Transient Natural Convection Flow Research Articles

Transient natural convection flows and heat transfer in a thermally stratified air-filled trapezoidal cavity

This paper focuses on studying the transient behavior of natural convective heat and fluid flow in a two-dimensional trapezoidal cavity subjected to a heated bottom surface, cooling from the top, and thermally stratified inclined surfaces. The Finite Volume (FV) method is employed to numerically simulate the transient flow. The study considers a thermally stratified environment with a Prandtl number of Pr set to 0.71 (for stratified air), an aspect ratio (A) of 0.5, and a large array of Rayleigh numbers (Ra) ranging from 100 to 108. The research examines how the Rayleigh numbers affect the flow structures, transient phenomena, and heat transfer (HT) characteristics within the cavity. The transitional flow reveals several supercritical bifurcations. These include a changeover from symmetric to asymmetric states known as a Pitchfork bifurcation, as well as a shift from a steady-state to a periodic state referred to as a Hopf bifurcation. The Pitchfork bifurcation happens between Ra values of 105 and 2 × 105, while the Hopf bifurcation happens within the range of the Ra values from 4.7 × 105 to 4.8 × 105. Moreover, another bifurcation from a periodic to a chaotic state is observed between Ra of 3 × 107 and 4 × 107. To examine the transient flows during the changeover to chaos, various techniques such as power spectral density (PSD), limit points, limit cycles, trajectory in phase space, and the largest Lyapunov exponent (LLE) are used. Furthermore, convective heat transfer is computed, and its corresponding impact on the Ra values is explained. The flow phenomena within the cavity are measured and verified.

Thermal performance investigation of transient natural convective nanofluid flow in a square cavity with inclined periodic magnetic field

The goal of this paper is to analyze the thermal exhibition of transient free convective nanofluid flow in a square cavity with inclined periodic magnetic field using one-component thermally equilibrium homogeneous model. Distinct thermal settings (constant, parabolic, and sinusoidal) for the left heated wall are deliberated when the right wall of the cavity is cold and the horizontal walls are insulated. For numerical simulations, eight types of nanofluids consisting Cu, Co, Zn, and Al2O3 nanoparticles along with H2O and kerosene as base fluids have been employed. During numerical computation, the impacts of different factors (Hartmann number, Rayleigh number, nanoparticles volume fraction, period, and inclination angle) on the fluid flow and heat transfer are examined. The numerical results show that cobalt-kerosene nanofluid distributes the maximum heat transfer rate compared to other 7 types of nanofluids. The results also indicate that sinusoidal thermal scenery at the left heated wall delivers the uppermost average Nusselt number compared to the other types of thermal approaches. The optimum thermal performance is achieved at magnetic field's inclination angle δ=π3 and period number λ = 1 for the case of sinusoidal scenery.

Transient natural convective heat transfer and fluid flow in an undulated cavity: Effects of localized heat sources

AbstractThe purpose of this research work is to investigate two‐dimensional transient natural convective heat transfer and fluid flows in an undulated cavity by placing solid objects with isolated heated surfaces on the bottom wall. We discretize the coupled nonlinear transport equations using a higher‐order compact finite‐difference scheme. First, we test our scheme using existing experimental and numerical data. Then, we analyze the transient and steady‐state natural convective flow phenomena for distributed heat sources on corrugations on the lower wall for a range of the Rayleigh number and Prandtl number . These simulated outcomes are presented in the form of central‐line velocity , local and averaged Nusselt numbers, streamlines , dispersion of isotherms , and so forth. It is found that the transient fluid flow behavior is more magnificent than the steady‐state solutions and shows the dominant behavior of the prominent primary cells over secondary cells, where it influences the heat transfer rates inside the entire enclosure. In steady states, at high Rayleigh numbers; convection dominates, formation of thermal boundary layers, compression of isotherms, and stratification of isotherms are significantly observed. Our results show many interesting flow phenomena that have not been analyzed previously.

Radiation effect on transient natural convective MHD flow over a fixed cylinder in a permeable medium with heat and mass transport

The thermal radiation impact on the unsteady magnetohydrodynamic flow of a Newtonian fluid past a stationary vertical cylinder with heat and solute transfer has been investigated. The viscous fluid is slightly electrically conductive, and the stationary cylinder is placed in a permeable medium. The linear PDEs that govern the flow is transformed to non-dimensional by suitable non-dimensional quantities, and the standard Laplace transform approach is used to derive the closed-form solutions. The impacts of the flow parameters are discussed through a table and graphs. It is found that the unsteady fluid velocity enhances with a rise in radiation parameter, permeability parameter and time, whereas it falls with reduced magnetic effect. The absolute skin friction value rises with an increase in thermal radiation and porosity parameter but falls with a rise in Schmidt number and transverse magnetic field.

Chemical reaction and Soret effect on an unsteady MHD heat and mass transfer fluid flow along an infinite vertical plate with radiation and heat absorption

In the current investigation, it is anticipated to examine the influence of heat absorption and radiation on an unsteady transient MHD heat and mass transfer natural convective flow of an optically thin non-Grey Newtonian fluid through an abruptly started infinite vertical porous plate with ramped wall temperature and plate velocity in the presence of Soret and chemical reaction of the first order is solved precisely. Using the similarity variables, the governed PDE's are converted into dimensionless governing equations and they are solved numerically by employing the finite element technique. Numerical calculations and graphs are used to illustrate the important features of the solution on fluid flow velocity, heat, and mass transfer characteristics under different quantities of parametric circumstances entering into the problem. Moreover, we computed the physical variables such as the coefficient of drag force, rate of heat, and mass transfer. The findings indicate that when the thermal radiation parameter increases, the thermal boundary layer becomes thinner. To establish the veracity of our present results, we compared them to previously published research and found substantial concordance.

Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species

AbstractThe present study deals with an unsteady magnetohydrodynamic natural convective flow of a viscous, incompressible fluid past an exponentially accelerated porous plate surrounded by a porous medium with suction or injection. The novelty of the current research is to analyze the behavior of the flow due to mass transfer with first‐order chemical reaction in the presence of a heat source in the energy equation. The existence of suction/injection and radiation parameters in the flow enhances the utility of the research as they are an integral part of nuclear reactors, thermal and chemical engineering processes, and many more. The Laplace transform technique (via Bromwich contour) is applied to solve exactly the governing equations. The nature of the flow velocity, temperature, and concentration profiles due to the impact of pertinent flow parameters are presented graphically. The numerical outcomes of coefficient of skin friction, rate of heat transfer, and mass transfer are obtained in tabular form. The results indicate that the skin friction increases slowly with the reaction parameter and largely with the suction parameter, whereas the concentration gradient increases at a much higher rate with the reaction parameter. The fluid injection has a negative impact on the velocity gradient. It is seen that the heat source enhances both velocity and temperature profiles throughout the flow field, whereas the first‐order chemical reaction acts reversely on the velocity and mass transfer process. The current research can be applied to identify the cause behind the drag force produced in seepage flow due to the heated or cooled accelerated plate.

Effect of chemical reaction, heat source/sink, and thermal diffusion on transient natural convection through a tube

AbstractA semi‐analytical investigation of the effect of a chemical reaction and thermal diffusion on transient natural convection flow of a viscous incompressible binary fluid with heat source/sink in a vertical and infinite tube is presented. The equations for the model are simplified with the help of the Laplace transform, solved analytically to obtain solutions whose expressions are given in modified Bessel functions. These solutions are then inverted numerically using the Riemann sum approximation method. An exhaustive model analysis is achieved by exhibiting the temperature, concentration, and velocity profiles graphically. Also, numerical values are displayed in tabular form for the Nusselt number, Sherwood number, and the shear stress. Furthermore, a version of the governing equations which are independent of time is solved analytically. The obtained results are found to coincide with the results of the time‐dependent problem at an appreciable value of time. A close examination of the results reveals that raising the generative chemical reaction parameter strengthens both the concentration and momentum of the flow while they are weakened with a surge of the destructive chemical reaction. As the heat source intensifies, both fluid temperature and velocity are elevated while the species concentration is abated with the reversed phenomenon occurring as the heat sink intensifies. An improvement is observed in the concentration and velocity distribution as the Soret parameter increases. This model is useful in petroleum reservoirs, the mining industry, and many industrial processes.

Analysis of Transient Buoyancy/Electroosmotic Driven Flow in a Vertical Microannulus with Velocity-Slip and Temperature-Jump

This article investigates the impact of electric body force on transient natural convection flow in a vertical microannulus with velocity slip and temperature jump. The governing momentum, energy, and Poisson-Boltzmann equations are presented for the current physical situation. The Laplace transform technique is employed to transform the governing partial differential equations into ordinary differential equations and then solved exactly in the Laplace domain using the method of undetermined coefficients. Line graphs and tables are simulated to properly explain the effect of various pertinent parameters entering flow formation and temperature distribution. It is found that the time taken to attain a steady-state solution significantly depends on slip-length and Electric Double Layer (EDL) length. In addition, the role of increasing the annular gap is to minimize the skin friction, electric field strength, and volumetric flow rate.

EXACT SOLUTION FOR TRANSIENT NATURAL CONVECTIVE FLOW THROUGH A VERTICAL CONCENTRIC CYLINDER FILLED WITH POROUS MEDIUM

EXACT SOLUTION FOR TRANSIENT NATURAL CONVECTIVE FLOW THROUGH A VERTICAL CONCENTRIC CYLINDER FILLED WITH POROUS MEDIUM

Impact of boundary conditions of third kind on nanoliquid flow and Radiative heat transfer through asymmetrical channel

The present study is devoted to analyze the influence of thermal radiation and chemical reaction on a transient incompressible natural convective flow of nanoliquid saturated porous medium through two rigid, parallel asymmetric plates with the negligible thickness and capable to transfer the heat with nano-liquid by convection. It is assumed that nano-liquids are made up with pouring various types of nanoparticles into the water based fluid. Single phase model is adopted to determine the thermo-physical properties of the nano-liquid and simple Darcy model is utilized to predict the flow through porous medium. The transport equations are solved to analyze the important characteristics of momentum, energy and concentration by Differential Transform Method. To compare these semi-analytical results, Crank-Nicolson finite difference scheme is used and it was in good agreement. The study reveals that Biot number influences appreciably on the velocity, temperature and concentration distributions. The significant variation in the concentration profile is found by imposing chemical reaction in the case of large Biot number.

Analysis of Transient Natural Convective Flow of a Nanofluid in a Vertical Tube

An analysis into the transient natural convective flow of a nanofluid in a vertical tube is made. The governing equations of momentum, heat transfer and nanoparticle volume fraction are deduced, and the influence of the thermophoresis parameter and Brownian motion is incorporated. By direct integration and variation of the parameter, analytical solutions are obtained for flow formation and heat/mass transfer at steady-state. On the other hand, due to the complexity of same problem at transient state, a numerical solution is used to solve the discretized equations of motion using the implicit finite difference technique. The influence of the thermophoresis parameter and Brownian motion is noted and well discussed. For accuracy check, a numerical comparison is made between the steady state and transient state solution at large time; this comparison gives an excellent agreement. The role of various principal parameters on velocity profile, temperature, concentration of nanoparticles, Sherwood and Nusselt numbers are presented graphically and well discussed. It is noted that the buoyancy ratio decreases the fluid velocity significantly.

Natural convection in a cavity with time-varying thermal forcing on a sidewall

Transient natural convection flow is investigated in a two-dimensional square enclosure, subjected to periodic heating and cooling on one sidewall. The thermal forcing applied on the heated sidewall varies with time as a sine wave around a zero mean at a frequency f, with all other walls adiabatic. The time-varying heating/cooling produces an alternating direction vertical natural convection boundary layer that entrains fluid from the cavity interior and discharges it alternatively at the top and bottom of the cavity. The behaviour of the flow is governed by three characteristic time scales, the forcing period, 1/f, the development time for the boundary layer and the filling time of the cavity. For low forcing frequency the filling time is less than the forcing period and the time average stratification S¯ is well approximated by S¯∼f4/5. For high forcing frequency the forcing period is smaller than the boundary layer development time and S¯∼f−2. The maximum S¯ occurs in a transition region, between the low and high frequency ranges. The maximum value of S¯ increases with increasing Rayleigh number, approaching S¯≅1.0 for the highest values of Rayleigh number considered.

Numerical simulation of convective heat transport within the nanofluid filled vertical tube of plain and uneven side walls

Two-dimensional transient natural convective flow in a vertical tube of plain and uneven side-walls containing cobalt-kerosene nanofluids is analyzed using a nonhomogeneous dynamic model. The vertical right wall of the enclosure is maintained at a constant low temperature and the left wall is heated by a uniform thermal condition whereas the horizontal side-walls are insulated. The Brownian motion and thermophoretic phenomena of the nanoparticles are considered in the model. The governing nonlinear momentum, energy, and concentration equations are solved numerically using a Galerkin weighted residual finite element method. The thermal, flow and concentration fields are obtained to understand the flow dynamics of cobalt-kerosene nanofluid in two types of enclosures. The local and average Nusselt numbers are analyzed for plain and uneven side walls of the tube for different parameters of the problem. The simulated results are compared with the experimental as well as with the numerical data available in the literature for some special cases. The outcomes show that the tube of having uneven vertical side-walls give higher heat transfer for lower values of the thermal Rayleigh number; whereas for the higher values of the thermal Rayleigh number, the tube of plain vertical side-walls exhibit significantly higher heat transfer rate.

Theoretical analysis of transient natural convection flow in a vertical microchannel with electrokinetic effect

ABSTRACTIn this article, a theoretical analysis is carried out to understand the role of electrokinetic effect on transient natural convection flow in a vertical microchannel. By incorporating the electrokinetic body force and the natural convection term in the classical Navier–Stokes equations, the governing momentum equation for the current investigation is developed and solved analytically using the classical Laplace transform technique. Due to the complexity of solutions obtained in Laplace domain, the Riemann-sum approximation (RSA) technique is used to transform the solutions from Laplace domain to time domain. For accuracy check, the steady-state solution is also computed and compared with the implicit finite difference method and RSA at large time. Results show that skin-friction at the walls as well as the mass-flux can be optimized by careful selection of flow controlling parameters. In addition, it is found that the time required to attain steady-state skin-friction and mass-flux is weakly dependent on EDL size while strongly dependent on Knudsen number.

A fourth-order accurate finite difference method to evaluate the true transient behaviour of natural convection flow in enclosures

PurposeModelling accurately the transient behaviour of natural convection flow in enclosures been a challenging task because of a variety of numerical errors which have limited achieving the higher order temporal accuracy. A fourth-order accurate finite difference method in both space and time is proposed to overcome these numerical errors and accurately model the transient behaviour of natural convection flow in enclosures using vorticity–streamfunction formulation.Design/methodology/approachFourth-order wide stencil formula with appropriate one-sided difference extrapolation technique near the boundary is used for spatial discretisation, and classical fourth-order Runge–Kutta scheme is applied for transient term discretisation. The proposed method is applied on two transient case studies, i.e. convection–diffusion of a Gaussian Pulse and Taylor Vortex flow having analytical solution.FindingsError magnitude comparison and rate of convergence analysis of the proposed method with these analytical solutions establish fourth-order accuracy and prove the ability of the proposed method to truly capture the transient behaviour of incompressible flow. Also, to test the transient natural convection flow behaviour, the algorithm is tested on differentially heated square cavity at high Rayleigh number in the range of 103-108, followed by studying the transient periodic behaviour in a differentially heated vertical cavity of aspect ratio 8:1. An excellent comparison is obtained with standard benchmark results.Research limitations/implicationsThe developed method is applied on 2D enclosures; however, the present methodology can be extended to 3D enclosures using velocity–vorticity formulations which shall be explored in future.Originality/valueThe proposed methodology to achieve fourth-order accurate transient simulation of natural convection flows is novel, to the best of the authors’ knowledge. Stable fourth-order vorticity boundary conditions are derived for boundary and external boundary regions. The selected case studies for comparison demonstrate not only the fourth-order accuracy but also the considerable reduction in error magnitude by increasing the temporal accuracy. Also, this study provides novel benchmark results at five different locations within the differentially heated vertical cavity of aspect ratio 8:1 for future comparison studies.

Impact of heat generation/absorption on transient natural convective flow in an annulus filled with porous material subject to isothermal and adiabatic boundaries

This article deliberated the effects of heat generation/absorption on transient natural convective flow in infinite vertical concentric cylinder filled with a porous material. The natural convective flow is as a result of constant heating at the inner cylinder while the inner surface of the outer cylinder is thermally insulated. A combination of Laplace transform technique and Riemann-sum approximation approach has been used to transform and invert the governing equation from the Laplace domain to the time domain respectively. The numerical values obtained from the Riemann-sum approximation excellently agree with the steady state solution at large time. The obtained results are represented graphically and the effects of the governing parameters on the velocity field, temperature field, mass flow rate, heat transfer as well as the skin-friction on both surfaces of the annulus are studied in detail. In the course of numerical computations, it is found that the fluid velocity and temperature both increases with time, while the fluid velocity and skin friction on both walls are seen to be proportional to Darcy number but inversely proportional to the viscosity ratio. Furthermore, it is found that the mass flow rate can be controlled by increasing/decreasing the heat generation/absorption parameter.

Computation of entropy generation in dissipative transient natural convective viscoelastic flow

AbstractEntropy generation is an important aspect of modern thermal polymer processing optimization. Many polymers exhibit strongly non‐Newtonian effects and dissipation effects in thermal processing. Motivated by these aspects in this study, a numerical analysis of the entropy generation with viscous dissipation effect in an unsteady flow of viscoelastic fluid from a vertical cylinder is presented. The Reiner‐Rivlin physical model of grade 2 (second‐grade fluid) is used, which can envisage normal stress variations in polymeric flow‐fields. Viscosity variation is included. The obtained governing equations are resolved using implicit finite difference method of Crank‐Nicolson type with well imposed initial and boundary conditions. Key control parameters are the second‐grade viscoelastic fluid parameter (), viscosity variation parameter (), and viscous dissipation parameter (). Also, group parameter (), Grashof number (Gr), and Prandtl number (Pr) are examined. Numerical solutions are presented for steady‐state flow variables, temperature, time histories of friction, wall heat transfer rate, entropy, and Bejan curves for distinct values of control parameters. The results specify that entropy generation decreases with augmenting values of , , and Gr. The converse trend is noticed with increasing Pr and . Furthermore, the computations reveal that entropy and Bejan lines only occur close to the hot cylinder wall.

Transient Natural Convection in Partitioned Enclosures

Abstract In this paper, the natural convection flow in a cavity heated differentially with a partition placed in the middle of the hot wall is numerically simulated. The aspect ratio of the geometry, Prandtl number are fixed at 0.24, 6.64, respectively, for different partitions lengths; however the Rayleigh number values were ranging from 106 to 3.77 × 109 in order to observe the transition regime. The fluid flow and the heat transfer described in terms of continuity, linear momentum and energy equations were predicted by using the finite volume method. To approach the physical reality experience, calculations were performed in a cavity with the same size and same priority of the fluid with an average temperature T m imposed on the cooled wall, also another simulation with an average temperature T m imposed on the horizontal wall. Time evolution, isotherms and mean Nusselt number are presented for all investigated values. Representative results illustrating the effects of the partition length for the heat transfer and the thermal boundary layer are also reported and discussed. The results indicate that the flow and heat transfer properties are altered by the presence of the partition, especially in the initial stage. In a certain sense, the partition blocks the flow and forces it to come off the hot wall. Since the partition parameters are critical for the transient natural convection flow in the cavity, different partition lengths on the warm wall have been studied.

Transient MHD Natural Convective Flow Past a Heated Vertical Non-porous Surface with Thermal Radiation and Double-Diffusion Effects


 
 
 
 The problem of transient MHD natural convective flow past a vertical plate with thermal radiation, cross-diffusion and zero suction effects is investigated. The governing one-dimensional spatial and non-linear partial differential equations of the Boussineq form are non-dimensionalized to, among others, bring out the necessary parameters. The evolving dimensionless equations are transformed into ordinary differential equations using the similarity transformation, and linearized using the regular perturbation expansion series solutions. The linearization leads to the zeroth and first order equations, and are solved semi-analytically using the Mathematica 11.0 computational software. Expressions for the temperature, concentration, velocity, Nusselt number, Sherwood number and Skin friction are obtained, computed and presented graphically. The analysis of results, amidst others, shows that the increase in the Dufour number increases the temperature, but decreases the Nusselt number; the increase in the Soret number decreases the concentration, but increases the Sherwood number; the increase in the Prandtl number decreases the temperature and concentration, but increases the Nusselt number and Sherwood number; the increase in the Hartmann number decreases the velocity and skin friction. These results are benchmarked with the existing reports in literatures, and are in good agreement.
 
 
 
 

An experimental study of a starting plume on a mountain

Transient natural convection is commonly present on a mountain owing to sun radiation. In this study, a starting plume rising from the mountain is experimentally investigated. Shadowgraph technology is employed to visualize transient natural convection flows on a heated copper mountain model in a water tank for a range of Rayleigh numbers from Ra = 7.2 × 106 to 6.44 × 107. Transient flows on the mountain model can be characterized by a thermal boundary layer in the conduction stage and by the starting plume in the transition to a quasi-steady state. A very simple scaling analysis is used to discuss the dynamics of transient natural convection flows on the mountain model. The scaling relations of the thickness and the velocity of the thermal boundary layer and the starting plume on the mountain are obtained, some of which, for example, the velocity of the starting plume in the head velocity increase stage, vP ~ κ2tRa/h3(1 + A−2)1/3, are validated by the experimental data. Additionally, the breaking of the plume head is described and quantified, and the flapping of the plume stem is also discussed.