MHD Mixed Convection in a Lid-Driven Cavity Including Heat Conducting Solid Object and Corner Heaters with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a top sided lid-driven square enclosure is numerically simulated in this paper following a finite volume approach based on the SIMPLEC algorithm. The enclosure is heated by corner heaters which are under isothermal boundary conditions with different lengths in bottom and right vertical walls. The lid is having lower temperature than heaters. The other boundaries of the enclosure are insulated. A uniform magnetic field is applied along the horizontal direction. A heat conducting horizontal solid object (a square cylinder) is placed centrally within the outer enclosure. Shear forces through lid motion, buoyancy forces due to differential heating and magnetic forces within the electrically conducting fluid inside the enclosure act simultaneously. Heat transfer due to forced flow, thermal buoyancy, Joule dissipation and conduction within the solid object are taken into account. Simulations are conducted for various controlling parameters such as the Richardson number (0.1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50) and Joule heating parameter (0 ≤ J ≤ 5) keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number and bulk fluid temperature are also plotted to show the effects of Ha, J and Ri on them.     

Laminar heat transfer in an asymmetrically heated rectangular duct

This paper presents a numerical study concerning the effects of non-uniform heating on the heat transfer of a thermally undeveloped gas flow in a horizontal rectangular duct; a vertical side wall is uniformly heated, and the other walls are insulated. As an initial step of the study, the duct flow is assumed to be laminar, and buoyancy effects are considered. The heat transfer rate and drag increase with the secondary flow due to buoyancy; the effects of the buoyancy force on the heat transfer and friction coefficient of the thermally undeveloped region are found to depend only upon modified Grashof numbers of the duct entrance.     

Interaction of Participating Medium Radiation with Thermosolutal Convection—A Critical Appraisal

The present study addresses the interaction effect of participating media radiation with the onset of double‐diffusive convection in a square enclosure. Vertical walls are imposed with constant temperature and concentration, and the horizontal walls are impermeable and adiabatic. The boundaries of the enclosure are diffuse‐gray, and the enclosed fluid isotropically scatters, emits, and absorbs thermal radiation. Numerical simulations have been performed for both aiding and opposing buoyancy conditions. The buoyancy ratio has been varied to simulate the effect of buoyancy driven flow and compositionally driven flow, along with transition of flow between the above. Optical properties like opacity of medium, scattering albedo, Planck number, and wall emissivity have been varied to depict their influence on flow and heat transfer. The modified MAC method is used for the solution of convective transport equations. Gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) is used for the discretization of the convective terms. The discrete ordinate method, with S8 approximation, is used to solve the radiative transport equation. The parametric results are provided in graphical and tabular form. Flow lines, isotherms, and isoconcentration contour maps are provided to bring clarity in the understanding of the momentum, heat, and solute transport phenomenon. The stabilization effect of thermal radiation at critical buoyancy ratio for buoyancy opposed flow is observed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21108     

Heat transfer enhancement for laminar flow of ethylene glycol through a square duct fitted with increasing and decreasing orders of twisted tape

The isothermal friction factor and heat transfer enhancement through a square duct fitted with increasing and decreasing order of twist ratio sets have been studied under nearly uniform wall temperature conditions. The ethylene glycol flows under laminar flow (Re = 30–1200) through a square duct and hot water flows through an annular channel formed between a square duct and circular tube, in a counter current fashion. The hot water at a very high flow rate is circulated though the annular channel to ensure a nearly uniform wall temperature condition. There is not much change in the magnitude of the heat transfer coefficient enhancement with the increasing twist ratio and with the decreasing twist ratio set, as the intensity of the swirl generated at the inlet or at the outlet in the order of increasing twist ratio or decreasing twist ratio, is the same in both the cases. Performance evaluation analysis on constant pumping power was made and a maximum performance ratio was obtained for each twist insert corresponding to a Reynolds number of 680. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20410     

The study of buoyancy influence on mean flow and heat transfer under conditions of mixed convection in annular channels

Laser Doppler anemometry (LDA) measurements are reported on mean flow and turbulence in water as it flows downwards through a long vertical passage of annular cross‐section having an inner surface which can be uniformly heated and an outer one which is adiabatic. Under buoyancy‐opposed conditions, which can be achieved by heating the core and operating at a reduced mass flow rate, the flow near the inner surface is retarded, turbulent velocity fluctuations and turbulent shear stress are increased and the effectiveness of heat transfer is enhanced. When the influence of buoyancy is very strong, flow reversal occurs near the inner surface. Under such conditions, turbulence is produced very readily and the heat transfer process remains very effective, even when the Reynolds number is reduced to values at which the flow is laminar in the absence of heating. The measurements of turbulence in buoyancy‐opposed flow made in this study provide direct confirmation of the validity of the ideas currently used to explain the influences of buoyancy on mixed convection in vertical passages. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(1): 9–17, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20041     

Magnetoconvective Transport in a Vertical Lid-Driven Cavity Including a Heat Conducting Square Cylinder with Joule Heating

The hydromagnetic mixed convection flow and heat transfer in a vertical lid-driven square enclosure is numerically simulated following a finite volume approach based on the SIMPLEC algorithm. Both the top and bottom horizontal walls of the enclosure are insulated, and the left and right vertical walls are kept isothermal with different temperatures. The left vertical wall is translating in its own plane at a uniform speed, while all other walls are stationary. Two cases of translational lid motion, viz. vertically upward and downward, are considered. A uniform magnetic field is applied along the horizontal direction normal to the translating wall. A heat conducting horizontal solid square cylinder is placed centrally within the outer enclosure. Simulations are conducted for various controlling parameters, such as the Richardson number (1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), and Joule heating parameter (0 ≤ J ≤ 5), keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ha, J, and Ri. Furthermore, the pertinent transport quantities such as the drag coefficient, Nusselt number, and bulk fluid temperature are also plotted to show the effects of Ha, J, and Ri on them.     

MIXED CONVECTION IN AN INCLINED CHANNEL WITH LOCALIZED HEAT SOURCES

Fully developed opposing mixed convection is numerically studied in an inclined channel that has discrete heating on the bottom and is insulated on the top. The numerical approach is based on the hypothesis that the solution is periodic according to the imposed wavelength of the heating elements. Considering that Ike heat produced by the heating elements is totally carried downstream, the temperature increment from one heating element to the other is defined on the basis of an energy balance. To verify the accuracy of the computational code, an analytical study of the extreme case with an entirely heated wall is investigated. Also, to validate that the solution of the problem is periodic with a wavelength corresponding to the imposed perturbation, a channel with entrance and exit sections containing four to six heating elements is simulated numerically. In the present study, the relative strength of the forced flow and buoyancy effects is examined for a broad range of Rayleigh numbers, Reynolds numbers, and inclination angles. Both overall and local recirculating flows are observed that are caused by buoyancy effects on the forced flow.     

Laminar mixed convection in an eccentric annular horizontal duct for a thermodependent non-Newtonian fluid

The present work focuses on the study of mixed convection of a purely viscous shear-thinning fluid in a horizontal annular eccentric duct. The inner and outer cylinders are heated with constant and uniform heat flux densities. The objective of this work is to study the effect of the variation of eccentricity, rheological behavior of the fluid as well as the thermodependency of the rheological parameters on the reorganization of the flow and thermal stratification caused by the buoyancy forces. At the entrance of the heating zone, the dynamic regime is assumed to be established and the temperature profile uniform. The conservation equations are solved numerically using a finite difference method with implicit schemes. A secondary azimuthal flow, induced by natural convection, develops downstream of the inlet section. This flow creates a stratification of the thermal field on a given section of the duct, which intensifies downstream from the entrance. On the other hand, the decrease in consistency with increasing temperature near the heated walls produces a centrifugal radial flow towards the walls. The presence of an eccentricity induces in turn a significant effect on the main dynamic field and the stratification of the thermal field. Two cases of upward and downward eccentricity are treated. These show that an upward shift increases the stratification of the thermal field, while the stratification begins to weaken from a certain amount of eccentricity in the case of downward shift. This represents an important result in terms of possible industrial applications. We may indeed conclude that an appropriate choice of downward eccentricity can reduce the thermal stratification, observed experimentally in the case of a concentric heated annular duct [1], when this stratification is undesirable. The choice of this eccentricity depends on rheological and thermal properties of the fluid.     

Numerical simulation of mixed convective heat transfer of a molten salt in a square tube with a thermally conductive wall

熔盐因具有传热能力强、工作温度高、使用温度广、系统压力低、经济适用等优点,成为太阳能热发电系统蓄热工质的理想选择。熔盐在实际应用中会因加热过程的非均匀性产生存在于固体表面和流体间的温差,造成流体工质中的密度梯度,因此出现重力导致的浮升力效应,其叠加到主流流动方向上即形成混合对流。管壁导热会对熔盐混合对流传热过程产生一定的影响。本文对熔盐在水平方管内非均匀加热条件下的单面加热的混合对流过程进行了数值模拟研究,在考虑壁厚的情况下研究了方管单面加热熔盐混合对流传热特性,分析了无量纲参数间的变化关系,并将结果与流型判定图和经典关联式进行对比。结果表明,非均匀加热时,浮升力效应会造成随流动距离增加主流核心区域的形状发生改变,且更加靠近加热壁面。Nu数随Re数、Ri数的增大而增大,局部Nu_x数随流动距离的深入先减小后增大。与忽略管壁导热数值模拟结果相比,主流核心区形状更加均匀,局部Nu_x更高且回升位置更加提前,流动特性和传热特性基本保持一致。     

Azimuthal wave number control of oscillatory thermocapillary convection in a liquid bridge

Thermocapillary convection in a half‐zone liquid bridge of high Prandtl number fluid is widely known to exhibit a three‐dimensional oscillatory flow after the onset of oscillation. The oscillatory flow presents ‘standing’ and ‘traveling’ flows depending upon the temperature difference between the top and bottom rods. In the oscillatory state, the flow shows a modal structure with an azimuthal wave number that depends on the aspect ratio of the liquid bridge and the intensity of the thermocapillarity expressed by the Marangoni number. The present study attempted to control the azimuthal wave number by heating the free surface locally with a prescribed frequency and intensity. The flow in the liquid bridge exhibited different modal structures depending on the heating conditions and a relationship between the frequency and the modal structure was obtained. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(7): 460–469, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20086     

Investigation of Mixed Convection in a Ventilated Cavity in the Presence of a Heat Conducting Circular Cylinder

The study is aimed to investigate the mixed convective transport within a ventilated square cavity in presence of a heat conducting circular cylinder. The fluid flow is imposed through an opening at the bottom of the left cavity wall and is taken away by a similar opening at the top of the right cavity wall. The cylinder is placed at the center of the cavity. Two cases are considered depending on the thermal conditions of the cavity walls. In the first case, the left and right vertical walls are kept isothermal with different temperatures and the top and bottom horizontal walls are considered as thermally insulated. For the second case, the top and bottom walls are maintained at different constant temperatures and the left and right walls are considered adiabatic. Heat transfer due to forced flow, thermal buoyancy, and conduction within the cylinder are taken into account. Effect of the cylinder size (0.1 ≤ D ≤ 0.5) and the solid–fluid thermal conductivity ratio (0.1 ≤ K ≤ 10) are explored for various values of Richardson number (0 ≤ Ri ≤ 5) at fixed Reynolds (Re = 100) and Prandtl (Pr = 0.71) numbers. The fluid dynamic and thermal transport phenomena are depicted through streamline and isotherm plots. Additionally, the global thermal parameters such as the average Nusselt number and average fluid temperature of the cavity are presented. It is found that the aforementioned parameters have significant influences on the fluid flow and heat transfer characteristics in the cavity.     

Heat transfer in a rectangular chamber with differentially heated horizontal walls: Effects of a vibrating sidewall

Heat transfer in a gas-filled closed enclosure with differentially heated horizontal walls is investigated numerically. One of the sidewalls vibrates with specified frequency and amplitude to induce forced convective flows in the enclosure. The vibrating and the stationary sidewalls are considered to be thermally insulated while the two horizontal walls are differentially heated. To simulate the flow field, the full compressible form of the Navier–Stokes equations is considered and solved by a highly accurate flux-corrected transport algorithm. In the numerical model, temperature dependant heat conductivity and viscosity are taken into account. The presence of acoustic streaming is found to have significant effect on the heat transfer. Also the presence of temperature gradients in the enclosure is found to affect the formation of acoustically induced streaming flows.     

Simulating magnetohydrodynamic natural convection flow in a horizontal cylindrical annulus using the lattice Boltzmann method

A numerical study is presented about the effect of a uniform magnetic field on free convection in a horizontal cylindrical annulus using the lattice Boltzmann method. The inner and outer cylinders are maintained at uniform temperatures and it is assumed the walls are insulating with a magnetic field. Detailed numerical results of heat transfer rate, temperature, and velocity fields have been presented for Pr=0.7, Ra=10³ to 5 × 10⁴, and Ha=0 to 100. The computational results show that in a horizontal cylindrical annulus the flow and heat transfer are suppressed more effectively by a radial magnetic field. It is also found that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. The average Nusselt number increases by increasing the radius ratio while it decreases by increasing the Hartmann number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21008     

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     

Experimental verification of the field synergy principle

In this paper, the basic idea of the field synergy principle (FSP) is briefly reviewed and is validated experimentally by incompressible flow through a square duct with an imposed temperature difference between vertical walls and perfectly insulated on the horizontal walls. This creates a situation where the steamwise flow velocity is normal to the cross section temperature gradient. The experimental results show the independency of crosswise heat transfer rate on the steamwise flow velocity. Detailed discussion is provided to account for some minor deviation from the expected results of FSP.     

Heat transfer inside a horizontal channel with an open trapezoidal enclosure subjected to a heat source of different lengths

The heat transfer phenomena inside a horizontal channel with an open trapezoidal enclosure subjected to a heat source of different lengths was investigated numerically in the present work. The heat source is considered as a local heating element of varying length, which is embedded at the bottom wall of the enclosure and maintained at a constant temperature. The air flow enters the channel horizontally at a constant cold temperature and a fixed velocity. The other walls of the enclosure and the channel are kept thermally insulated. The flow is assumed laminar, incompressible, and two‐dimensional, whereas the fluid is considered Newtonian. The results are presented in the form of the contours of velocity, isotherms, and Nusselt numbers profiles for various values of the dimensionless heat source lengths (0.16 ≤ ε ≤ 1). while, both Prandtl and Reynolds numbers are kept constant at (Pr = 0.71) and (Re = 100), respectively. The results indicated that the distribution of the isotherms depends significantly on the length of the heat source. Also, it was noted that both the local and the average Nusselt numbers increase as the local heat source length increases. Moreover, the maximum temperature is located near the heat source location.     

Flow and heat transfer of natural convection around an upward‐facing horizontal plate with a vertical plate at the edge

Natural convective flows around an upward‐facing horizontal heated plate with a vertical plate at the edge were investigated experimentally. Of particular concern were the influences of the vertical plate on the fluid flow and the heat transfer of the horizontal plate. The flow and temperature fields adjacent to the horizontal plate were visualized with dye and a liquid‐crystal thermometry. The results show that the vertical plate obstructs the flow from the top of the vertical plate, while the flow from the open edge of the horizontal plate covers the whole horizontal surface when the height of the vertical plate exceed H/W = 0.14 for adiabatic vertical plate and H/W = 0.1 for the heated vertical plate. The local heat‐transfer‐coefficients of the horizontal plate were also measured. It was found that the vertical adiabatic plates deteriorate the heat transfer, while the heated vertical plates enhance the heat transfer from the horizontal plates. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(8): 527–539, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20033     

Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

Thermo‐solutal convection in an inclined porous cavity with various aspect ratios under mixed thermal and species boundary conditions

The problem of laminar thermo‐solutal convective flow of a binary fluid mixture in an inclined rectangular cavity filled with a uniform porous medium is considered. Mixed heat and mass fluxes and uniform temperature and concentration conditions are applied on two opposing walls of the cavity while the other two walls are kept adiabatic and impermeable to mass transfer. The problem is put in terms of the stream function‐vorticity formulation. A numerical solution based on the finite‐difference methodology is obtained. Representative results illustrating the effects of the inclination angle of the cavity, buoyancy ratio, Darcy number, and the cavity aspect ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature, and concentration at mid‐section of the cavity are reported. In addition, numerical results for the average Nusselt and Sherwood numbers as well as some useful correlations are presented for various parametric conditions and discussed. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20369     

The creeping flow of a polymeric fluid through bent square ducts with heat dissipation

The 3D non-isothermal creeping flow of nylon-6 in a bent square duct with uniform temperature is studied numerically. The non-Newtonian characteristics of this fluid polymer are represented by a differential-type non-isothermal White-Metzner model. Computational results are obtained by the elastic-viscous split-stress (EVSS) finite element method, incorporating the streamline-upwind Petrov-Galerkin (SUPG) scheme. The generated thermal field is entirely due to viscous heating. Essential flow characteristics, including temperature distribution in the flow field, are predicted. The resulting average Nusselt numbers along the walls are obtained. Subsequently, the effects of flow-rate and geometry are investigated.