Transient Free Convection Research Articles

Transient free convection flow between long vertical parallel plates with ramped wall temperature at one boundary in the presence of thermal radiation and constant mass diffusion

The unsteady laminar free convection flow between two long vertical parallel plates with ramped wall temperature at one boundary has been investigated in the presence of thermal radiation and chemical species concentration. The exact solutions of the momentum, energy and concentration equations have been obtained using the Laplace transform technique. The velocity and temperature profiles, skin-friction and Nusselt number variations are shown graphically and the numerical values of the volume flow rate, the total heat rate and species rate added to the fluid are presented in a table. The influence of different system parameters such as the radiation parameter (R), buoyancy ratio parameter (N), Schmidt number (Sc) and time (t) has been analyzed carefully. A critical analysis of the coupled heat and mass transfer phenomena is provided. The free convective flow due to ramped wall temperature has also been compared with the baseline case of flow due to constant wall temperature.

Soret and Radiation Effects on Transient MHD Free Convection From an Impulsively Started Infinite Vertical Plate

An exact solution to the problem of MHD transient free convection and mass transfer flow of a viscous, incompressible, and electrically conducting fluid past a suddenly started infinite vertical plate taking into account the thermal diffusion as well as the thermal radiation is presented. Assuming the medium to be nonscattered and the fluid to be nongray, emitting–absorbing, and optically thin radiation limit properties, the equations governing the flow and heat and mass transfer are solved by Laplace transform technique. The expressions for the velocity field, the concentration field, the skin friction at the plate in the direction of the flow, and the coefficient of heat transfer and mass transfer from the plate to the fluid have been obtained, and their numerical values for different values of the physical parameters involved in the problem have been demonstrated in graphs and tables, and these are physically interpreted. It is found that the thermal radiation retards the fluid flow whereas the Soret effect accelerates the flow. The viscous drag on the plate is increased under the Soret and magnetic field effects whereas the thermal radiation reduces the skin friction. Further, the rate of heat transfer at the plate increases under thermal radiation effect. Also, in the presence of radiation, the Soret effect results in a steady increase in the mass flux from the fluid to the plate.

Transient Free Convection Flow Past an Infinite Moving Vertical Cylinder in a Stably Stratified Fluid

This paper presents an analytical treatment for the unsteady one-dimensional natural convective flow past an infinite moving vertical cylinder in the presence of thermal stratification. Exact solutions of the dimensionless unsteady coupled linear governing equations are obtained, in terms of Bessel functions by the Laplace transform technique, for the tractable case of unit Prandtl number. Numerical computations for velocity, temperature, skin-friction, and Nusselt number are made for various set of physical parameters and presented in graphs. Due to the presence of thermal stratification, the fluid velocity and temperature approach steady state, whereas the corresponding flow in an unstratified fluid does not. The steady state is attained at smaller times as the stratification increases. Furthermore, in the presence of stratification, the skin-friction and Nusselt number approaches fixed value as time progresses, while for unstratified fluid, there is a gradual decrease as time increases.

Flow past an Electrically Conducting Fluid over a Vertical Oscillating Plate with Chemical Reaction.

Effect of magnetic field on transient free convection flow past an electrically conducting fluid over an oscillating vertical plate with chemical reaction is studied here. Exact solutions obtained by Laplace Transform methods are presented graphically for different values of physical parameters. It is observed that chemical reaction parameter and magnetic parameter influence the velocity and concentration profiles significantly.

Transient free-convective flow of reactive viscous fluid in vertical tube

The problem of fully-developed transient free-convection flow of viscous reactive fluid in a vertical tube is analyzed both analytically and numerically. The study reports the effect of several operating parameters on the flow hydrodynamics and thermal characteristics. The solutions for transient state velocity and temperature fields are obtained by implicit finite difference method. To check the accuracy of the numerical solution steady-state solutions for temperature field and velocity field are obtained by using perturbation series method. Skin-friction and Nusselt number at the surface of tube are determined. The significant results from this study are that both velocity and temperature increase with the increase in the value of reactant consumption parameter and non-dimensional time until they reach steady-state value. The results also indicate that it takes longer time to attain steady-state in the case of water than air. During the course of computation, it was observed that the analytical and numerical solutions agree very well at large value of time.

Effects of viscous shear stress on thermoregulation of electronics. Transient free convection in diode enclosures induced by discrete heat bands under constant heat flux

Thermal and dynamic phenomena that occur in the immediate vicinity of electronic components during operation generate viscous shear stresses due to velocity gradients. When thermocouples used for thermal regulation of these assemblies are installed in this environment, temperature measurements may be erroneous. It is therefore essential to take into account viscous effects in the boundary layer when dealing with thermal control of electronics subjected to natural convection. These phenomena are particularly pronounced and complex when generation of heat at the active wall is not uniform. That is the case for the real device treated in this work. The natural convective flow is generated by a vertical wall composed by alternated adiabatic and heated bands under constant heat flux, representing a working electronic equipment. The 2D transient boundary layer near the vertical active hot wall of parallelogram-shaped enclosures is treated in order to determine the viscous shear stress. Results are obtained by numerical approach using the finite volume method and some measurements. Many geometrical configurations are treated while varying the inclination angle of the top and bottom passive adiabatic walls. The very different local distributions of viscous shear stresses and vertical thermal gradients confirm the necessity to take them into account to properly install the sensors used for thermoregulation.

Experimental transient natural convection heat transfer from a vertical cylindrical tank

In this paper heat transfer experimental data is presented and compared to general correlations proposed in the literature for transient laminar free convection from a vertical cylindrical tank. The experimental data has been obtained from heating and cooling experiments carried out with a cylindrical full-scale hot water storage tank working under real operating conditions. The experimental device and the data acquisition system are described. The calculation procedures established to obtain the experimental values of the heat transfer coefficients, as well as the data reduction process, are detailed. The local convection and radiation heat transfer coefficients are obtained from different heating power conditions for local Rayleigh numbers within the range of 1×105–3×108. The great quantity of available experimental data allows a detailed analysis with a reliable empirical base. The experimental local convection heat transfer coefficients are correlated and compared to correlations proposed in open literature for engineering calculations.

An electric simulator to solve education engineering problems in fluid mechanics

AbstractElectrical analogy, which is used to solve numerical problems in fluid mechanics, is used here to solve the classical problem of Couette flow between two parallel plates, Hagen–Poiseuille flow in a pipe and the transient free convection flow along a semi‐infinite vertical wall. The nonlinear system of partial differential equations is numerically solved by the Network Simulation Method, based on thermo‐electric analogy. A simulator of electrical devices, permits the direct visualization of the local and/or integrated transport variables (temperatures, velocities, concentrations, and fluxes) at any point or section of the medium. At the same time, the solution for both transient and steady‐state problems is obtained, the only requirement being finite‐difference schemes for the spatial variable. This educational tool is seen to be very useful for solving numerical problems in engineering and can be used to graduate in the University. © 2011 Wiley Periodicals, Inc. Comput Appl Eng Educ 21: 748–757, 2013

Chemical reaction and radiation effects on the transient MHD free convection flow of dissipative fluid past an infinite vertical porous plate with ramped wall temperature

A finite-difference analysis is performed to study the effects of thermal radiation and chemical reaction on the transient MHD free convection and mass transform flow of a dissipative fluid past an infinite vertical porous plate subject to ramped wall temperature. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. The dimensionless governing equations are unsteady, coupled and non-linear partial differential equations. An analytical method fails to give a solution. Hence an implicit finite difference scheme of Crank-Nicolson method is employed. The effect of the Magnetic parameter (M), Chemical reaction parameter (K), Radiation parameter (F), Buoyancy ratio parameter (N), Schmidt number (Sc) on the velocity field and skin friction for both air (Pr=0.71) and water(Pr=7) in the presence of both aiding (N>0) and opposing (N<0) flows are extensively discussed with the help of graphs.

Radiation and Mass Transfer Effects on Transient Free Convection Flow of a Dissipative Fluid past Semi-Infinite Vertical Plate with Uniform Heat and Mass Flux

Effect of radiation and mass transfer on the transient free convection flow of a dissipative past semi-infinite vertical plate with uniform heat and mass flux is analyzed, by taking into account the effect of viscous dissipation. This type of problems finds application in many technological and engineering fields such as plasma studies, petroleum industries, MHD energy generators, cooling of nuclear reactors, the boundary layer control in aerodynamics, crystal growth and furnace engineering. The Rosseland approximation is used to describe the radiative heat transfer in the limit of the optically thick fluid. The non-linear, coupled equations are solved using an implicit finite difference scheme of Crank-Nicolson type. Transient temperature, concentration and velocity profiles, local and average skinfriction coefficient, Nusselt number and Sherwood number are presented graphically and discussed. It is observed that, when the radiation parameter increases the velocity and temperature decrease accompanied by simultaneous reduction in both momentum and thermal boundary layers.

Transient free convection in passive buildings using 2D air-filled parallelogram-shaped enclosures with discrete isothermal heat sources

This work evaluates the transient convective exchanges taking place in a building wall made up of air-filled inclined cells. Each cell is formed by two vertical active walls connected by a channel of insulating material. The active hot wall is composed by alternated isothermal and adiabatic bands and is opposite to the active cold wall. Both walls are vertical and separated by a distance equal to their height. The channel connecting these walls is inclined at an angle α with respect to the horizontal, being the values considered in the present work 0° (square cell), ±15°, ±30°, ±45° and ±60°. Two-dimensional temperature fields and streamlines are presented at some representative instants. The temporal evolution of the average Nusselt number at each band of the hot wall is determined for all the treated configurations. Numerical results are validated by comparison with other experimental and numerical studies for cavities with isothermal hot wall in steady state. The maximum deviation found is about 9% for the Nusselt number. This can be considered as very satisfactory for this type of studies characterized by high Rayleigh numbers varying between 1 × 10 5 and 3 × 10 8, representative of real building installations.

Transient free convection flow of a viscoelastic fluid over vertical surface

In this paper, the viscoelsatic boundary layer flow and the heat transfer near a vertical isothermal impermeable surface and in a quiescent fluid are examined. The governing equations are formulated and solved numerically using MackCormak’s technique. The results show excellent agreement with previously published results by a comparision. Representative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers, and local skin friction coefficients are shown graphically for different values of viscoelsatic parameters. In general, it is found that the velocities increase inside the hydrodynamic boundary layers and the temperatures decrease inside the thermal boundary layers for the viscoelsatic fluid as compared with the Newtonian fluid due to favorable tensile stresses. Consequently, the coefficients of friction and heat transfer enhance for higher viscoelsatic parameters.

Free convection heat and mass transfer flow in a vertical channel with the Dufour effect

The purpose of this work is to investigate analytically the free-convection and mass transfer flow in a vertical channel formed by two vertical parallel plates. Fully developed laminar flow was considered with uniform temperature and concentration on the plates. The diffusion-thermo effect was taken into consideration. The velocity, temperature, and concentration profiles were obtained analytically using the Laplace transform technique and were used to compute the shear stress, Nusselt number, and mass flux. The present analytical results were compared with those available in the literature without mass transfer and the diffusion-thermo effect and excellent agreement was observed (Singh, A. K., Gholami, H. R., and Soundalgekar, V. M. Transient free convection flow between two vertical parallel plates. J. Heat Mass Transf., 1996, 31, 329—331.). During the course of computation, it was found that the transient solution at large time coincides with the steady-state solution derived separately. The diffusion-thermo effect is observed to create an anomalous situation in temperature and velocity profiles for small Prandtl numbers. The study also revealed that the steady state of the problem is independent of the Dufour effect.

Transient free convection in parallelogrammic cavities applied to the thermoregulation of avionics

This work addresses momentum and heat transfer phenomena that take place in closed cavities filled with air. The cavities are formed by two vertical active walls, one hot consisting of bands that are alternately insulated and heated at temperature Th and other cold, isothermal at Tc. The closing upper and lower passive walls can be tilted an angle αeither above or below the horizontal plane. When α is positive (hot wall below the level of the cold one), the air movement is favoured while the opposite occurs for negative angles. These cavities are thus either transferring or insulating, which confers them the quality of a so-called convective diode. Such geometry is applied in this work to the thermoregulation of the on-board aviation electronics. The flows corresponding to different angles and temperature differences ΔT = Th – Tc are examined both numerically and experimentally. We consider in particular the transient transport phenomena which occur at the very beginning, a critical stage in the operation of the on-board materials.

Transient magneto-micropolar free convection heat and mass transfer through a non-Darcy porous medium channel with variable thermal conductivity and heat source effects

The laminar, fully developed, transient magnetohydrodynamic (MHD) free convection heat and mass transfer of an electrically conducting micropolar fluid between two vertical plates containing a non-Darcy porous medium with heat generation/absorption and asymmetric wall temperature and concentration has been discussed in this article. A similarity transformation is used to render the problem into a system of coupled, partial, differential equations, which are solved using the finite-element method (FEM). The solutions are validated with a robust finite difference method (FDM) solver. The present work examines the effect of Darcian parameter, Forchheimer parameter, heat absorption/generation parameter, vortex viscosity parameter, buoyancy ratio parameter, magnetic parameter, and variable thermal conductivity parameter on velocity, angular velocity, temperature and concentration profiles. Space—time graphs of velocity and microrotation are also plotted to provide a better perspective of the flowfield evolution with respect to time. Applications of the study may arise in, for example, packed-bed chemical reactors, materials processing, magnetic field control of chemical engineering transport processes in filter media, purification of hydrocarbons with electromagnetic fields, etc.

Geometrical and Rayleigh number effects in the transient laminar free convection between two vertically eccentric spheres

PurposeThe purpose of this paper is to study the transient natural convection of a Newtonian fluid which develops in a closed spherical annulus delimited by two vertically eccentric spheres by using a bispherical coordinates system. The inner sphere is heated by a heat flux of constant density and the outer one is maintained isothermal.Design/methodology/approachThe transfer equations are written by using a bispherical coordinates system. The Navier‐Stokes equations are solved and coupled with the energy equation by using the alternating direction implicit (ADI) and the successive over relaxation (SOR) methods.FindingsThe study of the stream function and the Nusselt number shows that the convection motion is reinforced for the geometries characterized by positive values of the eccentricity with heat exchange increasing. The Nusselt number increases with the modified Rayleigh number. The heat exchange increases with the radius ratio. The results show that the steady state is reached faster when the modified Rayleigh number increases and the influence of the eccentricity is very low on the establishment of the steady state. The fluids flow depends strongly on the eccentricity and the modified Rayleigh number.Research limitations/implicationsSimulations are performed for modified Rayleigh numbers ranging from 103 to 106, for eccentricities varying between –0.6 and +0.6 and for radius ratio between 1.5 and 2.Originality/valueThe results of eccentricity and modified Rayleigh number effects in transient natural convection between vertically eccentric spheres have been displayed.

Unsteady buoyancy driven saline water over a vertical flat plate

The effect of heat and mass transfer on transient laminar free convection flows for saline water over a vertical flat surface is studied. The non-Boussinesq equation to approximate temperature variations with density in buoyancy term is applied. The governing equations are written in their dimensionless form and then solved numerically using an implicit finite difference technique. Two parameters are found to describe the problem; the first one is the density parameter, the second one is the dimensionless Grashof number. Velocity profiles, temperature profiles and Nusselt numbers are discussed.

Theoretical Analysis of Radiative Effects on Transient Free Convection Heat Transfer past a Hot Vertical Surface in Porous Media

The purpose of the present investigation deals with the unsteady free convective flow of a viscous incompressible gray, absorbing-emitting but non-scattering, optically-thick fluid occupying a semi-infinite porous regime adjacent to an infinite moving hot vertical plate with constant velocity. We employ a Darcian viscous flow model for the porous medium. The momentum and thermal boundary layer equations are non-dimensionalized using appropriate transformations and then solved subject to physically realistic boundary conditions using the Laplace transform technique. Thermal radiation effects are simulated via a radiation-conduction parameter, Kr, based on the Rosseland diffusion approximation. The influence of Grashof (free convection) number, radiation-conduction parameter (Kr), inverse permeability parameter (Kp) and dimensionless time (t) are studied graphically. We observe that increasing thermal radiation parameter causes a noticeable increase in the flow velocity, u. Temperature, θ, is significantly increased within the boundary layer with a rise in Kr since the latter represents the relative contribution of thermal radiation heat transfer to thermal conduction heat transfer. Increased radiation therefore augments heat transfer, heats the fluid and increases the thickness of the momentum and thermal boundary layers. Velocity is found to decrease with an increase in Kp (inverse permeability parameter) as are shear stress function ( ∂u/∂y | y=0) magnitudes owing to greater resistance of the porous medium for lower permeabilities, which decelerate the flow. An increase in Kr however boosts the shear stress function magnitudes i.e. serves to accelerate the flow. Temperature gradient, ∂θ/∂y | y=0 is also positively affected by an increase in thermal radiation (Kr) and with time. The present study has applications in geological convection, forest fire propagation, glass heat treatment processes at high temperature, metallurgical processing etc.

Numerical and experimental investigation of laminar free convection around a thin wire: Long time scalings and assessment of numerical approach

Transient and steady free convection around a line heat source is studied experimentally and numerically. Experiments are performed with a thin platinum wire of 50 μm in radius immersed in water and heated by Joule effect. Time evolution of velocity and temperature fields are measured by PIV (Particle Image Velocimetry) and micro-thermocouple for three different heating rates. Numerical simulations are done using a time-stepping algorithm based on a velocity–pressure formulation. The equations are discretized on a domain of limited extension, using spectral type approximations and a domain decomposition technique, and a pressure condition is imposed at the outer boundary. A three-stage scenario is proposed for the development of transient free convection around a thin wire, and, at each stage, the numerical approach is assessed through detailed comparison between numerical and experimental results. Previously established scaling laws for the onset of convective motion are checked for long time behavior. Numerical and experimental results confirm that these laws remain meaningful at long time and a qualitative similarity is observed for the transients. In addition, a steady case of a heated wire in air is studied and compared with the experimental study of Brodowicz and Kierkus [Brodowicz, K., Kierkus, W., 1966. Experimental investigation of free-convection in air above horizontal wire with constant flux. Int. J. Heat Mass Trans. 9, 81–94]. Despite a wire superheat of 210 K, good agreement is observed between the experiment and numerical simulations performed under the Boussinesq assumption. In particular, numerical simulations match with the scaling laws of the far-field above the wire.

Transient free convection flow over an isothemal vertical cylinder with temperature dependent viscosity

A numerical analysis is performed to study the influence of temperature-dependent viscosity and Prandtl number on unsteady laminar free convection flow over a vertical cylinder. The governing boundary layer equations are converted into a non-dimensional form and a Crank-Nicolson type of implicit finite-difference method is used to solve the governing non-linear set of equations. Numerical results are obtained and presented for different viscosityvariation parameters and Prandtl numbers. Transient effects of velocity and temperature are analyzed. The heat transfer characteristics against the viscosity-variation parameter are analyzed with the help of average skin-friction and Nusselt number and are shown graphically.