Three-dimensional Mixed Convection Research Articles

Thermophoresis and MHD mixed convection three-dimensional flow of viscoelastic fluid with Soret and Dufour effects

Heat and mass transfer effects in three-dimensional mixed convection flow of viscoelastic fluid over a stretching surface with convective boundary conditions are investigated. The fluid is electrically conducting in the presence of constant applied magnetic field. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. First order chemical reaction effects are also taken into account. By using the similarity transformations, the governing boundary layer equations are reduced into the ordinary differential equations. The transformed boundary layer equations are computed for the series solutions. Dimensionless velocity, temperature, and concentration distributions are shown graphically for different values of involved parameters. Numerical values of local Nusselt and Sherwood numbers are computed and analyzed. It is found that the behaviors of viscoelastic, mixed convection, and concentration buoyancy parameters on the Nusselt and Sherwood numbers are similar. However, the Nusselt and Sherwood numbers have qualitative opposite effects for Biot number, thermophoretic parameter, and Soret-Dufour parameters.

Unsteady three-dimensional mixed convection flow with variable viscosity and thermal conductivity

An analysis has been carried out to investigate the influence of variable viscosity and thermal conductivity in the mixed convection three-dimensional flow of viscous fluid by an exponential stretching surface with heat transfer. Temperature distribution of the surface is also assumed to vary exponentially. The governing system is transformed into ordinary differential equations by appropriate transformations and non-similar solutions are computed. The effects of pertinent parameters on the flow field and heat transfer characteristics have been examined qualitatively through graphs and numerical values. Comparisons of the present work is shown with the existing previous results in the limiting sense.

Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid

Purpose – The purpose of this paper is to numerically solve the problem of an unsteady squeezing three-dimensional flow and heat transfer of a nanofluid in rotating vertical channel of stretching left plane. The fluid is assumed to be Newtonian, incompressible and electrically conducting embedded with nanoparticles. Effect of internal heat generation/ absorption is also considered in energy equation. Four different types of nanoparticles are considered, namely, copper (Cu), alumina (Al2O3), silver (Ag) and titanium oxide (TiO2) with the base fluid as water. Maxwell-Garnetts and Brinkman models are, respectively, employed to calculate the effective thermal conductivity and viscosity of the nanofluid. Design/methodology/approach – Using suitable similarity transformations, the governing partial differential equations are transformed into set of ordinary differential equations. Resultant equations have been solved numerically using Runge-Kutta-Fehlberg fourth fifth order method for different values of the governing parameters. Effects of pertinent parameters on normal, axial and tangential components of velocity and temperature distributions are presented through graphs and discussed in detail. Further, effects of nanoparticle volume fraction, squeezing parameter, suction/injection parameter and heat source/sink parameter on skin friction and local Nusselt number profiles for different nanoparticles are presented in tables and analyzed. Findings – Squeezing effect enhances the temperature field and consequently reduces the heat transfer rate. Large values of mixed convection parameter showed a significant effect on velocity components. Also, in many heat transfer applications, nanofluids are potentially useful because of their novel properties. They exhibit high-thermal conductivity compared to the base fluids. Further, squeezing and rotation effects are desirable in control the heat transfer. Originality/value – Three-dimensional mixed convection flows over in rotating vertical channel filled with nanofluid are very rare in the literature. Mixed convection squeezing three-dimensional flow in a rotating channel filled with nanofluid is first time investigated.

Three-dimensional oscillatory mixed convection in a Czochralski silicon melt under the axial magnetic field

A three-dimensional time dependent computational model is developed to simulate the oscillatory mixed convection of the melt during the crystal growth in Czochralski crucible. To study the magnetic damping effects on the growth process, an axial steady magnetic field is considered. The governing equations of continuity, momentum, energy, and electric potential subject to Boussinesq approximation applied to gravity term, have been solved numerically by a computer program developed in FORTRAN language based on finite volume method in conjunction with SIMPLER and TDMA Algorithms. The obtained results show a good agreement with experimental data available in the literature. Without magnetic field, the flow structure shows an irregularity, and the critical Reynolds number decreased in function of Richardson number owing to the destabilizing contribution of the convection. The applied of the magnetic field involves an important regulation of the flow structure and the instability delayed for higher values of the Reynolds number. The magnetic stability diagram which is established shows the dependence of the critical Reynolds number with the increase of the Hartmann number, for various values of the Richardson number. This work confirms the possibility of stabilization of a liquid metal flow in mixed convection by application of a magnetic field.

Three-dimensional transient heat transfer and airflow in an indoor ice rink with radiant heat sources

Three-dimensional mixed convection in an ice rink heated by thermostatically controlled radiant heaters was simulated numerically using the standard k–e model with wall functions. This large building was modelled under transient conditions by considering the real outdoors atmospheric conditions for a typical spring day in Montreal, Canada. Results indicate the usefulness of the CFD technique as a powerful tool which provides a detailed description of the flow and temperature fields as well as the heat fluxes into the ice. The most important results are: Heating is needed only during the night (from 22 h to 7 h) when the outdoors temperature is relatively low. The On/Off switching of the radiant panels influences the temperature profiles throughout the ice rink; even the ice surface temperature is affected although the view factor between these two surfaces is zero. The radiation heat flux towards the ice increases significantly when the radiant panels are turned On; this can influence ice quality. The resurfacing operation increases the ice temperature and, by convection, the temperature of the air immediately above the stands. The air near the ice surface (1 meter over the ice) is essentially stagnant and significant air velocities can only be found above the stands and near the ceiling above the ice. The volumetric flow rate and temperature of the air evacuated from the building vary significantly between the different outlets.

Numerical Study of Turbulent Mixed Convection of Nanofluids in Three-Dimensional Horizontal Concentric Annuli

Three-dimensional turbulent mixed convection flow using nanofluids in horizontal concentric annuli is numerically simulated. The continuity, Navier-Stokes and energy equations are solved using finite volume method (FVM) and the SIMPLE algorithm scheme is applied to examine the effects of turbulent flow on heat transfer characteristics. In this study, several parameters such as different types of nanoparticles (Al2O3, CuO, SiO2 and ZnO), different volume fractions in the range of 1% to 4%, different nanoparticles diameter in the range of 20 to 80 nm were used. Reynolds numbers are considered in the turbulent range of 6000 =Re = 18000. Different nanoparticle shapes (i.e., blades, platelets, cylindrical, bricks, and spherical), and effects of inner cylinder and outer cylinder heat fluxes were analyzed. Hydraulic diameter ratio was also examined. The numerical results indicate that the nanofluid with SiO2 has the highest Nusselt number and pressure drop compared with other nanofluids types. Heat transfer characteristic increases as the volume fraction of nanoparticles increases while it decreases as the nanoparticles diameter increases. Effects of hydraulic diameter ratio, nanoparticle shapes and location of applying heat flux on heat transfer characteristics are significant.

Enhanced Three-Dimensional Mixed Convection in a Horizontal Channel Using a Baffle

Three-dimensional mixed convection inside a horizontal rectangular channel with a square heated surface on one of the vertical sidewalls and an infinitely thin baffle installed on the opposite insulated sidewall is numerically investigated. Attention is focused on the influence of the baffle position (−2 to 2), the inclination angle between the baffle and the horizontal (15° to 90°), and the baffle height (0.2 to 0.9) on the flow and thermal characteristics. The other parameters remain unchanged: the Reynolds number (100), Grashof number (50,000) and Prandtl number (0.71). The results show recirculation around the top portion of the heated surface due to strong buoyancy. The heat transfer depends strongly on the relative positions of the baffle and the recirculation. Heat transfer enhancement is obtained with a higher baffle and a larger inclination angle if the baffle is close to the cold main stream. In contrast, the average Nusselt number is slightly smaller if the baffle is surrounded by the recirculation than it is without the baffle. An accurate correlation is proposed for calculating the average Nusselt number over the investigated range of the baffle position and the inclination angle for a fixed baffle height (0.75).

Three-dimensional mixed convection flow of viscoelastic nanofluid over an exponentially stretching surface

Purpose – The purpose of this paper is to investigate the three-dimensional mixed convection flow of viscoelastic nanofluid induced by an exponentially stretching surface. Design/methodology/approach – Similarity transformations are utilized to reduce the partial differential equations into the ordinary differential equations. The corresponding non-linear problems are solved by homotopy analysis method. Findings – The authors found that an increase in thermophoresis and Brownian motion parameter enhance the temperature. Here thermal conductivity of fluid is enhanced due to which higher temperature and thicker thermal boundary layer thickness is obtained. Practical implications – Heat and mass transfer effects in mixed convection flow over a stretching surface have numerous applications in the polymer technology and metallurgy. Such flows are encountered in metallurgical processes which involve the cooling of continuous strips or filaments by drawing them through a quiescent fluid and that in the process of drawing, these strips are sometimes stretched. Originality/value – Three-dimensional flows over an exponentially stretching surface are very rare in the literature. Three-dimensional flow of viscoelastic nanofluid due to an exponentially stretching surface is first time investigated.

Three-Dimensional Mixed Convection Flow of Viscoelastic Fluid with Thermal Radiation and Convective Conditions

The objective of present research is to examine the thermal radiation effect in three-dimensional mixed convection flow of viscoelastic fluid. The boundary layer analysis has been discussed for flow by an exponentially stretching surface with convective conditions. The resulting partial differential equations are reduced into a system of nonlinear ordinary differential equations using appropriate transformations. The series solutions are developed through a modern technique known as the homotopy analysis method. The convergent expressions of velocity components and temperature are derived. The solutions obtained are dependent on seven sundry parameters including the viscoelastic parameter, mixed convection parameter, ratio parameter, temperature exponent, Prandtl number, Biot number and radiation parameter. A systematic study is performed to analyze the impacts of these influential parameters on the velocity and temperature, the skin friction coefficients and the local Nusselt number. It is observed that mixed convection parameter in momentum and thermal boundary layers has opposite role. Thermal boundary layer is found to decrease when ratio parameter, Prandtl number and temperature exponent are increased. Local Nusselt number is increasing function of viscoelastic parameter and Biot number. Radiation parameter on the Nusselt number has opposite effects when compared with viscoelastic parameter.

Numerical Study of Three-Dimensional Mixed Convection in an Eccentric Annulus

Mixed convection of air with a Prandtl number of 0.7 in eccentric horizontal annuli is numerically investigated. The inner cylinder is at a higher temperature, while the inner and outer cylinders can be rotated either clockwise or counterclockwise with a constant angular velocity. The effects of various parameters, such as the eccentricity of the annulus and the Rayleigh number, are studied using a three-dimensional model. The Navier–Stokes equations, along with the energy equation, are solved in an orthogonal structured grid of a bipolar coordinate system employing a finite volume method based on the SIMPLE algorithm. Here, both steady and unsteady results are presented in two separate codes. Three-dimensional considerations lead to a complicated flow pattern, whereas Taylor vortices have a major role on heat and flow characteristics. It is shown that the axial component of velocity in some configurations has a considerable value, therefore, flow pattern and heat transfer characteristics change in comparison with a two-dimensional approach. Eccentricity leads to a different flow pattern in the upper and lower parts of the annulus. Mean and local heat transfer results are obtained. The physics of the flow underlying the observed heat transfer behavior is revealed by the velocity vectors and the isotherm plots of the numerical solutions. Results show that flow and heat transfer are strongly influenced by the eccentricity of the inner cylinder and Raleigh number, and that three-dimensionality consideration is inevitable.

A numerical study of the longitudinal thermoconvective rolls in a mixed convection flow in a horizontal channel with a free surface

This paper presents a numerical study of three-dimensional laminar mixed convection within a liquid flowing on a horizontal channel heated uniformly from below. The upper surface is free and assumed to be flat. The coupled Navier–Stokes and energy equations are solved numerically by the finite volume method taking into account the thermocapillary effects (Marangoni effect). When the strength of the buoyancy, thermocapillary effects and forced convective currents are comparable (Ri⋍O(1) and Bd=Ra/Ma⋍O(1)), the results show that the development of instabilities in the form of steady longitudinal convective rolls is similar to those encountered in the Poiseuille–Rayleigh–Bénard flow. The number and spatial distribution of these rolls along the channel depend on the flow conditions. The objective of this work is to study the influence of parameters, such as the Reynolds, Rayleigh and Biot numbers, on the flow patterns and heat transfer characteristics. The effects of variations in the surface tension with temperature gradients (Marangoni effect) are also considered.

Transient process of three-dimensional mixed convection and heat transfer in a horizontal square duct with uniform heated wall temperature

Transient process of three-dimensional mixed convection and heat transfer in a horizontal square duct with uniform heated wall temperature

Effects of Prandtl number on three-dimensional mixed convection in a horizontal square duct with heated and cooled side walls

We examined the effects of Prandtl number on three-dimensional mixed convection in a horizontal square duct with heated and cooled side walls numerically. Non-dimensional governing equations were solved for Re = 100, Pr = 0.1–10, and Ri = 36.44 by the SIMPLE method. The numerical results show that the swirl flow was generated along the flow direction, and its pitch lengthened with the increase of Pr. We also examined the strength of swirl flow using the swirl number, S, and we discuss heat transfer behavior as it corresponded to the flow. Heat transfer was promoted by the swirl flow with all Pr, and the optimum value existed within these Pr. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/htj.20319

Simulation and performance enhancement of the air cooling system in the valve halls of a DC/AC power converter station

The present article reports on a ventilation system that uses impinging air jets to remove a portion of the heat generated in DC/AC converter towers. Each tower is a vertical stack of electronic components used in the power conversion. Airflow from the ventilation system enters the room through inlet ports located on the ground at two opposite sides of the DC/AC converter towers. The existing ventilation system circulates sufficient airflow in terms of the total heating load; however, elevated temperatures were reported within the towers due to poor air circulation. A numerical study has been conducted to investigate steady three-dimensional (3-D) turbulent mixed (combined free and forced) convection air cooling of vertical stacks of heat-generating blocks simulating typical towers in two valve halls of a DC/AC power converter station. The simulation results include the magnitudes of the net airflows for all the inter-block gaps, the maximum temperature in each gap, and the flow structure represented by streamlines at various locations of the 3-D domain. The location of the inlet, the inlet size and aspect ratio, and the location on the tower at which the airflow was aimed were varied parametrically to improve the ventilation relative to the existing design. These results demonstrate that, for fixed inlet mass flow rate, all the towers’ heat generating surfaces can be kept under 60°C via simple modifications of the variables used in the parametric study.

A numerical study of three-dimensional laminar mixed convection past an open cavity

A numerical study has been carried out to analyze the effects of mixed convective flow over a three-dimensional cavity that lies at the bottom of a horizontal channel. The vertical walls of the cavity are isothermal and all other walls are adiabatic. The cavity is assumed to be cubic in geometry and the flow is laminar and incompressible. A direct numerical simulation is undertaken to investigate the flow structure, the heat transfer characteristics and the complex interaction between the induced stream flow at ambient temperature and the buoyancy-induced flow from the heated wall over a wide range of the Grashof number (10 3–10 6) and two Reynolds numbers Re = 100 and 1000. The computed thermal and flow fields are displayed and discussed in terms of the velocity fields, streamlines, the temperature distribution and the averaged Nusselt number at the heated and cooled walls. It is found that the flow becomes stable at moderate Grashof number and exhibit a three-dimensional structure, while for both high Reynolds and Grashof numbers the mixed convection effects come into play, push the recirculating zone further upstream and the flow becomes unsteady with Kelvin–Helmholtz instabilities at the shear layer.

Effects of Prandtl Number on Three-dimensional Mixed Convection in a Horizontal Square Duct with Heated and Cooled Side Walls

We examined the effects of Prandtl number on three-dimensional mixed convection in a horizontal square duct with heated and cooled side walls numerically. Non-dimensional governing equations were solved for Re = 100, Pr = 0.1–10, and Ri = 36.44 by the SIMPLE method. The numerical results show that the swirl flow was generated along the flow direction, and its pitch lengthened with the increase of Pr. We also examined the strength of swirl flow using the swirl number, S, and we discuss heat transfer behavior as it corresponded to the flow. Heat transfer was promoted by the swirl flow with all Pr, and the optimum value existed within these Pr. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/htj.20319

Three-Dimensional Mixed Convection in Plane Symmetric-Sudden Expansion: Bifurcated Flow Regime

Simulations of three-dimensional laminar mixed convection in a vertical duct with plane symmetric sudden expansion are presented to illustrate the effects of the buoyancy-assisting force and the duct’s aspect ratio on flow bifurcation and heat transfer. The stable laminar bifurcated flow regime that develops in this geometry at low buoyancy levels leads to nonsymmetric temperature and heat transfer distributions in the transverse direction, but symmetric distributions with respect to the center width of the duct in the spanwise direction. As the buoyancy force increases, due to increases in wall heat flux, flow bifurcation diminishes and both the flow and the thermal fields become symmetric at a critical wall heat flux. The size of the primary recirculation flow region adjacent to the sudden expansion increases on one of the stepped walls and decreases on the other stepped wall as the wall heat flux increases. The maximum Nusselt number that develops on one of the stepped walls in the bifurcated flow regime is significantly larger than the one that develops on the other stepped wall. The critical wall heat flux increases as the duct’s aspect ratio increases for fixed Reynolds number. The maximum Nusselt number that develops in the bifurcated flow regime increases as the duct’s aspect ratio increases for fixed wall heat flux and Reynolds number.

Modeling of Flow Field and Heat Transfer in a Copper-Base Automotive Radiator Application

This paper describes a methodology used for designing louvered fins. Louvered fins are commonly used in many compact heat exchangers to increase the surface area and initiate new boundary layer growth. Detailed measurements can be accomplished with computational models of these louvered fins to gain a better understanding of the flow field and heat distribution. The particular louver geometry studies for this work have a louver angle of 23° and fin count of 17 fpi. The flow and heat transfer characteristics for three-dimensional mixed convection flows in a radiator flat tube with louvered fins are analyzed numerically. A three-dimensional model is developed to investigate flow and conjugate heat transfer in the copper-based car radiator. The model was produced with the commercial program FLUENT. The theoretical model has been developed and validated by comparing the predictions of the model with available experimental data. The thermal performance and temperature distribution for the louvered fins were analyzed and a procedure for optimizing the geometrical design parameter is presented. One fin specification among the various flat tube exchangers is recommended by first considering the heat transfer and pressure drop. The effects of variation of coolant flow conditions and external air conditions on the flow and the thermal characteristics for the selected radiator are investigated also. The results will be used as fundamental data for tube design by suggesting specifications for car radiator tubes.

D201 水平正方形流路内のベナール型複合対流の可視化

This paper describes the flow visualization of the Benard-type three-dimensional mixed convection in a horizontal square duct with heat transfer bottom wall (T H=40°C) and upper wall (T L=20°C) by dye injection method. The working fluid is water. Three-dimensional spiral flows are observed along the longitudinal direction of the duct. Direction of rotation of the spiral flow depends on the difference between the inlet fluid temperature and the symmetrical spiral flows are collapsed in the downstream region.

Simultaneous Thermal and Mass Diffusion on Three-Dimensional Mixed Convection Flow through a Porous Medium

Simultaneous Thermal and Mass Diffusion on Three-Dimensional Mixed Convection Flow through a Porous Medium