Thermo-bioconvection in a suspension of gravitactic micro-organisms in vertical cylinders

We investigate the effect of heating or cooling from below at constant temperature and constant heat flux on the development of gravitactic bioconvection in vertical cylinders with stress free sidewalls. The governing equations are the continuity equation, the Navier–Stokes equations with the Boussinesq approximation, the diffusion equation for the motile micro-organisms and the energy equation. The control volume method is used to solve numerically the complete set of governing equations. The governing parameters are the thermal and bioconvection Rayleigh numbers, the bioconvection Peclet number, the Lewis number, the Schmidt number and the aspect ratio. We found that subcritical bifurcations of bioconvection became supercritical bifurcations when the thermal Rayleigh number Ra_T is different than zero. For Ra_T < 0, i.e. for cooling from below, we have opposing buoyancy forces, the convection is decreased and the critical thermo-bioconvection Rayleigh number is increased with respect to that of bioconvection. For Ra_T > 0, i.e. for heating from below, we have cooperating buoyancy forces, the convection is increased and the critical thermo-bioconvection Rayleigh number is decreased with respect to that of bioconvection. Heating and cooling from below at constant temperature and heat flux modify considerably the pattern formation of the gravitactic bioconvection.     

Cooling effect of thermally significant blood vessels in perfused tumor tissue during thermal therapy

This purpose of this article was focused on the cooling effects of thermally significant blood vessels on the extent of thermal lesion during heating treatments. The thermal modeling here based on the Pennes bio-heat transfer equation, describing the heat transfer of perfused tumor tissue, and the energy transport equation governing the heat convection and diffusion of the blood flow. The explicit finite difference method was used to solve the transient equation for the temperature field of a perfused tumor tissue encompassing a blood vessel in an axis-symmetric configuration during thermal therapy. As a result of simulation, the short-duration high-intensity heating is more effective on covering the treated tumor inside with a blood vessel 200 μm in diameter. For a blood vessel inside tumor tissue with a diameter larger than 2 mm, it is observed that neither longer heating duration nor higher heating power density is sufficient for complete necrosis of tumor.     

Theoretical and experimental investigation of a constant-pressure adsorption process

This paper presents a theoretical and experimental analysis of a constant pressure adsorption process. The governing heat and mass transfer equations derived from local thermodynamic equilibrium and energy balance are solved numerically. The model is validated by comparison with experimental results. It is then used to analyze the effect of some operating and design parameters on a constant-pressure sorption process. The adsorbent thickness and heat transfer coefficient between the adsorbent and the heating/cooling fluid have the strongest influence on sorption kinetics and on the cooling capacity of adsorption systems.     

Nonlinear analysis of tilted toroidal thermosyphon models

We analyze one-dimensional models for single-phase tilted toroidal thermosyphons for three different heating conditions: known heat flux, known wall temperature and mixed heating. For the first two the governing equations lend themselves to exact reduction to a set of three ordinary differential equations, while for the third the equations remain coupled as an infinite set. For all three cases, the tilt angle is stabilizing while the heat rate is a destabilizer. A nonlinear analysis is carried out using center manifold theory and normal form analysis. The known heat flux solutions lose stability through a supercritical Hopf bifurcation, while for the other two heating conditions the Hopf bifurcation is supercritical under some conditions and subcritical under others. Stable limit-cycle oscillations exist only for the supercritical cases, otherwise instability leads directly to chaos. Analysis also provides an estimate for the amplitude of oscillation for the supercritical conditions. Numerical experiments have confirmed the theoretical predictions qualitatively and quantitatively.     

Effect of Newtonian heating/cooling on free convection in an annular permeable region in the presence of heat source/sink

The influence of Newtonian heating/cooling in the presence of heat source/sink has been investigated on laminar free convective flow in a vertical annular permeable region. The mathematical model for the problem has been considered as a boundary value problem consisting of two simultaneous ordinary differential equations. The boundary value problem has been transformed to nondimensional form. This has given rise to a number of parameters representing both geometrical and physical features of the problem. Closed‐form analytical solutions of the governing equations have been obtained for two different cases of internal heat generation/absorption. To assess the effects of governing parameters on the fluid velocity and temperature, a number of profiles of these field variables have been presented. The efficacy of the distinct processes on the field variables has been discussed extensively. The main outcome obtained in this study is that the velocity as well as temperature is enhanced in the case of the Newtonian heating while the opposite behavior occurs in the Newtonian cooling for both cases of source and sink. Furthermore, the influence of the governing parameters has been shown on the skin friction, volume flow rate, and the Nusselt number.     

Numerical Study of an Electro-Osmotically Driven Microchannel Flow with Joule Heating Effect

A convection-diffusion reaction scheme is applied to solve the transient transport equations for the prediction of steady electro-osmotic microchannel flow behavior. The governing equations for the total electric field include the Laplace equation for the effective electrical potential and the Poisson-Boltzmann equation for the electrical potential established in the electric double layer. The transport equations governing the hydrodynamic field variables comprise mass conservation equation for the electrolyte and equations of motion for the incompressible charged fluid flow subject to an electro-osmotic body force. The main aim of the study is to elucidate the effect of Joule heating, which can affect the electrohydrodynamic behavior. Investigation into the region near the negatively charged channel wall is made through the simulated velocity boundary layer, diffuse layer, and electric double layer.     

Mixed convection boundary layer flow over a thin vertical cylinder with localized injection/suction and cooling/heating

The effects of localized cooling/heating and injection/suction on the mixed convection flow on a thin vertical cylinder have been studied. The localized cooling/heating and (or) injection/suction introduce a finite discontinuity in the mathematical formulation of the problem which increases its complexity. In order to overcome this difficulty, a nonuniform distribution of wall temperature (heat flux) and surface mass transfer is considered at certain sections of the cylinder. The nonlinear coupled parabolic partial differential equations governing the mixed convection flow under boundary layer approximations have been solved numerically by using an implicit finite-difference scheme. The effects of the localized cooling/heating and (or) injection/suction on the heat transfer are found to be significant, but the effects of cooling/heating on the skin friction are comparatively small. The positive buoyancy force which assists the flow and the curvature parameter increase the skin friction and heat transfer.     

An analysis of the hopf bifurcation in a hydroturbine governing system with saturation

A set of state equations of the polarization index governing system with saturation nonlinearity is established for a hydroturbine in small perturbation. The dynamic behavior of the proportional-integral governor (controller) governing system with saturation is analyzed and the conditions for the existence of a Hopf bifurcation are obtained by using a simple nonlinear model. The stability condition, which must be satisfied in the governing system, is simulated and supported by numerical calculations. The analysis and simulation show that a supercritical Hopf bifurcation may exist in hydraulic turbine systems. The results of this paper can be considered as an explanation for the sustained oscillations recorded in hydroelectric power stations.     

Solar enhanced natural draft dry cooling tower for geothermal power applications

This paper presents a new concept of hybrid cooling, named solar enhanced natural draft dry cooling tower (SENDDCT), in which solar collectors are added to traditional natural draft dry cooling towers to increase their performance. The purpose of using solar energy in this new cooling system is to increase the suction through the tower so that more air flow is achieved through the compact heat exchangers that cool condensers of a geothermal power plant. For the same size of the cooling tower, more air flow across the heat exchangers means more heat can be rejected by the system. The governing equations for the SENDDCT are similar to those of a conventional natural draft dry cooling tower except that solar heating is added after the heat exchanger bundles. Performance comparisons show that SENDDCT has substantial advantages over conventional natural draft dry cooling towers for geothermal power plants as well as standalone solar chimney power plants.     

A critical investigation into the heat and mass transfer analysis of counterflow wet-cooling towers

This study gives a detailed derivation of the heat and mass transfer equations of evaporative cooling in wet-cooling towers. The governing equations of the rigorous Poppe method of analysis are derived from first principles. The method of Poppe is well suited for the analysis of hybrid cooling towers as the state of the outlet air is accurately predicted. The governing equations of the Merkel method of analysis are subsequently derived after some simplifying assumptions are made. The equations of the effectiveness-NTU method applied to wet-cooling towers are also presented. The governing equations of the Poppe method are extended to give a more detailed representation of the Merkel number. The differences in the heat and mass transfer analyses and solution techniques of the Merkel and Poppe methods are described with the aid of enthalpy diagrams and psychrometric charts. The psychrometric chart is extended to accommodate air in the supersaturated state.     

Transient Thermal Fracture Analysis of Transversely Isotropic Magneto-Electro-Elastic Materials

Modern materials such as magneto-electro-elastic materials are used in the development of smart structures. The magneto-electro-elastic materials possess the dual features that the application of electric field induces magnetization and magnetic field induces electric polarization. The theory of linear magneto-electro-elasticity is applied to solve transient thermal fracture in magneto-electro-elastic cylinder under sudden heating on its outer surface. The equilibrium equations are obtained from the constitutive equations. The governing partial differential equations are deduced by using equilibrium equations of elastic, electric and magnetic fields. The heat conduction equation is solved by separation of variable technique. Hankel transform is applied to solve elastic displacements, electric potential and magnetic potential. The problem is reduced into integral equation involving Bessel functions which is treated exactly using Abel's integral equation. Transient distributions of temperature, stress, displacement and magnetic inductions are derived for magneto-electro-elastic cylinder. Thermal stress, electric displacement and magnetic induction-intensity factors are obtained. The solutions are valid for both impermeable and permeable crack models. The studies are valuable for such material analysis and design.     

Bioconvection of gravitactic microorganisms in a vertical cylinder

Patterns formation of gravitactic microorganism in a vertical cylinder is described by the Navier–Stokes equation coupled with the microorganism conservation equation. The control volume method is used to solve numerically these equations. It is found that when the Peclet number is decreased, the critical Rayleigh number also decreases to approach the value corresponding to Bénard convection under fixed-flux heating condition. However, at high Peclet numbers, the development convection is very different from that of Bénard convection. The most fundamental difference is that, while Bénard convection is a supercritical instability, the gravitactic bioconvection is shown to be a subcritical bifurcation from the diffusion state.     

BUOYANCY-AIDED MIXED CONVECTION WITH CONDUCTION AND SURFACE RADIATION FROM A VERTICAL ELECTRONIC BOARD WITH A TRAVERSABLE DISCRETE HEAT SOURCE

This article presents the results of a comprehensive fundamental numerical study of the problem of buoyancy-aided mixed convection with conduction and surface radiation from a vertical electronic board provided with a traversable, flush-mounted, discrete heat source. Air, a radiatively transparent medium, is considered to be the cooling agent. The governing equations in primitive variables for fluid flow and heat transfer are first converted into stream function–vorticity form, and are later converted into algebraic form using the finite-volume method. The resulting finite-difference equations are solved by Gauss-Seidel iterative technique. The governing equation for temperature distribution along the electronic board is obtained by appropriate energy balance. The effects of pertinent parameters, viz., location of the discrete heat source, surface emissivity of the board, and modifiedRichardson number, on various results, including local temperature distribution along the board, maximum board temperature, and contributions of convection and surface radiation to heat dissipation from the board, are studied in great detail. The fact that any design calculation that ignores surface radiation in problems of this kind would be error-prone is clearly highlighted.     

A Turbulent Impinging Jet on a Plate Covered with a Porous Layer

This work shows numerical results for a turbulent jet impinging against a flat plane covered with a layer of permeable material, which is kept at a higher temperature than that of the incoming fluid. Parameters such as porosity, permeability, thickness, and thermal conductivity of the porous layer are varied in order to analyze their effects on the local distribution of Nu. The macroscopic equations for mass, momentum, and energy are obtained based on volume-average concept. The numerical technique employed for discretizing the governing equations was the control volume method with a boundary-fitted nonorthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure–velocity coupling. Results indicate that inclusion of a porous layer decreases the peak in Nu avoiding excessive heating or cooling at the stagnation point. Also found, was that the integral heat flux from the wall is enhanced for certain ranges of values of porosity, layer thickness, and thermal conductivity ratio.     

Laser shortpulse heating: determination of lagging time due to different pulse parameters

The governing equations of energy transport during laser shortpulse heating is solved analytically for heating periods less or comparable to thermalization time of the substrate material. Since the lattice site temperature rise is considerably low in the time domain considered, the diffusional energy term in the governing equation is neglected. The effect of laser pulse shape parameter on the electron and lattice site temperature rise is investigated. It is found that rate of electron temperature rise in the heating period is lower than that corresponding to longer heating periods. The temporal behavior of electron and lattice site temperatures are similar, provided that the rise of lattice site temperature is low, which is in the order of 1.5 K after 4.5 × 10⁻¹² s heating period. The lagging time between electron and lattice site temperature is more pronounced as the pulse parameter (β/γ) increases.     

Sudden or smooth transitions in porous media natural convection

In porous media isothermal flow a transition from the Darcy regime, via an inertia dominated regime, towards turbulence is anticipated. In porous medium natural convection the transition to turbulence follows a different route. The first transition from a motionless-conduction regime to steady natural convection is followed by a direct second transition to a non-steady (time dependent) and non-periodic regime (referred to as weak turbulent), prior to the amplitude of the convection reaching such large values as to involve inertial, non-Darcy effects. The latter is due to an additional non-linear interaction that appears in natural convection as a result of the coupling between the equations governing the fluid flow and the energy equation. The present paper deals with identifying whether the transitions are sudden or possibly smooth. The latter is accomplished by using a truncated Galerkin representation of the natural convection problem in a porous layer heated from below (an extended Darcy model) leading to the familiar Lorenz equations for the evolution of the convection amplitudes with time. Two different formulations (named the “original” and the “modified” systems) are being used in an anticipation to obtaining a smooth transition in the form of an imperfect bifurcation from the “modified” system formulation. The results show that the transition remains sudden and the accuracy of the “modified” system results is being tested in comparison with the “original” system showing a sufficiently high degree of accuracy.     

Thermal Analysis of an Impinging Jet on a Plate With and Without a Porous Layer

This work shows numerical results for a jet impinging against a flat plane covered with a layer of a porous material, which is maintained at a higher temperature than the incoming fluid. Parameters such as permeability and thickness of the porous layer and thermal conductivity ration are varied in order to analyze their effects on the local distribution of Nu. The macroscopic equations for mass, momentum, and energy are obtained based on a volume-average concept. The numerical technique employed for discretizing the governing equations was the control volume method with a boundary-fitted nonorthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure-velocity coupling. Results indicate that inclusion of a porous layer decreases the peak in Nu avoiding excessive heating or cooling at the stagnation point. Also found was that the integral heat flux from the wall is enhanced for certain range of values of layer thickness, porosity, and thermal conductivity ratio.     

THERMOACTIVE STABILIZATION OF A COMPOSITE LEIPHOLZ COLUMN

A model of the Leipholz column made of orthotropic layers is analyzed. Apart from reinforcing fibers, the layers contain thermoactive shape memory alloy fibers. A nonlinear equation of motion that takes into account moderate deflections of the column, as well as Brazier's cross-section flattening effect, is examined. The effect of the martensite transformation due to external cooling and heating on the system stability expressed in terms of the critical load is investigated. The temperature change is also shown to affect the characteristics of the column nonlinear response, because it can lead to conversion of subcritical bifurcation into a supercritical one.     

LASER SHORT PULSE HEATING WITH CONVECTIVE BOUNDARY CONDITION

Laser short pulse heat can be applied widely in industry. The modelling of laser heat is fruitful when exploring the physical process involved during interaction between laser and workpiece. In this study, a modelling of laser short pulse heating is considered with convection boundary conditions. Electron kinetic theory and the Fourier heating model are taken into account when modelling the heating process. The governing equations are nondimensionalized and the numerical method employing a finite difference scheme is introduced for solving the governing equations. The range of Biot number ( Bi ) values is considered to account for the convection loss from the surface during the heating process. The predictions of electron kinetic theory and the Fourier heating model are compared with the two-equation model predictions. It is found that the effect of the Bi is significant on the temperature rise in the surface vicinity. The electron kinetic theory predictions at high Bi approach the Fourier heating model findings as the heating progresses.     

Optimization of Mixed Convection in a Lid-Driven Enclosure with a Heat Generating Circular Body

The physical model considered here is a lid-driven enclosure with bottom heating and top cooling conditions, and a heat generating circular body is placed at the center. The vertical walls of the cavity are kept thermally insulated, and the top lid moves at a constant speed. The steady two-dimensional governing equations for the physical problem are transformed in a dimensionless form with dimensionless governing parameters that decide the fluid flow and heat transfer characteristics in the system. The solution of these transport equations is obtained numerically with the finite element approach using the Galerkin method of weighted residuals. The parametric study has been carried out for variation of the heat generation parameters, the Reynolds numbers, solid-fluid thermal conductivity ratios as well as the Richardson numbers. The working fluid is assigned as air with a Prandtl number of 0.71 throughout the simulation. Results are presented in the form of streamlines, isotherms, average Nusselt number, bulk temperature, and drag force for the afore mentioned parameters. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as average Nusselt number, average bulk temperature, and drag force. An optimum combination of the governing parameters would result in higher heat transfer and lower drag force.