Unsteady Natural Convection Research Articles

Fluid–structure interaction analysis of free convection in an inclined square cavity partitioned by a flexible impermeable membrane with sinusoidal temperature heating

The problem of unsteady natural convection inside an inclined square cavity partitioned by a flexible impermeable membrane is studied numerically using the finite-element method along with the Arbitrary Lagrangian–Eulerian (ALE) approach. The bottom and top walls of the cavity are kept adiabatic. The left side wall is kept isothermal at a high temperature, while the right wall is cooled in a sinusoidal fashion. The cavity is provided by two eyelets to compensate volume changes due to the movement of the flexible membrane. The studied pertinent parameters are the Rayleigh number (in the range of 1E4–1E7), the amplitude of the sinusoidal wall temperature (A in the range of 0–1.0), the inclination angle of the cavity (in the range of −π/3 to π/3), and the body force parameter (Fv in the range of −1.64E−2 to +1.64E−2) whereas the Prandtl number is fixed at 6.2. The results show that at a low Rayleigh number, the membrane shape is a function of the imposed body force. While at a high Rayleigh number, the buoyancy force becomes responsible for the membrane deflection. The natural convection is appreciably affected by the inclination angle of the cavity which in turn, affects the concave or convex shape of the membrane.

Influence of viscous dissipation on unsteady MHD natural convective flow of Casson fluid over an oscillating vertical plate via FEM

Abstract In this paper, an unsteady magnetohydrodynamic natural convection, heat transfer, electrically conductive non-Newtonian Casson fluid over an oscillating vertical porous plate taken in to the account with an influence of viscous dissipation. An efficient computational Finite Element Method (FEM) employed to solve non-dimensional boundary layer partial differential equations for velocity and temperature distribution with the influence of emerging dimensionless parameters. Also, the local Skin-friction and local Nusselt number coefficients are obtained and analyzed through graphical and tabular forms. The results shows that increasing of Eckert number leads to increase in the velocity and temperature distribution while decrease in the local Skin-friction and Nusselt number coefficients. An increasing of Casson parameter leads to decrease in the velocity distribution and the local Skin-friction coefficient. Compared the present results with earlier reported studies of analytical solutions of Newtonian and non-Newtonian fluid flow problems. The current results are in excellent agreement with earlier existed results. The velocity and temperature distributions are closure for various mesh (grid) size. Therefore, these computational results are stable and converge. FEM is flexible and simplest method to solve this type of problems in various cases like Newtonian and non-Newtonian fluid flow problems.

Unsteady MHD Heat Transfer in Couette Flow of Water at 4°C in a Rotating System with Ramped Temperature via Finite Element Method

An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at <i>4°C</i> (Pr = <i>11.40</i>) in a rotating system has been considered. A Finite Element Method (FEM) was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at <i>4°C</i> as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid) size and the present numerical solutions through the Finite Element Method (FEM) are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT). These are shown in tabular and graphical forms.

Radiation Effect on MHD Flow Past an Inclined Plate With Variable Temperature and Mass Diffusion

ABSTRACT The present study is carried out to examine the effects of radiation and Hall current on unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively started inclined plate under the influence of transversely applied uniform magnetic field. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The results obtained are discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof number, Prandtl number, Hall current parameter, radiation parameter, magnetic field parameter and Schmidt number. The numerical values obtained for skin-friction and Nusselt number have been tabulated. The results obtained are in agreement with the actual flow phenomenon. The motive of this study is to analyze radiation and the Hall effect on the flow model. In the study, we found that the velocity in the boundary layer increases with the values of radiation and Hall current parameters. It is also observed that radiation and the Hall current increases the drag at the plate surface.

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

This paper presents an analytical solution of unsteady one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless coupled linear governing partial differential equations are solved by Laplace transform technique for unit Prandtl number and Schmidt number. Effects of various physical parameters are presented with graphs. Numerical values of boundary layer thickness for different parameters are presented in table. Due to the effects of thermal and mass stratifications, the velocity, temperature, and skin friction, Nusselt number shows oscillatory behaviour at smaller times and then reaches steady state at larger times.

Unsteady conjugate natural convection in a porous cavity boarded by two vertical finite thickness walls

The objective of this study is to investigate unsteady conjugate natural convection in a porous cavity sandwiched by finite conductive walls considering time-periodic boundary conditions and local thermal non-equilibrium. The top and bottom boundaries are assumed to be isolated and the continuity of temperature and heat transfer are considered in interface boundaries. The effect of varying a plethora of parameters such as Rayleigh number, Thermal conductivity ratio, wall thickness, and non-dimensional frequency on the streamlines, isotherms, and Nusselt number has been studied. It is shown that, apart from non-dimensional frequency and wall thickness, the amplitude of periodic fluid Nusselt number is an increasing function of all aforementioned parameters. Furthermore, aside from Rayleigh number and heat transfer coefficient, the behavior of the solid Nusselt number is the same as fluid Nusselt number. Eventually, the time-averaged Nusselt number and heat transfer through the vertical walls for different values of non-dimensional frequencies are calculated.

Transient two-dimensional natural convection flow of a nanofluid past an isothermal vertical plate using Buongiorno’s model

PurposeThe purpose of this paper is to present a numerical investigation of the transient two-dimensional natural convective boundary-layer flow of a nanofluid past an isothermal vertical plate by incorporating the effects of Brownian motion and thermophoresis in the mathematical model.Design/methodology/approachThe problem is formulated using the Oberbeck–Boussinesq and the standard boundary-layer approximations. The governing coupled non-linear partial differential equations for conservation of mass, momentum, thermal energy and nanoparticle volume fraction have been solved by using an efficient implicit finite-difference scheme of the Crank–Nicolson type, which is stable and convergent. Numerical computations are performed and the results for velocity, temperature and nanoparticle volume fraction are presented in graphs at different values of system parameters such as Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number, Lewis number and dimensionless time. The results for local and average skin-friction and Nusselt number are also presented graphically and discussed thoroughly.FindingsIt is found that the velocity, temperature and nanoparticle volume fraction profiles enhance with respect to time and attain steady-state values as time progresses. The local Nusselt number is found to decrease with increasing thermophoresis parameter, while it increases slightly with increasing Brownian motion parameter. To validate the present numerical results, the steady-state local Nusselt number results for the limiting case of a regular fluid have been compared with the existing well-known results at different Prandtl numbers, and the results are found to be in an excellent agreement.Research limitations/implicationsThe present analysis is limited to the transient laminar natural convection flow of a nanofluid past an isothermal semi-infinite vertical plate in the absence of viscous dissipation and thermal radiation. The unsteady natural convection flow of a nanofluid will be investigated for various physical conditions in a future work.Practical implicationsUnsteady flow devices offer potential performance improvements as compared with their steady-state counterparts, and the flow fields in the unsteady flow devices are typically transient in nature. The present study provides very useful information for heat transfer engineers to understand the heat transfer enhancement with the nanofluid flows. The present results have immediate relevance in cooling technologies.Originality/valueThe present research work is relatively original and illustrates the transient nature of the natural convective nanofluid boundary-layer flow in the presence of Brownian motion and thermophoresis.

Applications of non-integer Caputo time fractional derivatives to natural convection flow subject to arbitrary velocity and Newtonian heating

Unsteady time fractional natural convection flow of incompressible viscous fluid due to arbitrary velocity with radiation and Newtonian heating is investigated. By introducing dimensionless variables and functions, the resulting equations are solved by the Laplace transform technique. Exact solutions for temperature and velocity fields are obtained by Caputo time fractional derivatives in dimensionless form, and they are expressed in terms of Robotnov–Hartley function and Wright’s function. The rate of heat transfer on plate is obtained in terms of Nusselt number. Some known solutions from the existing literature are obtained as limiting case when \(\alpha = 1\). At the end, we have seen the significant influence of fractional parameter \(\alpha\) on the temperature and velocity graphically and observed that it has shown an opposite behavior on temperature and velocity for small and large values of time t, respectively. This shows that how fractional parameter \(\alpha\) affects the fluid flow.

Modeling of natural circulation for the inherent safety analysis of sodium cooled fast reactors

The paper discusses a set of developed integrated one-dimensional models of thermal-hydraulic processes that contribute to the removal of decay heat in a BN-type reactor. The assumptions and constraints involved in one-dimensional equations of unsteady natural convection in closed circuits have been analyzed. It has been shown that the calculated values of the primary circuit sodium temperature and flow rate in conditions with a loss of heat sink and with a forced circulation of the primary coolant are in a reasonable agreement with the results of a benchmark experiment in the PHENIX reactor. The model makes it possible to assess the effects general thermophysical and geometrical parameters and the selected technology have on the efficiency of passive heat removal by the natural coolant convection in the reactor tank and in the emergency heat removal system's intermediate circuit and by the heat transfer through the reactor vessel. The model is a part of an integrated algorithm used to assess the inherent safety level of advanced fast neutron reactors and is intended primarily to develop, at the early conceptual design stage, the recommendations and requirements with respect to the reactor equipment parameters leading to an increase in the reactor inherent safety. The model will be used to identify the set of quantitative thermal-hydraulic criteria that have an effect on the dynamics of emergency transients leading to a potential loss of integrity by the reactor safety barriers, and to formulate such limits for the defined criteria as would cause, if observed, the requirement for the safety barrier integrity to be met under any combination of the accident initiating events.

Conjugate Effect of Joule Heating and Unsteady MHD Natural Convection in a Differentially Heated Skewed Porous Cavity Saturated by Cu-water Nanofluid

Conjugate Effect of Joule Heating and Unsteady MHD Natural Convection in a Differentially Heated Skewed Porous Cavity Saturated by Cu-water Nanofluid

Modification of SIMPLE algorithm to handle natural convection flows with zero-isothermal compressibility

The conventional SIMPLE algorithm for the pressure–velocity coupling has been adopted by many commercial and non-commercial CFD codes. It encounters convergence problem when it is used to solve unsteady natural convection flows with zero-isothermal compressibility. In this paper, a modified version of this algorithm is proposed to remedy this drawback. The modification includes updating of the density at each time step based on its value at the previous time step to satisfy the continuity equation. As an example of utilizing the modified SIMPLE algorithm, the unsteady natural convection in a rectangular cavity with isothermal vertical walls and adiabatic horizontal walls was computed. Physically consistent results were obtained.

Transition to unsteady natural convection flow in a prismatic enclosure of triangular section

Natural convection in a prismatic enclosure of triangular section with the top cooling and the bottom heating is investigated using three dimensional (3D) numerical simulations for a wide range of Rayleigh numbers from 100 to 1.25 × 106. The numerical result has been compared with the experiment. The development of natural convection flows in the cavity following sudden heating and cooling involves three stages: an initial stage, a transitional stage and a fully developed stage. Transition to unsteady natural convection flow in the fully developed stage, dependent on the Rayleigh number, is described. The flow structure including transversal and longitudinal rolls is characterized and the corresponding mechanism is discussed. The critical Rayleigh number for the transition to unsteady natural convection flow is obtained. The dependence of heat transfer on the Rayleigh number is quantified.

Analysis of fluid-solid interaction in MHD natural convection in a square cavity equally partitioned by a vertical flexible membrane

This paper investigates numerically the problem of unsteady natural convection inside a square cavity partitioned by a flexible impermeable membrane. The finite element method with the arbitrary Lagrangian-Eulerian (ALE) technique has been used to model the interaction of the fluid and the membrane. The horizontal walls of the cavity are kept adiabatic while the vertical walls are kept isothermal at different temperatures. A uniform magnetic field is applied onto the cavity with different orientations. The cavity has been provided by two eyelets to compensate volume changes due the movement of the flexible membrane. A parametric study is carried out for the pertinent parameters, which are the Rayleigh number (105–108), Hartmann number (0–200) and the orientation of the magnetic field (0–180°). The change in the Hartmann number affects the shape of the membrane and the heat transfer in the cavity. The angle of the magnetic field orientation also significantly affects the shape of the membrane and the heat transfer in the cavity.

SORET, HALL CURRENT, ROTATION, CHEMICAL REACTION AND THERMAL RADIATION EFFECTS ON UNSTEADY MHD HEAT AND MASS TRANSFER NATURAL CONVECTION FLOW PAST AN ACCELERATED VERTICAL PLATE

The heat and mass transfer characteristics of the unsteady hydromagnetic natural convection flow with Hall current and Soret effect of an incompressible, viscous, electrically conducting, heat absorbing and optically thin radiating fluid flow past a suddenly started vertical infinite plate through fluid saturated porous medium in a rotating environment are taken into account in this paper. Derivations of exact analytical solutions are aimed under different physical properties. The velocity, concentration and temperature profiles, Sherwood number and Nusselt number are easily examined and discussed via the closed forms obtained. Soret effect and permeability parameter tends to accelerate primary and secondary fluid velocities whereas hall current, radiation and heat absorption have reverse effect on it. Radiation and heat absorption have tendency to enhance rate of heat transfer at the plate. The results obtained here may be further used to verify the validity of obtained numerical solutions for more complicated transient free convection fluid flow problems.

Effect of unsteady natural convection mass transfer caused by g-jitter on protein crystal growth under microgravity

ABSTRACTDetailed numerical analysis is presented for the effect of unsteady natural convection caused by g-jitter on protein crystal growth (PCG) under microgravity. The results show that for step impulse disturbances with the strength of 10−2 g0, the convection can decrease the crystal growth rate, especially for the higher-frequency g-jitter. For sinusoidal impulse disturbance with different amplitudes g*, the effect of convection on PCG is good for g* = 10−4 g0 and it is bad for g* = 10−3 g0. In comparison with the case of crystal at the bottom, the effects of unsteady convection caused by g-jitter for crystal suspended are more obvious due to the larger values of r. However, the crystal suspended in the container can more easily remain regular shaped.

Three-dimensional numerical investigation on thermosolutal convection of power-law fluids in anisotropic porous media

The present study simulates the 3D unsteady double-diffusive natural convection subject to opposing thermal and solutal buoyancy forces (N<0) in a porous cubic by a generalized non-Darcy model, in which the effects of the crucial parameters such as the porous thermal Rayleigh numbers, buoyancy ratio and anisotropy ratio on the flow structure, heat and mass transfer of power-law fluids are investigated independently. The top and bottom walls are given different temperatures and concentrations, while the other walls are adiabatic and impermeable. A compact high order finite volume method is adopted to describe the flow structure and the resulting heat and mass transfer characteristic of non-Newtonian fluids in the anisotropy porous cubic. Our simulations show that the flow structure develops from conduction-dominated to convection-dominated as buoyancy ratio or anisotropy ratio or porous thermal Rayleigh number increases. The average Nusselt and Sherwood numbers keep constants during the conduction-dominated stage, then increase along the transition route. On the other hand, the impacts of different power-law indexes on the convection are mainly manifested in rheological properties, which elucidate that the shear-thinning fluids is more effective in heat and mass transfer enhancement than shear-thickening fluids. The studies may help us establish a physically reasonable methodology to systemically assess double-diffusive convection of non-Newtonian power-law fluids in anisotropy porous media in the real world.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

UNSTEADY HYDROMAGNETIC HEAT AND MASS TRANSFER NATURAL CONVECTION FLOW PAST AN EXPONENTIALLY ACCELERATED VERTICAL PLATE WITH HALL CURRENT AND ROTATION IN THE PRESENCE OF THERMAL AND MASS DIFFUSIONS

In the present analytical study, we have considered unsteady hydromagnetic heat and mass transfer natural convection flow of an electrically conducting, heat absorbing and chemically reacting fluid past an exponentially accelerated vertical plate in a uniform porous medium taking Hall current and rotation into account. The species concentration near the plate is considered to be varies linearly with time. Two particular cases for plate temperature are considered i.e. (i) plate temperature is uniform and (ii) plate temperature varies linearly with time and after some time it is maintained at uniform temperature. The coupled partial differential equations governing the fluid flow problem are solved analytically for fluid velocity, temperature and species concentration using Laplace transform method. To examine the physical characteristic of this problem the graphs for velocity, temperature, species concentration, skin friction, Nusselt number and Sherwood number distributions are computed and generated for various values of different pertinent flow parameters. It is observed that for small thermal diffusion, the free stream value of velocity and temperature are achieved nearer to the plate in comparison to that for large thermal diffusion.

Numerical optimization of unsteady natural convection heat transfer from a pair of horizontal cylinders

This paper presents the results of a numerical study of unsteady natural convection heat transfer from a pair of isothermally heated horizontal cylinders in water. In conjunction with the developed numerical model, a genetic algorithm is designed to search for the optimal spacing between the two cylinders that maximizes their overall heat transfer. When the cylinders are vertically aligned, the heat transfer effectiveness of the upper cylinder is affected by buoyancy-induced fluid flow induced by the lower cylinder. The established and validated CFD model is used to analyse spectral data of local Nusselt number and velocity. The optimization procedure identifies the optimal spacing for Rayleigh numbers ranging from 1e+6 to 1e+7.

The effect of nanoparticles added to heated micropolar fluid

This paper presents an analysis of momentum, angular momentum and heat transfer during the unsteady natural convection in micropolar nanofluids. Presented phenomena are modelled in the vicinity of a vertical plate and heat flux which rises suddenly at a given moment, using the boundary layer concept. Differential equations of angular momentum conservation are used according to the theory of micropolar fluids developed by Eringen. Finite difference method is used to solve the equations for conservation of mass, energy, momentum and angular momentum. Selected nanofluids treated as single phase fluids contain small particles with diameter size d = 10 nm and d = 38.4 nm. In particular, two ethylene glycol based nanofluids and one water-based nanofluid are analysed. Volume fraction of these solutions is 6%. First ethylene glycol solution contain Al2 O3 nanoparticles (d = 38.4 nm), and the second ethylene glycol solution contained Cu nanoparticles (d = 10 nm). Water based nanofluid contain Al2 O3 nanoparticles (d = 38.4 nm). As a result of solving conservation equations, unsteady velocity field (U, V), temperature (T), microrotation component normal to (x, y) plane (N), velocity gradient ∂U/∂Y and temperature gradient ∂T/∂Y are obtained. These results are compared to theoretical and experimental results presented in literature. At the end of this paper, heat transfer enhancement for analysed nanofluids is estimated.