Model of flame dynamics of laminar premixed flame subject to the low frequency equivalence ratio oscillations

The effect of the non-uniform profile of scalar variables, such a fuel at the upstream and temperature at the downstream of the flame zone was discussed theoretically to elucidate; (1) the deviation of motion from the steady state case and (2) the hysteresis of premixed flames response to the equivalence ratio oscillations seen in an experimental and numerical works. One-dimensional integral model for the non-uniform scalar variable profile with low frequency equivalence ratio oscillation has been developed. Here, the wavelength of the oscillation is assumed to be larger than the nominal flame thickness. Through the integral analysis, we obtained the relation of the flame propagation speed for steady and unsteady cases depending on the non-uniform scalar profile at the upstream and downstream of the flame zone. Hysteresis of the flame propagation speed is found due to the transport of fuel and heat by the non-uniform scalar profile at the upstream and downstream of the flame zone. This result qualitatively agreed with the numerical results of a response of the stagnation laminar CH₄/air premixed flames for a low equivalence ratio oscillation frequency.     

Thermal effects on mixed electro-osmotic and pressure-driven flows in triangle microchannels

A numerical investigation on the mixed electro-osmotic and pressure-driven flows in triangle microchannels with constant wall temperature is reported in the present study. The Galerkin method is employed to solve the Poisson equation, energy equation and Navier–Stokes equations for the flow driven by electro-osmotic and pressure gradient synchronously under the conditions of favorable pressure gradients and backpressure gradients. The physical properties of the electrolyte solution are considered to be varying with the temperature, and the dimensionless velocity profile, dimensionless temperature profile as well as dimensionless mass flux of the electrolyte solution are obtained. Furthermore, the parameters studies including pressure gradient, length ratio and Joule heating on mass flux of the electro-osmotic flows are performed, respectively. The numerical results show that a large Joule number leads to large dimensionless mass flux and dimensionless temperature of the electrolytic solution in the triangular microchannels for both conditions. For the electro-osmotic flows under the favorable pressure gradient, the increase in dimensionless mass flux resulted from Joule heating is enlarged with increasing pressure gradient and length ratio. However, for the electro-osmotic flows under the backpressure gradient, Joule heating results in a reverse flow in the channel, and the dimensionless mass flux of the reverse flow increases with increasing backward pressure gradient and decreasing length ratio. It is further found that the Joule heating induces a more significant increase in the dimensionless mass flux under favorable pressure gradient compared with that under backpressure gradient.     

On effect of non-uniform basic temperature gradient on Bénard–Marangoni convection in micropolar fluid

Linear stability analysis is performed to study the effect of non-uniform basic temperature gradients on the onset of Bénard–Marangoni convection in a micropolar fluid. The influence of various parameters on the onset of convection has been analysed. The possibility of delaying the onset of convection by the application of a cubic basic state temperature profile is demonstrated.     

Influence of heat transfer on a peristaltic flow of Johnson Segalman fluid in a non uniform tube

The present investigation deals with the peristaltic motion of an incompressible non-Newtonian fluid in a non-uniform tube for long wavelength. The mechanical properties of the material are represented by the constitutive equation for a Johnson Segalman fluid. The resulting problem for velocity field and temperature profile is solved using (i) Regular perturbation method (ii) Homotopy analysis method. The influence of various emerging parameters on the flow is shown through graphs and discussed.     

Nonlinear dynamic behavior of non-convective zone in salt gradient solar pond

Non-Convective Zone (NCZ) of salt gradient solar pond is a typical double diffusive system of salinity and temperature, and it is subjected to instable effects of adverse temperature gradient. The onset of instability may occur as an oscillatory motion because of the stabilizing effect of the salinity. In this paper, the marginal state between the steady state and the convection of the NCZ is studied. The stability of the Boussinesq approximation of the Navier-Stokes equations is analyzed by a perturbation approach. The marginal states for the onset of convection are obtained by analytical method, which is based on the linearization of the ordinary differential equations, and then numerical method is used to solve the nonlinear ordinary differential equations. Numerical results provide the trajectories of the temperature and velocity coefficients in the three-dimensional phase space, as well as the two-dimensional temperature, salinity and velocity fields in NCZ. The results demonstrate that the numerical study is in agreement with the marginal stability and the critical Rayleigh number derived from linear stability analysis. Both the linear and nonlinear studies indicate that oscillation is a narrow region above the stable region; however, the nonlinear numerical results indicate that the linear stability analysis leans to a larger upper boundary in the oscillatory regions.     

Transient natural convection in an enclosure with vertical solutal gradients

Transient natural convection in an enclosure with vertical solutal gradients has been studied in this paper. Transfers in a rectangular cavity configuration translating hydrodynamic and thermal phenomena are numerically predicted by means of computational fluid dynamics (CFD) in transient regime.The objective of this numerical study is to give a fine knowledge of the hydrodynamic and thermal characteristics during energy storage in an enclosure filled with water stratified by downward salinity gradient. The enclosure is divided into three zones with different salinity level such as salt gradient pond (SGP). Water is heated by a heating device at the bottom of the cavity.The Navier–Stokes, energy and mass equations are discretized using finite-volume method, and a two-dimensional analysis of the hydrodynamic and thermal behaviors generated in transient regime in the cavity are performed. The mathematical modelling has allowed the prediction of the storage performances by developing parametrical study in view to search the convective heat transfer coefficient at the bottom of the enclosure. Velocity vector fields show the presence of recirculation zones caused only in the lower region and permit to explain the increase of the temperature in the lower convective zone (LCZ).This study shows also the importance of the salinity in the preservation of the high temperature in the bottom of the cavity, and the important reduction of the phenomenon of thermal transfer across the non-convective zone (NCZ).     

Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime

We have measured the pressure drop and convective heat transfer coefficient of water-based Al₂O₃ nanofluids flowing through a uniformly heated circular tube in the fully developed laminar flow regime. The experimental results show that the data for nanofluid friction factor show a good agreement with analytical predictions from the Darcy’s equation for single-phase flow. However, the convective heat transfer coefficient of the nanofluids increases by up to 8% at a concentration of 0.3 vol% compared with that of pure water and this enhancement cannot be predicted by the Shah equation. Furthermore, the experimental results show that the convective heat transfer coefficient enhancement exceeds, by a large margin, the thermal conductivity enhancement. Therefore, we have discussed the various effects of thermal conductivities under static and dynamic conditions, energy transfer by nanoparticle dispersion, nanoparticle migration due to viscosity gradient, non-uniform shear rate, Brownian diffusion and thermophoresis on the remarkable enhancement of the convective heat transfer coefficient of nanofluids. Based on scale analysis and numerical solutions, we have shown, for the first time, the flattening of velocity profile, induced from large gradients in bulk properties such as nanoparticle concentration, thermal conductivity and viscosity. We propose that this flattening of velocity profile is a possible mechanism for the convective heat transfer coefficient enhancement exceeding the thermal conductivity enhancement.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source

In this paper, visco-elastic boundary layer flow and heat transfer over a stretching sheet in presence of viscous dissipation and non-uniform heat source have been discussed. Analytical solutions of highly non-linear momentum equation and confluent hypergeometric similarity solution of heat transfer equations are obtained. Here two types of different heating processes are considered namely (i) prescribed surface temperature (PST) and (ii) prescribed wall heat flux (PHF). The effect of various parameters like visco-elastic parameter, Eckert number, Prandtl number, and non-uniform heat source/sink parameter on temperature distribution are analyzed and effect of all these parameters on wall temperature gradient and wall temperature are tabulated and discussed.     

A study of methanol steam reforming on distributed catalyst bed

Heterogeneous catalytic fixed bed usually suffers from severe limitations of mass and heat transfer. These disadvantages limit reformers to a low efficiency of catalyst utilization. Three catalyst activity distributions have been applied to force the reactor temperature profile to be near isothermal operation for maximization of methanol conversion. A plate-type reactor has been developed to investigate the influence of catalyst activity distribution on methanol steam reforming. Cold spot temperature gradients are observed in the temperature profile along the reactor axis. It has been experimentally verified that reducing cold spot temperature gradients contributes to the improvement of the catalytic hydrogen production. The lowest cold spot temperature gradient of 3 K is obtained on gradient catalyst distribution type A. This is attributed to good characteristics of local thermal effect. Low activity at the reactor inlet with gradual rise along with the reactor flow channel forms the optimal activity distribution. Hydrogen production rate of 161.3 L/h is obtained at the methanol conversion of 93.1% for the gradient distribution type A when the inlet temperature is 543 K.     

Effect of volumetric radiation on natural convection in a square cavity using lattice Boltzmann method with non-uniform lattices

This study deals with the effect of volumetric radiation on the natural convection in a square cavity containing an absorbing, emitting and scattering medium. Numerical simulation has been carried out using lattice Boltzmann method (LBM) with non-uniform lattices. Non-uniform lattices/control volumes have been implemented to deal with the sharp gradients and achieve reasonably accurate solutions. Separate equations dealing with different particle distribution functions in the LBM are used to calculate the density and velocity fields and the thermal fields. The finite volume method (FVM) is used to compute the radiative term of the energy equation. The results obtained in the present study is compared and validated against available results in literature. The centerline temperature across the cavity, the isotherms, the vertical velocity in the horizontal mid-plane, the horizontal velocity in the vertical mid-plane and the streamlines are studied for different parameters such as Rayleigh number, conduction–radiation parameter, extinction coefficient and scattering albedo. The results obtained by using the non-uniform lattices-based LBM are compared with the results for uniform lattice based-LBM. It is found that the non-uniform lattice-based LBM provides accurate results and it is computationally more efficient.     

Modeling the dynamics of the mixed layer in solar ponds

A new model is proposed to explain the Nielsen's equilibrium condition. This model takes into account the effects of both turbulent entrainment and diffusion on the growth/erosion of the gradient zone. The existing turbulent entrainment model is modified to make it applicable near the equilibrium condition. The new model predictions indicate the dependence of the equilibrium condition on the mixed layer depth, apart from the salinity and temperature gradients in the gradient zone.     

Influence of ramped pressure gradient on transient flow formation in a horizontal porous channel

The transient flow formation in a horizontal porous channel assuming a ramped pressure gradient is presented. The equation governing the flow is modeled into a partial differential equation (PDE) which is solved by employing the Laplace transformation technique to transform the PDE to an ordinary differential equation (ODE). The obtained ODE is solved by employing the method of undetermined coefficients to obtain the velocity profile in the Laplace domain. The Riemann sum approximation technique is then adopted to change the obtained solution from the Laplace domain into the time domain. For accuracy checks, the numerical results of the obtained equation are reckoned with previously published work, and an excellent agreement is found. For a clearer understanding of the impact of various flow parameters entering the solutions obtained, graphical and tabular representations are offered using MATLAB software. We noticed that the velocity is slower with ramped pressure gradient compared to a constant pressure gradient. This is because the motion of the fluid occurs gradually with ramped pressure gradient.     

Effects of thermal nonequilibrium and non-uniform temperature gradients on the onset of convection in a heterogeneous porous medium

The simultaneous effect of local thermal nonequilibrium (LTNE), vertical heterogeneity of permeability, and non-uniform basic temperature gradient on the criterion for the onset of Darcy-Benard convection is studied. The eigenvalue problem is solved numerically using the Galerkin method. The interaction of various types of permeability heterogeneity and non-uniform basic temperature gradient functions on the stability characteristics of the system is analyzed. It is observed that the linear variation (about the mean) of the permeability and the basic temperature gradient with depth has no added effect on the criterion for the onset of convection. However, the concurrent variation in heterogeneous permeability and non-uniform basic temperature gradient functions has more stabilizing effect on the system, while opposite is the trend when the effect of non-uniform basic temperature gradient alone is present.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet

Studies are made on the viscoelastic fluid flow and heat transfer characteristics over a stretching sheet with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for the cases of prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The momentum equation is decoupled from the energy equation for the present incompressible boundary layer flow problem with constant physical parameters. Exact solution for the velocity field and the skin-friction are obtained. Also, the solutions for the temperature and heat transfer characteristics are obtained in terms of Kummer’s function. The work due to deformation in energy equation, which is essential while formulating the viscoelastic boundary layer flow problems, is considered. This paper examines the effect of viscoelastic parameter, Eckert number, Prandtl number and non-uniform heat source/sink parameter on temperature distribution, wall temperature gradient for PST-case and wall temperature for PHF-case.     

Optimum design of inhomogeneous rotating discs under secondary creep

Rotating discs commonly used in the aerospace industry often operate under high mechanical stresses due to centrifugal forces, while subject to high temperature gradients. High stresses and temperatures lead to creep in such rotating disc applications. This problem is particularly important in turbine discs under continuous operation. Since such discs are subject to secondary creep effects during most of their useful lives, it is important that they be optimized for minimum weight for the steady-state creep stresses. In this investigation, by considering the variable physical properties of the rotating disc materials under a high temperature gradient, a procedure for weight minimization for the steady-state creep stresses is proposed. The method aims to design the disc thickness profile so as to have minimum weight while the equivalent secondary creep stresses of the rotating disc under a high temperature gradient at all points simultaneously approach but do not exceed an allowable stress. An example is given to illustrate the method.     

Joule heating and viscous dissipation in flow of nanomaterial by a rotating disk

This paper aims to analyze the flow of second grade nanoliquid by a rotating disk. Nanofluid under investigation strongly depends upon Brownian motion and thermophoresis. Heat transfer is studied subject to dissipation and Joule heating. Governing problems are made dimensionless. After this the out coming problems for momentum, temperature and concentration are solved. The convergence criteria related to solutions is spelled out. Convergence interval for solutions is analyzed. Impact of different variables on velocity, concentration and temperature is elucidated by plotting graphs. Velocity and temperature gradients are calculated and discussed. The obtained results demonstrate that velocity field enhances for larger estimation of viscoelastic variable. Further results also demonstrate that velocity gradient has opposite effects for Hartman number and viscoelastic parameter. Temperature gradient is more for higher estimation of Reynolds number.     

Geothermal gradients of Alberta in Western Canada

55,246 bottom hole temperature (BHT) values from petroleum exploration well logs of 28,260 wells have been used to estimate geothermal gradients in Alberta. A general decrease in geothermal gradient towards the east is apparent. High gradient areas occur in the Hinton - Edson area of west central Alberta, in the Fort McMurray area of northeast Alberta, in the Steen River area of northwest Alberta, and at the northwest corner of the province. Comparison with gravity, aeromagnetic and relief maps indicates close correspondence between topographic features and geothermal gradients. It is suggested that subsurface temperature distribution in Alberta is strongly influenced by groundwater motion.     

Flame temperatures along a laminar premixed flame with a non-uniform stretch rate

We investigated experimentally the effects of a spatially non-uniform stretch rate on the flame temperature. A flame surface with a non-uniform stretch rate was formed by creating a wrinkled laminar premixed flame in a spatially periodic flow field of a lean propane/air mixture. The measured flame temperature was lower/higher than the adiabatic flame temperature at flame segments with positive/negative stretch rates. This was a result of the effects of flame stretch and preferential diffusion for Lewis number greater than unity. The flame temperature estimated using the conventional flame stretch theory, which is based on a uniform stretch rate along the flame surface, did not agree quantitatively with the measured temperature. Therefore, we revised the theory, taking into account heat transfer along the flame surface, and then produced estimates that agreed with the measured temperature. We found that the effect of flame stretch and preferential diffusion is changed along the flame surface which has spatially non-uniform stretch rate, causing a temperature gradient along the surface, which in turn transfers heat and changes the flame temperature. Thus, heat transfer along the flame surface is an important factor in estimating flame temperature. In addition, a second temperature gradient appears downstream just behind the flame, because the temperature of the burned gas is also non-uniform. Therefore, conductive heat transfer is believed to occur between the flame and the burned gas. The effect of the downstream heat transfer is not as large as that of the heat transfer along the flame surface.     

Pattern formation of drops in thermocapillary migration

The behavior of a drop cloud in thermocapillary motion in zero gravity is examined for both mono-dispersed and poly-dispersed cases. Numerical simulations of the thermocapillary motion of two- and three-dimensional fully deformable light drops are presented. The Navier–Stokes equations coupled with the energy conservation equation are solved by a front-tracking/finite-difference method. The material properties of the drop fluid and the ambient fluid are different, and the interfacial tension depends on the temperature. At moderate Reynolds (Re) and Marangoni (Ma) numbers, the results show that drops form layers nearly perpendicular to the temperature gradient.     

A novel numerical method for steady-state thermal simulation based on loop-tree and HBRWG basis functions

Abstract

This article presents a novel numerical method for steady-state thermal simulation. This method firstly solves the heat flux efficiently by applying the loop-tree basis functions. Then, the temperature is obtained by finding solutions of the gradient equation. The half boundary Rao-Wilton-Glisson (HBRWG) basis functions are employed for handling arbitrary boundary conditions. In addition, the triangulation-based interpolation technique is utilized to interpolate temperature profile with obtained results in post-processing. Three examples with mixed boundary conditions are studied to validate the accuracy of proposed method for simulating steady-state thermal problems. Numerical results show that our method has a good accuracy and is well capable of handling arbitrary boundary conditions.