom channels’ walls is studied by comparing 15 forms of the baffle, which are simple (flat rectangular), triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, double V (or W), Z, T, G and epsilon (or e)-shaped, with the Reynolds number changing from 12,000 to 32,000.

The baffled channel flow model is controlled by the Reynolds-averaged Navier–Stokes equations, besides the k-epsilon (or k-e) turbulence model and the energy equation. The finite volume method, by means of commercial computational fluid dynamics software FLUENT is used in this research work.

Over the range investigated, the Z-shaped baffle gives a higher thermal enhancement factor than with simple, triangular, trapezoidal, cascaded rectangular-triangular, diamond, arc, corrugated, +, S, V, W, T, G and e-shaped baffles by about 3.569-20.809; 3.696-20.127; 3.916-20.498; 1.834-12.154; 1.758-12.107; 7.272-23.333; 6.509-22.965; 8.917-26.463; 8.257-23.759; 5.513-18.960; 8.331-27.016; 7.520-26.592; 6.452-24.324; and 0.637-17.139 per cent, respectively. Thus, the baffle of Z-geometry is considered as the best modern model of obstacles to significantly improve the dynamic and thermal performance of the turbulent airflow within the solar channel.

This analysis reports an interesting strategy to enhance thermal transfer in solar air channels by use of attachments with various shapes

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to investigate the flow and the heat transfer characteristics of a two‐dimensional rib‐roughned rectangular duct with the two principal walls subjected to uniform heat flux. In particular, the main goal is to generate friction and heat transfer data, for different values of p/e with square, rectangular, trapezoidal and triangular shape ribs for Reynolds numbers in the range between 20,000 and 60,000 and different heights and to describe the temperature and fluid‐dynamic fields around the ribs.

The model is constituted by a two‐dimensional duct. On the duct wall square, rectangular, triangular and trapezoidal ribs are introduced by changing different geometry ratios. Governing equations are solved numerically by means of the finite‐volume method.

Simulations show that maximum Nusselt numbers are detected in correspondence with dimensionless pitch equal to 12 and 10 for the square, trapezoidal and rectangular ribs, and triangular ones, respectively. Heat transfer rate is at most 2.45 times higher than the smooth duct, when dimensionless height is equal to 0.05, and 1.85 at a dimensionless height equal to 0.02; furthermore, the friction factor is the highest at a pitch ratio of ten for the rectangular, trapezoidal and square ribs while the triangular ones show the maximum values at a dimensionless pitch equal to 8. For Re>40,000 an asymptotic behavior is detected. Best thermal performances are provided by triangular ribs with w/e=2.0 while the rectangular ribs with w/e=2.0 present the lowest friction factor values. Local Nusselt number profiles reveal that the maximum values are detected from three to five times the rib height from the downstream turbulator. Finally, temperature fields and stream function contours are given in order to visualize the temperature distribution and flow pattern in presence of d‐type and k‐type roughness behavior also for triangular ribs.

The paper investigates evaluation of temperature and velocity fields thermal and fluid‐dynamic behaviors (in terms of average and local Nusselt number profiles and friction factors ones) of roughned ducts with different shapes, heights and aspect ratios of ribs in turbulent regime. The thermo‐physical properties of fluid are assumed to be dependent on temperature. The paper is useful to thermal designers.

To focus on grid generation which is an essential part of any analytical tool for effective discretization.

This paper explores the application of the possibility of unstructured triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements using piecewise polynomial parametric surfaces which interpolate prescribed R³ scattered data using spaces of parametric splines defined on R² triangulations in the case of surfaces in engineering sciences. The method is based upon minimizing a physics‐based certain natural energy expression over the parametric surface. The geometry is defined as a set of stitched triangles prior to the grid generation. As for derivational continuities between the two triangular patches C⁰ and C¹ continuity or both, as per the requirements, has been imposed. With the addition of a penalty term, C² (approximate) continuity can also be achieved. Since, in this work physics‐based approach has been used, the grid is analyzed using intersection curves with three‐dimensional planes, and intrinsic geometric properties (i.e. directional derivatives), for derivational continuity and smoothness.

The triangular grid generation that deals with derivationally continuous, smooth, and fair triangular elements has been implemented in this paper for surfaces in engineering sciences.

This paper deals with the important problem of grid generation which is an essential part of any analytical tool for effective discretization. And, the examples to demonstrate the theoretical model of this paper have been chosen from different branches of engineering sciences. Hence, the results of this paper are of practical importance for grid generation in engineering sciences.

The paper is theoretical with worked examples chosen from engineering sciences.

The purpose of this paper is to investigate thermohydraulic characteristics of turbulent flow of water (4,000 = Re = 10,000) in a rectangular channel equipped with perforated chevron plat-fin (PCPF) with different vortex generators (VGs) shapes.

First, three general shapes of VGs including rectangular, triangular and half circle, are compared to each other. Then, the various shapes of rectangular VGs, (horizontal, vertical and square) and triangular VGs, (forward, backward and symmetric) are evaluated. To comprehensively evaluate the thermohydraulic performance of the PCPF with various VG shapes, the relationship between the Colburn factor and the friction factor (j/f) is presented, then a performance index (η) is applied using these factors.

Results show that the enhanced models of the PCPF, which are equipped with VGs, have higher values of j/f ratio and η as compared with the reference model (R). Further, the half-circle VG with the lowest pressure drop values (about 2.4% and 4.9%, averagely as compared with the S and ST vortex generators), shows the highest thermohydraulic performance among the proposed shapes. The maximum of performance index of 1.14 is found for the HC vortex generator at Re = 4,000. It is also found that the square and forward triangular VGs, have the best thermohydraulic performance among the rectangular and triangular VGs respectively and the highest performance index of 1.13 and 1.11 are reported for these VGs.

The thermohydraulic performance of the PCPF with different vortex generators VGs shapes have been investigated.

Sets out to discuss laminar free convection characteristics of air confined to a square cavity and a horizontal rectangular cavity (aspect ratio A=2) along with the viable isosceles triangular cavities and right‐angle triangular cavities that may be inscribed inside the two original cavities.

The three distinct cavities shared the base wall as the heated wall, while the remaining sides and upper walls are cold. The finite volume method is used to perform the numerical computation of the transient conservation equations of mass, momentum and energy. The methodology takes into account the second‐order‐accurate quick scheme for the discretization of the convective term, whereas the pressure‐velocity coupling is handled with the simple scheme. The working fluid is air, which is not assumed as a Boussinesqian gas, so that all influencing thermophysical properties of air are taken as temperature‐dependent. The cavity problem is examined over a variety of height‐based Grashof numbers ranging from 10³ to 10⁶.

Numerical results are reported for the velocity fields, the temperature field as well as the local and mean wall heat fluxes along the heated base wall. It was found that the airflow remains symmetric for the isosceles triangular cavity with aspect ratio A=1 even at high Grashof numbers. In contrast, for an isosceles triangular cavity with an aspect ratio A=2, a pitchfork bifurcation begins to form at a critical Grashof number of 2 × 10⁵, breaking the airflow symmetry. The computed local and mean heat fluxes along the hot base wall are compared for the three configurations under study and the corresponding maximum heat transfer levels are clearly identified for the two aspect ratios A=1 and 2.

As a continuity of this work, there are two avenues that future research could explore and indeed are presently being explored by the authors within these geometries. The first deals with heat transfer enhancement using mixture of gases. The second is to re‐examine the problem under turbulent conditions.

The present study seeks to maximize the convection heat transport in cavities and minimize their sizes. The peculiarity of the derived cavities is their cross‐section area being half of the cross‐section area of the basic cavities.

Use of packed beds, enhanced tubes, nano-fluids and artificial ribs are few passive techniques to increase heat transfer in solar air heaters (SAHs). Artificial ribs attached to the absorber plate of the SAH will enhance the turbulence near the plate. Experimental analyses are conducted to find the thermal performance of SAH with ribs of regular geometries including rectangular, semi-circular and triangular in cross section. This paper aims to present the improvement in thermal performance of SAH with modified-arc.

Absorber plates are designed with ribs of rectangular, triangular, semi-circular and modified-arc in cross-section using existing data in literature. Physical dimensions of the ribs are designed by adapting procedure from literature. Absorber plates are manufactured with ribs and coated with blackboard paint and fixed to the existing SAH. Experiments are conducted with a variable-speed blower fixed to the inlet section of the SAH, which is used to supply air at different mass flow rates in a range between 0.495 and 0.557 kg/min.

Efficiency is found to be a strong function of mass flow rate of air through the SAH from the present experimental investigations. It was found that use of modified-arc ribs enhanced the efficiency of SAH by 105.35 per cent compared to SAH with plane absorber plate. Efficiency of SAH with modified-arc ribs is found to be higher by 24.43, 45.61 and 63.21 per cent, respectively, for SAH with semi-circular, rectangular and triangular arc ribs on its absorber plate.

Experiments on SAH are conducted during daytime from 9:00 am to 5:00 pm in open atmospheric conditions. Solar intensity is continuously changing during the experimentation from morning to evening. Calculations are made based on the observations with average values of solar intensity and temperature readings. More accurate values of SAH efficiency can be obtained with constant heat supply to the absorber plate by simulating the experimental setup in indoor conditions. Temperature and flow rate observations could be more accurate with sophisticated instrumentation rather than using simple thermocouples and orifice meters.

SAHs are basically used to supply hot air for both rural and industrial applications. These are used for crop drying, preheating of air, removal of moisture from leather, chemicals, etc. Conventionally, formers in India are using open sun drying to remove moisture from agricultural products. In this method, the moisture can be removed up to a level of 20 to 25 per cent. Use of SAH can remove moisture up to below 5 per cent and process is clean without reducing the quality of agricultural products. Enhancing the efficiency of SAHs will surely increase its usage by formers for crop drying.

Use of artificial ribs on absorber plate of SAH is most economical among many of the active and passive techniques. Numerical and experimental investigations are found in literature with regular cross-sectional ribs, including rectangular, triangular and semi-circular. The present work proposed new shape of the ribs named as modified-arc, which was not presented in the literature. Experimental analysis proved that the use of modified-arc makes the SAH more efficient in heat transfer.

According to very small dimensions of the microchannels, producing a microchannel with smooth surfaces is approximately impossible. The surface roughness can have a specific effect on microchannel performances. This paper aims to investigate the changes in friction and pressure drop in the microchannels by considering the different roughness elements on microchannel wall and changes in elementary geometry and flow conditions. Results show a significant effect of roughness on the pressure drop and friction.

Two-dimensional fluid flow in the rough microchannels is analyzed using FLUENT. Microchannels have a height of 50 µm. Water at room temperature (25°C) has been used as working fluid. The Reynolds numbers are considered in laminar flow range and from 50 to 300.

The results show that the value of friction factor reduces nonlinearly with an increase in Reynolds number. But, the pressure drops and the Poiseuille number in the microchannels increase with an increase in Reynolds number. The values of the pressure drop and the friction factor increase by increasing the height and size of the roughness elements, but these values reduce with an increase in the distance of roughness elements.

The roughness elements types in this research are rectangular, trapezoidal, elliptical, triangular and complex (composed of multiple types of roughness elements). The effects of the Reynolds number, roughness height, roughness distance and roughness size on the pressure drop and friction in the rough microchannels are investigated and discussed. Furthermore, differences between the effects of five types of roughness elements are identified.