Unsteady Natural Convection Research Articles

Fluid-structure interaction analysis of transient convection heat transfer in a cavity containing inner solid cylinder and flexible right wall

PurposeThis paper aims to investigate the fluid structure interaction analysis of conjugate natural convection in a square containing internal solid cylinder and flexible right wall.Design/methodology/approachThe right wall of the cavity is flexible, which can be deformed due to the interaction with the natural convection flow in the cavity. The top and bottom walls of the cavity are insulated while the right wall is cold and the left wall is partially heated. The governing equations for heat, flow and elastic wall, as well as the grid deformation are written in Arbitrary Lagrangian–Eulerian formulation. The governing equations along with their boundary conditions are solved using the finite element method.FindingsThe results of the present study show that the presence of the solid cylinder strongly affects the transient solution at the initial times. The natural convection flow changes the shape of the flexible right wall of the cavity into S shape wall due to the interaction of the flow and the structure. It is found that the increase of the flexibility of the right wall increases the average Nusselt number of the hot wall up to 2 per cent.Originality/valueTo the best of the authors' knowledge, the unsteady natural convection in an enclosure having a flexible wall and inner solid cylinder has never been reported before.

Stability and convergence of two‐grid Crank‐Nicolson extrapolation scheme for the time‐dependent natural convection equations

In this paper, we consider the Crank‐Nicolson extrapolation scheme for the 2D/3D unsteady natural convection problem. Our numerical scheme includes the implicit Crank‐Nicolson scheme for linear terms and the recursive linear method for nonlinear terms. Standard Galerkin finite element method is used to approximate the spatial discretization. Stability and optimal error estimates are provided for the numerical solutions. Furthermore, a fully discrete two‐grid Crank‐Nicolson extrapolation scheme is developed, the corresponding stability and convergence results are derived for the approximate solutions. Comparison from aspects of the theoretical results and computational efficiency, the two‐grid Crank‐Nicolson extrapolation scheme has the same order as the one grid method for velocity and temperature in H1‐norm and for pressure in L2‐norm. However, the two‐grid scheme involves much less work than one grid method. Finally, some numerical examples are provided to verify the established theoretical results and illustrate the performances of the developed numerical schemes.

Natural convection in a fluid-saturated porous enclosure with a pair of vertical diathermal partition

Unsteady natural convection in a fluid saturated porous enclosure with a pair of vertical diathermal partition separated at equal distance from centre of enclosure is studied in this paper. The purpose is to curtail the convection heat transfer rate across a differentially heated enclosure. The governing equations are based on Darcy's model and solved using Successive Accelerated Replacement and explicit scheme. Streamlines and isotherms are observed for various values of partition ratio, where partition ratio is the ratio of distance of from enclosure centre to either of the partition to the total length of the enclosure; while Nusselt number is evaluated to manifest the heat transfer rate of each configuration. It is found that, employing partition in the porous enclosure substantially attenuates the value of Nusselt number. It has been also found that lower the value of partition ratio, higher will be the reduction in Nusselt number.

General Solution for Unsteady Natural Convection Flow with Heat and Mass in the Presence of Wall Slip and Ramped Wall Temperature

This work is focused on the effect of heat and mass transfer with unsteady natural convection flow of viscous fluid along with ramped wall temperature under the assumption of the slip wall condition at the boundary. Analytical solutions are obtained by using Laplace transformation to the non-dimensional set of governing equations containing velocity, temperature and concentration. Moreover, the expression for skin-friction is derived by differentiating the analytical solutions of fluid velocity. Numerical tables for Skin-friction, Sherwood number and Nusselt-number are examined. For the physical aspects of the flow, we use various values of involved physical parameters such as Prandtl number (Pr), slip parameter (η), Schmidt number (Sc), buoyancy ratio parameter (N), Sherwood number (Sh), and time (t). Additionally, the general solutions are plotted graphically and a comprehensive theoretical section of numerical discussions is included.

Numerical study of unsteady natural convection heat transfer of Newtonian and non-Newtonian fluids in a square enclosure under oscillating heat flux

This paper presents a numerical study on the unsteady natural convective flow of Newtonian and non-Newtonian fluids in a square enclosure. A heat source with oscillating heat flux is located on the bottom wall of the enclosure. The top wall is thermally insulated and the other walls are at a relatively low temperature. The continuity, momentum, and energy equations for a computational domain encompassing the enclosure are solved numerically using the SIMPLE algorithm. The flow and temperature fields and the heat transfer performance are examined for different non-Newtonian fluids and heat source locations. The results are presented for different values of power-law index, Rayleigh number, and fluctuation period. It is found that the flow and temperature fields vary as the oscillating heat flux is changed. The pseudoplastic non-Newtonian fluid $$(n < 1)$$ is associated with a higher heat transfer, and the dilatant non-Newtonian fluid $$(n > 1)$$ is associated with a lower heat transfer with respect to the Newtonian fluid. The heat source oscillation period significantly affects the maximum flow temperature in the enclosure. This study provides useful information for the designers of electronic cooling systems using non-Newtonian fluids.

Buoyancy Effects on Unsteady MHD Chemically Reacting and Rotating Fluid Flow Past a Plate in a Porous Medium

An unsteady magnetohydrodynamic natural convection transfer of mass and heat flow over a vertical porous sheet under the influence of thermal radiation and thermo-diffusion effect. The dimensionless governing equations are solved analytically by employing Laplace transform technique. The impact of various physical parameters on momentum, energy and concentration are discussed and analyzed with the aid of graphs. Furthermore, the numerical values for local Skin friction, Nusselt number and Sherwood number are noted and examined. Increasing the values of thermal diffusion results in increasing of the concentration, but it decreases with Schmidt number. Skin friction reduces for increasing values of thermo-diffusion are discussed with the help of tables.

Experimental investigation of heat transfer by unsteady natural convection at a vertical flat plate

The present study considers the influence of unsteady flow structures in natural convection on the heat transfer from a vertical flat plate to air. The mean and momentary intensity of convective heat transfer were determined experimentally for specific variations of the boundary conditions. For cyclic and step-like changing operation modes of a direct-electrically heated, 2 m-high copper plate, laminar, transitional and turbulent flow regimes were considered. Compared to a quasi-stationary approach, mean deviations of up to 22.0% for cyclic variations and up to 30.2% for step-like changes occur during an unsteady phase. The extent of the deviations shows a dependence on the mean Grashof number, as well as further influencing factors. Phenomenological observations of the unsteady convection flow in the form of visualizations show a temporarily increased mixing of the boundary layer, which also deviates distinctly from a quasi-stationary development. In particular, a temporary occurrence of Kelvin-Helmholtz vortices can be observed.

Unsteady MHD natural convection flow of heat generating/absorbing fluid near a vertical plate with ramped temperature and motion

This work investigates the unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid near an infinite vertical plate with ramped temperature and ramped motion. A unified closed form solution is obtained for the velocity field and skin friction coefficient corresponding to the case when the magnetic field fixed relative to the fluid or the moving boundary. It is assumed that the boundary plate has a ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the supposition of negligible induced magnetic field. Exact solutions of energy and momentum equations are obtained using the Laplace transform techniques. Graphical representations are attained for different values of the Prandtl number, magnetic field and heat sink parameter. Results show that wall ramped temperature and ramped motion tend to decrease fluid temperature, velocity, Nusselt number and skin friction.

Unsteady Natural Convection in a Differentially Heated Rectangular Enclosure Possessing Sinusoidal Corrugated Side Walls Loaded with Power Law Non-Newtonian Fluid

This research is a numerical analysis exhaustively investigating two-dimensional (2D) transient convective heat transfer in a differentially heated rectangle, possessing sinusoidal corrugated side walls at constant temperatures. The quadrilateral space is filled with a power-law non-Newtonian fluid, plus the right and left walls are uniformly cooled and heated, respectively. The top and bottom walls are retained as adiabatic and the side walls are recast exploiting sinusoidal corrugated shape. The governing equations of the problem are solved using the finite volume method. The evaluation of fluid flow and heat transfer is conducted in such a manner that the power law index n varies from 0.6 to 1.4, the Rayleigh number Ra from 103 to 107, the corrugation amplitude CA from 0.1 to 0.5, and the corrugation frequency CF of the sinusoidal side walls is in the range of 1 to 5. The results are studied at different values of Ra, n, CA, and CF; they are presented in the form of streamlines, isotherms, and average Nusselt numbers ( $$\overline{\rm{Nu}}$$ ) of the hot side wall. Further, the heat transfer characteristics are presented and the effect of sudden differential heating, as well as its consequential transient behavior, on the fluid flow, velocity, and temperature plots are demonstrated in accordance with the scope of the governing parameters.

A high-order compact finite-difference lattice Boltzmann method for simulation of natural convection

In the present work, compact finite-difference lattice Boltzmann method (CFDLBM) is extended to simulate natural convection in square and concentric-circular-annulus cavities, in two-dimensions, for Rayleigh numbers in the range of 103 to 109. Owing to the finite-difference discretization of the method, non-uniform and curvilinear grids with a finer near-wall grid resolution could be used in the present simulations. The use of high-order methods further enabled the simulations to be run on relatively coarse meshes when compared with simulations that used classical lattice Boltzmann method. The simulation results are analyzed with the help of streamlines, isothermal contours and temperature, velocity, Nusselt number variations along the walls. The average Nusselt number on the hot wall shows less than 1% error for natural convection in the square cavity study. The circular-annular-cavity is found to have laminar flow for Rayleigh numbers in the range of 103–106 and it becomes unsteady and chaotic from 107 onwards. The instantaneous and time-average contours of isotherms and streamlines were used to study the unsteady behavior of the flow. A universal near-wall velocity profile is found to exist in all the unsteady natural convection studies in the annular cavity case. The location of the maximum velocities occurring in the annulus is analyzed for all the Rayleigh numbers. The spectra of velocity magnitude fluctuations and temperature fluctuations indicate that the unsteadiness in the cavity is dominant around 0.001 Hz. Natural convection in sine-walled and concentric star shaped cavities are simulated to demonstrate the ability of the present solver to handle complex geometries. The present results indicate that CFDLBM can be successfully used to simulate steady and unsteady chaotic natural convection flows in both rectangular and curvilinear geometries accurately.

Conjugate Effects of Thermal and Mass Diffusion on Natural Convection Flow from a Heated Sphere with Internal Heat Generation or Absorption

We examine the conjugate effects of thermal and mass diffusion on the unsteady natural convection flow from a heated sphere. The mathematical model of the problem is made into a system of nonsimilar partial differential equations introducing appropriate transformations. We solve this system employing the implicit finite difference technique. Numerical solutions have been elucidated with the skin friction as well as heat and mass transfer for varying Prandtl number, Schmidt number, combined buoyancy parameter, and heat generation or absorption parameter.&#x0D; Dhaka Univ. J. Sci. 67(1): 13-20, 2019 (January)

Numerical investigation of fractional-order unsteady natural convective radiating flow of nanofluid in a vertical channel

In the current article, we analyzed the unsteady natural convection with the help of fractional approach. Firstly, the unsteady natural convection radiating flow in an open ended vertical channel beside the magnetic effects. We assumed the channel is stationary with non-uniform temperature. Secondly, we utilized a fractional calculus approach for the constitutive relationship of a fluid model. The modeled problem is transformed into nondimensional form via viable non-dimensional variables. In order to investigate the numerical solutions of non-dimensional system of partial differential equations finite difference approach coupled with Crank Nicolson method is developed and successfully applied. The beauty of Crank Nicolson finite difference scheme is, this scheme is unconditionally stable. A very careful survey of literate witnesses that this scheme has never been reported in the literary for fluid problems. The physical changes are discussed with the help of graphics. The expression for both velocity field and temperature distribution has been made via said scheme. A comprehensive discussion about the influence of various related dimensionless parameters upon the flow properties disclosed our work. It is observed that velocity field decreases as enhancing the magnetic field effects. Heat transfer enhanced as enhancing the nanoparticle volume fraction parameter. Velocity field and heat transfer shows the dominant behavior for the case of Cu-based nanofluid as compare to Al2O3 based nanofluid. Comparative study also included to show the accuracy of the proposed finite difference scheme. It is to be highlighted that the proposed scheme is very efficient and well-matched to investigate the solutions of modeled problem and can be extended to diversify problems of physical nature.

Thermo-diffusion effects on the magnetohydrodynamic natural convection flow of a chemically reactive Brinkman type nanofluid in a porous medium

An investigation on the unsteady MHD natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible, chemically reactive and heat-absorbing nanofluid of Brinkman type past an exponentially accelerated moving vertical plate with ramped wall temperature and ramped surface concentration is carried out. Governing equations are non-dimensionalized and Laplace Transform Technique is used to find the exact solutions for fluid velocity, fluid temperature and species concentration. The quantities of physical interest, i.e. skin friction, rates of heat and mass transfers at the plate are also calculated. Numerical results for the velocity, temperature and species concentration of the fluid are demonstrated with the help of graphs whereas those of skin friction, rate of heat and mass transfers at the plate are displayed in tables for various flow parameters.

The dependence of the crystallization front shape on the heat exchange regime in the Bridgman-Stockbarger method

The growth of a silicon ingot in the Bridgman-Stockbarger crystal-melt-crucible system, similar to that used in real technology is studied numerically in the axisymmetric formulation by the finite element method. The simulation was carried out taking into account the heat of phase transition under conditions of unsteady thermal conductivity and natural convection at the initial heating of the melt up to 40 K and two rates of crucible lowering. The temperature gradient along the lower part of the side wall of the crucible is linear and equal to 35 K/cm or 70 K/cm. A comparison between the crystallization processes in the unsteady heat conduction regime and the natural convection regime is carried out. The dependence of the shape of the crystallization front on the heat transfer modes is investigated. It has been shown that in all heat conduction modes being considered, the crystallization front has a convex shape during the entire crystallization process. Moreover, the shape of the crystallization front in the examined range of parameters weakly depends on the crucible lowering rate, but is drastically influenced by the temperature gradient on the crucible walls. Under conditions of hermogravitational convection the shape of the crystallization front strongly depends on the crucible lowering rate and temperature gradient on the side walls of the crucible. At some parameters, a secondary convective vortex can be generated over the crystal during the crystallization process. Depending on the combinations of temperature gradient on the side walls and the lowering rate of the crucible, the shape of the crystallization front can be either concave or convex.

Shape determination for prescribing flow velocity in unsteady natural convection fields

Shape determination for prescribing flow velocity in unsteady natural convection fields

Numerical Analysis of the Transient Process of Flow and Heat Transfer at High Rayleigh Number in a Partially Open Habitat Heated from Above

In this work, we studied the thermoconvective instabilities in a pentagonal cavity containing a Newtonian fluid. The cavity provided with a side opening is uniformly heated from above by a constant heat flux. The natural ventilation phenomenon in the classic habitat of the hot climate is thus numerically analyzed with unsteady natural convection equations formulated with vorticity and stream-function variables. The finite volume predictions of two-dimensional laminar natural convection at high Rayleigh number are presented. Results show that the incoming fresh air and the hot air discharge begin with the late start of the convection. The phenomenon intensifies with time and the birth of instabilities improves the homogenisation of temperatures which imply the elimination of very cold and very hot areas. However, the competition between the incoming fresh air and the hot air expansion leads to a perpetual displacement of the thermal front. The cross-sections at the opening of the incoming fresh and outgoing hot air are time-varying and the penetration depth of the fresh air is highlighted by the large convective cells originated from the aperture. The non monotonic variation of the Nusselt number reflects not only the multicell nature of the flow but also expresses the heat lost by the active walls due to the fresh air.

Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

Unsteady natural convection in a partially porous cavity having a heat-generating source using local thermal non-equilibrium model

PurposeThe purpose of this study is a numerical analysis of transient natural convection in a square partially porous cavity with a heat-generating and heat-conducting element using the local thermal non-equilibrium model under the effect of cooling from the vertical walls. It should be noted that this research deals with a development of passive cooling system for the electronic devices.Design/methodology/approachThe domain of interest is a square cavity with a porous layer and a heat-generating element. The vertical walls of the cavity are kept at constant cooling temperature, while the horizontal walls are adiabatic. The heat-generating solid element is located on the bottom wall. A porous layer is placed under the clear fluid layer. The governing equations, formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions, are solved using implicit finite difference schemes of the second order accuracy. The governing parameters are the Darcy number, viscosity variation parameter, porous layer height and dimensionless time. The effects of varying these parameters on the average total Nusselt number along the heat source surface, the average temperature of the heater, the fluid flow rate inside the cavity and on the streamlines and isotherms are analyzed.FindingsThe results show that in the case of local thermal non-equilibrium the total average Nusselt number is an increasing function of the interphase heat transfer coefficient and the porous layer thickness, while the average heat source temperature decreases with the Darcy number and viscosity variation parameter.Originality/valueAn efficient numerical technique has been developed to solve this problem. The originality of this work is to analyze unsteady natural convection within a partially porous cavity using the local thermal non-equilibrium model in the presence of a local heat-generating solid element. The results would benefit scientists and engineers to become familiar with the analysis of convective heat transfer in enclosures with local heat-generating heaters and porous layers, and the way to predict the heat transfer rate in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Validation of a two-dimensional gas-kinetic scheme for compressible natural convection on structured and unstructured meshes

Gas-kinetic schemes (GKS) have been developed as a kinetic Finite-Volume approach to computational fluid dynamics. The GKS a priori allows to obtain approximate solutions of the fully compressible Navier-Stokes equations. In our contribution we show simulation results of compressible natural convection at large temperature differences and low Mach numbers beyond the applicable range of the Boussinesq approximation. The simulations were performed on non-uniform quadrilateral and unstructured triangular grids. The dependence of the critical Rayleigh number on the temperature difference for compressible Rayleigh-Bénard convection, predicted by theory, is accurately reproduced. Moreover, heat transfer in a buoyancy driven square cavity with differentially heated sides at large Rayleigh numbers and large temperature differences is investigated. Temperature and velocity profiles as well as Nusselt numbers show good agreement with benchmark results in literature. After validating the scheme for thermal compressible convection, we investigate unsteady natural convection at a Rayleigh number of Ra=5⋅109 and at a large temperature difference of Th/Tc=4. We find that compressibility has a leading influence on the stability of the boundary layers, such that the flow at the heated wall becomes unstable, whereas the flow at the cooled wall remains stable. This phenomenon has not yet received much attention.

The influence of thermal radiation on unsteady free convection in inclined enclosures filled by a nanofluid with sinusoidal boundary conditions

PurposeThe purpose of this study is a numerical analysis of transient natural convection in an inclined square cavity filled with an alumina-water nanofluid under the effects of sinusoidal wall temperature and thermal radiation by using a single-phase nanofluid model with empirical correlations for effective viscosity and thermal conductivity.Design/methodology/approachThe domain of interest includes the nanofluid-filled cavity with a sinusoidal temperature distribution along the left vertical wall. Horizontal walls are supposed to be adiabatic, while right vertical wall is kept at constant low temperature. Temperature of left wall varies sinusoidally along y-coordinate. It is assumed in the analysis that the thermophysical properties of the fluid are independent of temperature and the flow is laminar. The governing equations have been discretized using the finite difference method with the uniform grid. Simulations have been carried out for different values of the Rayleigh number, cavity inclination angle, nanoparticles volume fraction and radiation parameter.FindingsIt has been found that a growth of radiation parameter leads to the heat transfer enhancement and convective flow intensification. At the same time, an inclusion of nanoparticles illustrates a reduction in the average Nusselt number and fluid flow rate.Originality/valueThe originality of this work is to analyze unsteady natural convection in a square cavity filled with a water-based nanofluid in the presence of a sinusoidal temperature distribution along one wall. The results would benefit scientists and engineers to become familiar with the analysis of convective heat and mass transfer in nanofluids and the way to predict the properties of nanofluid convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors, electronics, etc.