Unsteady Natural Convection Heat Research Articles

Unsteady natural convection heat transfer from a pair of vertically aligned 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. Particular attention is paid to the interaction between the two buoyant plumes and the relationship between unsteady fluid flow and heat transfer enhancement. 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. Moreover, strong oscillations appear in the local heat transfer rate and fluid flow field. A computational fluid dynamics model (CFD) is established and validated against experimental results for both averaged and local Nusselt number, for a range of Rayleigh numbers between 1.7×106 and 5.3×106 and a centre-to-centre cylinder spacing between 2 and 4 diameters. The validated CFD model is used to identify 3.5 diameters as the spacing which maximises the averaged Nusselt number on the upper cylinder among the values of Rayleigh number and spacing which were presently investigated. The transient CFD model is used to characterise the peak frequencies of the oscillating thermal plume, as well as analyse Fourier transforms and spectral coherence of the local Nusselt number and fluid velocity. This detailed numerical analysis has complemented previous experimental measurements, confirming some hypotheses on the mechanisms of heat transfer enhancement in this configuration.

Finite Element Analysis of Unsteady Natural Convective Heat Transfer and Fluid Flow of Nanofluids inside a Tilted Square Enclosure in the Presence of Oriented Magnetic Field

In this paper, the problem of unsteady natural convective heat transfer flow of nanofluids having various sizes of nanoparticles inside an inclined square enclosure in the presence of oriented magnetic field is investigated numerically. The Brownian motion of nanoparticles is taken into consideration in the thermal conductivity model construction. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. Galerkin weighted residual finite element technique has been employed to solve the governing nonlinear dimensionless equations. In order to ensure the accuracy of the present numerical code, comparisons with previously published works are performed and excellent agreement is obtained. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, inclination angle of magnetic field, inclination angle of the geometry, diameter and Brownian motion of the nanoparticles on the fluid flow and heat transfer are investigated. The results indicate that an increment in Rayleigh number and nanoparticle volume fraction increases the heat transfer rate in a significant way, whereas, an increment in Hartmann number decreases the overall heat transfer rate. It is also observed that the heat transfer enhancement strongly depends on the diameter of the nanoparticles as well as the types of the nanofluids. It is observed that the time taken to reach the steady state is controlled by the different model parameters and in particular, it is longer for low Rayleigh number and shorter for high Rayleigh number. A comparison between the two studies of with and without Brownian motion shows that when Brownian motion is considered, the solid volume fraction has more significant effects on the heat transfer rate at all Rayleigh numbers considered in the square cavity. Finally, the distribution of average heat transfer rate for different cavity inclination angle along with various model parameters has been found as almost parabolic shape.

Magnetohydrodynamic Convective Double Diffusive Laminar Boundary Layer Flow Past an Accelerated Vertical Plate

This manuscript presents the diffusion thermo and thermo diffusion effects on unsteady MHD natural convection heat and mass transfer flow past an accelerated vertical porous plate in the presence of thermal radiation, variable temperature and also variable concentration. The non-dimensional governing equations are coupled non-linear partial differential equations for which the exact solution is not possible. Hence these equations are solved numerically by using finite difference scheme. The effects of different physical parameters involved in the problem are presented and discussed with the help of graphs. The fluid velocity increases with the increasing values of Grashof number, modified Grashof number, Soret number, Dufour number and permeability of the porous medium, but a reverse behavior is found in the case of magnetic parameter and Prandtl number. The fluid temperature falls down for increasing values of radiation parameter, heat sink parameter and Prandtl number, whereas enhancement in the fluid temperature is found in the case of Soret and Dufour effects. Increasing values of Soret number results in rising of the concentration, but it falls down under the influence of Dufour number and Schmidt number.

Unsteady natural convection heat transfer of nanofluid in an annulus with a sinusoidally heated source

ABSTRACTWe study the unsteady natural convection of nanofluid between the outer and inner surfaces of a concentric annulus. The inner surface is heated sinusoidally with time about a fixed mean temperature but the outer boundary is kept at a constant temperature. The effects of Brownian motion and thermophoresis are taken into account. Numerical solutions are presented using the continuous finite-element method. Results indicate that the heat and mass transfer rates are significantly influenced by inner wall temperature oscillation, which presents periodic triangle fluctuation for the considered parameters of amplitude A, inner circle radius R, and frequency F.

Numerical investigation of unsteady natural convection heat transfer from the outer surface of helical coils

The main purpose of this work is a numerical study on unsteady natural convection from outer surface of helical coils. Each heat exchanger consisted of a helical coil and a shell. The helical coil was mounted in the shell vertically. The cold water was in the shell and the hot water was flowing through the coil and was cooled by unsteady natural convection. A CFD code has been used for heat exchanger simulation. The analyses have been carried out for 27 helical coils with different geometries. The effect of helical coil geometry on natural convective heat transfer is investigated. All of continuity, momentum, energy, and turbulence equations are solved for both of fluids simultaneously, so there is no need to simplifying assumptions for boundary conditions. Results are compared with previous experimental researches. Statistical analyses have been done on data points of temperature and natural convection Nusselt number. It is revealed that shell-side fluid temperature and the Nusselt number of the outer surface of coils are functions of in-tube fluid mass flow rate, geometrical parameters of helical coils, and time. A new correlation is presented for calculating the temperature changes of bath fluid. Some other fluids are used as coil and bath fluids and results show that the presented correlation for bath temperature computing have an acceptable accuracy for them.

Large Eddy Simulation of turbulent buoyancy-driven flow with alternating staggered heating walls

Unsteady turbulent natural convection flow and heat transfer in an open-ended channel with non-uniformly heated walls has been investigated. A two-wall-heated staggered arrangement in both vertical and tilted (45°) flow channels is analyzed to better understand the mechanism of perturbing the developing fluid and thermal boundary layers along the heated walls. Effect of different convective fluxes and fixed air gap distances on velocity and temperature fields is investigated. Large Eddy Simulation (LES) results demonstrate that better cooling enhancement is achieved in the two-wall-heated staggered arrangement with a higher chimney effect being experienced in the vertical configuration.

Natural convection in square enclosure induced by inner circular cylinder with time-periodic pulsating temperature

The periodic unsteady natural convection flow and heat transfer in a square enclosure containing a concentric circular cylinder is numerically studied. The temperature of the inner circular cylinder fluctuates periodically with time at higher averaged value while the temperature of the enclosure keeps lower constant, and the natural convection is driven by the temperature difference. The two-dimensional natural convection is simulated with high accuracy temporal spectral method and local radial basis functions method. The Rayleigh number is studied in the range 103⩽Ra⩽106, the temperature pulsating period ranges from 0.01 to 100 and the temperature pulsating amplitudes are a=0.5, 1.0 and 1.5. Numerical results reveal that the fluid flow and heat transfer is strongly dependent on the pulsating temperature of inner cylinder. Comparing with the steady state natural convection, the heat transfer is enhanced generally for the time-periodic unsteady natural convection, and the local maximum heat transfer rate is observed for Ra=105 and 106. Moreover, the phenomenon of backward heat transfer is discussed quantitatively. Also, the influence of pulsating temperature on the unsteady fluid flow and heat transfer are discussed and analyzed.

MHD Natural Convection Heat and Mass Transfer Flow Past a Time Dependent Moving Vertical Plate with Ramped Temperature in a Rotating Medium with Hall Effects, Radiation and Chemical Reaction

AbstractAn investigation of unsteady hydromagnetic natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible and optically thick radiating fluid past an impulsively moving infinite vertical plate embedded in a uniform porous medium in a rotating system with Hall effects in the presence of homogeneous first order chemical reaction is carried out when temperature of the plate has a temporarily ramped profile. Exact solution of the governing equations is obtained in closed form by Laplace transform technique. Expressions for skin friction due to primary and secondary flows and Nusselt number are derived for both ramped temperature and isothermal plates. Expression for Sherwood number is also derived. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically whereas those of skin friction are presented in tabular form for various values of pertinent flow parameters. In order to highlight the influence of ramped temperature distribution within the plate on the flow-field, the fluid flow past a ramped temperature plate is compared with the one past an isothermal plate.

State space approach to unsteady magnetohydrodynamics natural convection heat and mass transfer through a porous medium saturated with a viscoelastic fluid

A technique of the state space approach and the inversion of the Laplace transform method are applied to dimensionless equations of an unsteady one-dimensional boundary-layer flow due to heat and mass transfer through a porous medium saturated with a viscoelastic fluid bounded by an infinite vertical plate in the presence of a uniform magnetic field is described. Complete analytical solutions for the temperature, concentration, velocity, and induced magnetic and electric fields are presented. The inversion of the Laplace transforms is carried out by using a numerical approach. The proposed method is used to solve two problems: boundary-layer flow in a viscoelastic fluid near a vertical wall subjected to the initial conditions of a stepwise temperature and concentration and viscoelastic fluid flow between two vertical walls. The solutions are found to be dependent on the governing parameters including the Prandtl number, the Schmidt number, the Grashof number, reaction rate coefficient, viscoelastic parameter, and permeability of the porous medium. Effects of these major parameters on the transport behavior are investigated methodically, and typical results are illustrated to reveal the tendency of the solutions. Representative results are presented for the velocity, temperature, concentration, and induced magnetic and electric field distributions, as well as the local skin-friction coefficient and the local Nusselt and Sherwood numbers.

Modeling of Unsteady Natural Convection for Double-Pipe in a Partially Cooled Enclosure

In this article, a model is developed for unsteady natural convection heat transfer and fluid flow in a partially cooled enclosure with a hollow cylinder through it. The right vertical wall of the enclosure is cooled partially. The location of the partial cooling is set up in three different configurations; namely, bottom (P 1), middle (P 2), and top (P 3). A hollow cylinder is located at the middle of the enclosure to simulate a double-pipe heat exchanger. Three values of Grashof number are applied in this work, i.e., 104, 105 and 106, and three lengths of the cooler, i.e., 0.2, 0.4 and 0.6. Finite element method was utilized to solve the unsteady dimensionless conservation equations of mass, momentum and energy. It is found that the length and location of cooler does not have a significant effect on the natural convection for the case of the low Grashof number. The maximum heat transfer rate is reached when the cooler is located at the middle of the vertical wall.

A BINARY CHEMICAL REACTION ON UNSTEADY FREE CONVECTIVE BOUNDARY LAYER HEAT AND MASS TRANSFER FLOW WITH ARRHENIUS ACTIVATION ENERGY AND HEAT GENERATION/ABSORPTION

We investigate a local similarity solution of an unsteady natural convection heat and mass transfer boundary layer incompressible fluid flow past a moving vertical porous plate in the presence of the heat absorption and generation. The effects of chemical reaction rate which is function of temperature and Arrhenius activation energy on the velocity, temperature and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing local similarity transformation (Maleque, 2010a). Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim- Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity, temperature and concentration profiles. The corresponding skin friction coefficient, the Nusselt number and the Sherwood number are also calculated and displayed in table showing the effects of various parameters on them.

Experimental and numerical study on unsteady natural convection heat transfer in helically coiled tube heat exchangers

Both of experimental and numerical investigations were performed to understand unsteady natural convection from outer surface of helical coils. Four helical coils with two different curvature ratios were used. Each coil was mounted in the shell both vertically and horizontally. The cold water was entered the coil and the hot water in the shell was cooling by unsteady natural convection. A CFD code was developed to simulate natural convection heat transfer. Equations of tube and shell are solved simultaneously. Statistical analyses have been done on data points of temperature and natural convection Nusselt number. It was revealed that shell-side fluid temperature and the Nusselt number of the outer surface of coils are functions of in-tube fluid mass flow rate, specific heat of fluids and geometrical parameters including length, inner diameter of the tube and the volume of the shell, and time.

Unsteady natural convection in Al2O3–water nanoliquid filled in isosceles triangular enclosure with sinusoidal thermal boundary condition on bottom wall

Unsteady natural convection heat transfer in an isosceles triangular enclosure filled with Al2O3 nanoparticle is studied by using finite element method. The bottom of the isosceles triangular cavity is heated non-uniformly and temperature of the inclined wall is lower than that of the bottom wall. The governing parameters are Rayleigh number, solid volume fraction, aspect ratio (H/L) of the enclosure and dimensionless-time. It is found that addition of the nanoparticle into base fluid (water) affects both heat transfer and fluid flow. Heat transfer increases with addition of nanoparticle and increasing of Rayleigh number. Conduction mode of heat transfer becomes dominant for the lower values of aspect ratio.

Effects of Exothermic/Endothermic Chemical Reactions with Arrhenius Activation Energy on MHD Free Convection and Mass Transfer Flow in Presence of Thermal Radiation

A local similarity solution of unsteady MHD natural convection heat and mass transfer boundary layer flow past a flat porous plate within the presence of thermal radiation is investigated. The effects of exothermic and endothermic chemical reactions with Arrhenius activation energy on the velocity, temperature, and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing locally similarity transformation (Maleque (2010)). Numerical solutions to the reduced nonlinear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are obtained for both steady and unsteady cases then presented graphically in the form of velocity, temperature, and concentration profiles. Comparison has been made for steady flow () and shows excellent agreement with Bestman (1990), hence encouragement for the use of the present computations.

Natural convection heat transfer of nanofluids along a vertical plate embedded in porous medium

The unsteady natural convection heat transfer of nanofluid along a vertical plate embedded in porous medium is investigated. The Darcy-Forchheimer model is used to formulate the problem. Thermal conductivity and viscosity models based on a wide range of experimental data of nanofluids and incorporating the velocity-slip effect of the nanoparticle with respect to the base fluid, i.e., Brownian diffusion is used. The effective thermal conductivity of nanofluid in porous media is calculated using copper powder as porous media. The nonlinear governing equations are solved using an unconditionally stable implicit finite difference scheme. In this study, six different types of nanofluids have been compared with respect to the heat transfer enhancement, and the effects of particle concentration, particle size, temperature of the plate, and porosity of the medium on the heat transfer enhancement and skin friction coefficient have been studied in detail. It is found that heat transfer rate increases with the increase in particle concentration up to an optimal level, but on the further increase in particle concentration, the heat transfer rate decreases. For a particular value of particle concentration, small-sized particles enhance the heat transfer rates. On the other hand, skin friction coefficients always increase with the increase in particle concentration and decrease in nanoparticle size.

Unsteady Natural Convection Boundary Layer Flow with Mass Transfer and a Binary Chemical Reaction

We investigate a locally similarity solution of unsteady natural convection heat and mass transfer boundary layer flow past a flat porous plate. The effects of chemical reaction rate and Arrhenius activation energy on the velocity, temperature and concentration are also studied in this paper. The governing partial differential equations are reduce d to ordinary differential equations by introducing locally similarity transformation Maleque [14]. Numerical solutions to the reduced nonlinear similarity equations are then obtained by adopting Runge-Kutta and shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity, temperature and concentration profiles. The corresponding skin friction coefficient, the Nusselt number and the Sherwood number are also ca lculated and displayed inTableshowing the effects of various parameters on them.

The effect of the horizontal vibrations on natural heat transfer from an isothermal array of cylinders

A numerical investigation is carried out to study an unsteady laminar natural convection heat transfer caused by an array of isothermal oscillating circular cylinders. Under oscillating conditions, flow and thermal fields are categorized into a class of moving boundary problems. In this study, the moving interfaces between the fluid and cylinders have been considered. The numerical model used in the present paper, is based on a 2D Navier–Stokes momentum and energy equations for an incompressible flow solver on an unstructured grid. Discretization of the governing equations including continuity, momentum and energy equations is achieved through a finite element scheme based on characteristic based split algorithm using the arbitrary Lagrangian–Eulerian approach to satisfy boundary movement. Besides a dual time stepping method is employed to capture unsteady flow and thermal characteristics. The working fluid is designated a Prandtl number of 0.71(air) and assumed to be incompressible with constant physical properties. The radiation, viscous dissipation and pressure work are also assumed to be negligible throughout this investigation. Fluid flow and heat transfer characteristics are examined in the domain of the Rayleigh number, cylinders spacing, amplitude, and frequency of oscillations such that: 103 ≤ Ra ≤ 105, 2 ≤ s/d ≤ 4, 0.5 ≤ l ≤ 2, and 0.1 ≤ f ≤ 0.4. The obtained results reveal that increment of Rayleigh number and cylinders’ spacing augment the average Nusselt of each cylinder as well as higher oscillation amplitude and frequency. Moreover, it was found that horizontal vibration makes vortices appear in the left and right area of the cylinders. These vortices reduce heat transfer from two upper cylinders.

NATURAL CONVECTION IN CONFINED CYLINDRICAL ENCLOSURE OF POROUS MEDIA WITH CONSTANT AND PERIODIC WALL TEMPERATURE BOUNDARY CONDITIONS

Numerical investigations of unsteady natural convection heat transfer through a fluid-saturated porousmedia in inclined cylindrical enclosure are studied by solving the governing (3-D) Darcy-Boussinesqequations using finite difference method. The momentum equation of flow was solved by Relaxation method and the energy equation by using Alternating Direction Implicit (ADI) method. The problem is analyzed for modified Rayleigh number with range of (50-300),angles of inclination (0°,25°,45°60°90°), amplitude of sinusoidal temperature (0.2, 0.4, 0.8) and period (0.005, 0.01, 0.02). Results indicate an increase in the heat transfer with increasing of Rayleigh number, time, amplitude, angle of inclination and period. Also average and local Nusselt number were calculated and it is found that Maximum temperature and velocity occur at angle α=45 and this indicate a strong buoyancy force effect on convective flow.

Unsteady natural convection heat transfer from a heated horizontal circular cylinder to its air-filled coaxial triangular enclosure

Unsteady natural convection heat transfer in a horizontal annular region bounded by a heated inner circular cylinder and a coaxial outer triangular cylinder is numerically studied for a wide range of Grashof numbers, aspect ratios, and inclination angles of the triangular enclosure. Different phases are identified during the course of flow development through the evolutions of the average Nusselt number over the inner circular wall. Snapshots of streamlines and isotherms for two typical cases are presented to exhibit identification among these phases. The flow development time and time-averaged Nusselt number over the inner circular wall are predicted and scaled with Grashof number. Additionally, the onset and evolution of pitchfork bifurcation are quantitatively investigated.

NON‐NEWTONIAN CANNED LIQUID FOOD, UNSTEADY FLUID MECHANICS AND HEAT TRANSFER PREDICTION FOR PASTEURIZATION AND STERILIZATION

ABSTRACTUnsteady fluid mechanics and natural convective heat transfer during pasteurization and sterilization for aqueous (CMC solution) and fatty (soybean oil) liquid foods were numerically predicted by means of noncommercial computational program developed in this work. This software is based on the finite volume method and the food simulants are assumed to be non‐Newtonian fluids with a temperature‐dependent power‐law viscosity model. Different cylindrical container materials were analyzed (LDPE, PA, PP, galvanized steel), with h/d equal to 0.53, 1.56 and 3.12. Results obtained show that the time required for sterilization is strongly dependent on the liquid food rheological behavior. A recirculating flow pattern was found inside the cylindrical container for the aqueous food stimulant. The Tshz variation with the dimensionless time was faster heating when the h/d decreases. The fastest heating pasteurization and sterilization processes were obtained for CMC solutions inside cylindrical packages with a pseudoplastic behavior.PRACTICAL APPLICATIONSThere is a vast body of literature about transport phenomena of thermal treatment of packaged food. However, this literature is restricted when the analyzed foods show a non‐Newtonian behavior. The methodology described in this paper aims to contribute to the understanding of pasteurization and sterilization of packaged non‐Newtonian liquid foods through the implementation of a fast and accurate tool for the optimization of the operational parameters in these treatments, as well as in the design of packaging materials. Commercially available computational fluid dynamics is a powerful tool for the analysis of transient heat transfer packages that allow it to simulate almost any geometry or even import it as Computer Aided Design (CFX, FLUENT and others). Also, rheological properties can be introduced by applying user‐defined functions. The noncommercial computational program developed in this work allows modifying operation, rheological and design parameters without restrictions. The versatility of these tools can complement experimental studies decreasing the time required to the design of the package and its associated costs.On the other hand, an accurate prediction of the unsteady fluid mechanics and natural convective heat transfer during thermal treatments allows estimating the adequate conditions to preserve the quality of packaged foods, along with reduction in energy consumption, resulting in low contamination.