Dynamical responses of non-isothermal flow between two independently rotating disks with time-dependent wall conditions

The present work develops a theoretical model of rotational convection and uses it to investigate the dynamical responses of the flow and heat transfer between two disks rotating at different rates under the influences of time-dependent disturbances. The unsteady non-isothermal flow model is formulated by extending a recently developed steady-state similarity model of axi-symmetric rotational convection. In the new model all the rotation-induced buoyancy forces are considered. Using one disk as reference, effects of the time-dependent changes in wall temperature or rotating rate of the other disk on the flow and heat transfer are explored. Various rotational modes with asymptotic or fluctuating change in boundary condition of temperature or disk rotation are studied. The present time-dependent model for this non-isothermal rotating flow is numerically solved by a finite-difference method. By using the present results, the complicated flow and heat transfer mechanisms with thermal-flow coupling in the class of time-dependent rotational convection are manifested.     

Local nonsimilarity solution for the impact of the buoyancy force on heat and mass transfer in a flow over a porous wedge with a heat source in the presence of suction/injection

Combined heat and mass transfer in free, forced and mixed convection flows along a porous wedge with internal heat generation in the presence of uniform suction or injection is investigated. The boundary-layer analysis is formulated in terms of the combined thermal and solute buoyancy effect. The flow field characteristics are analyzed using the Runge-Kutta-Gill method, the shooting method, and the local nonsimilarity method. Due to the effect of the buoyancy force, power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally nonsimilar. Numerical calculations up to third-order level of truncation are carried out for different values of dimensionless parameters as a special case. The effects of the buoyancy force, suction, heat generation, and variable wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are studied. The results obtained are found to be in good agreement with previously published works.     

Influence of lateral mass flux on mixed convection heat and mass transfer over inclined surfaces in porous media

 The effect of lateral mass flux on mixed convection heat and mass transfer in a saturated porous medium adjacent to an inclined permeable surface is analyzed. A similarity solution is obtained when surface temperature and concentration, free stream velocity and injection/suction velocity of fluid are prescribed as power functions of distance from the leading edge. The cases when the flow and buoyancy forces are in the same and opposite directions are discussed both for aiding and opposing buoyancy effects. The governing parameters are the mixed convection parameter Gr, the Lewis number Le, the buoyancy ratio N, the lateral mass flux parameter f _w, representing the effects of injection or withdrawal of fluid at the wall, and λ which specifies three cases of the inclined plate. The interactive effect of these parameters on heat and mass transfer rates are presented. It is observed that the diffusion ratio (Le) has a more pronounced effect on concentration field than on flow and temperature fields. It is found that the rates of heat and mass transfer increase with suction and decrease with injection of the fluid. Received on 31 August 2000 / Published online: 29 November 2001     

浮力对混合对流流动及换热特性的影响

用热线和冷线相结合的技术测量垂直圆管内逆混合对流流体的平均速度、 温度以及它们的脉动. 较详细地研究了浮力对逆混合对流的流动特性和传热特性的影响. 评 估了实验中采用的冷线测量温度补偿速度探头温度敏感的影响. 逆混合对流的传热结果用无 量纲参数Ω (Ω= Grd / Red2 )来表示，其中，基于管道直 径的雷诺数Red变化范围为900~18000, 浮力参数Ω变化范围为 0.004899~0.5047. 研究结果表明，浮力对逆混合对流的换热有强化作用. 随着葛拉晓夫数Grd的增加，温度脉动，流向雷诺正应力和流向温度通量增 大，并且在靠近壁面的流体区域尤其明显. 热线与冷线相结合的技术适合于研究非绝热的流 动测量，可以用于研究浮力对流动和换热特性的影响.     

Non-darcy double-diffusive mixed convection from heated vertical and horizontal plates in saturated porous media

The non-darcy mixed convection flows from heated vertical and horizontal plates in saturated porous media have been considered using boundary layer approximations. The flows are considered to be driven by multiple buoyancy forces. The similarity solutions for both vertical and horizontal plates have been obtained. The governing equations have been solved numerically using a shooting method. The heat transfer, mass transfer and skin friction are reduced due to inertial forces. Also, they increase with the buoyancy parameter for aiding flow and decrease for the opposing flow. For aiding flow, the heat and mass transfer coefficients are found to approach asymptotically the forced or free convection values as the buoyancy parameter approaches zero or infinity.     

Boundary layer flow and heat transfer over an unsteady stretching vertical surface

The solution to the unsteady mixed convection boundary layer flow and heat transfer problem due to a stretching vertical surface is presented in this paper. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching velocity and the surface temperature. The governing partial differential equations with three independent variables are first transformed into ordinary differential equations, before they are solved numerically by a finite-difference scheme. The effects of the unsteadiness parameter, buoyancy parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Both assisting and opposing buoyant flows are considered. It is observed that for assisting flow, the solutions exist for all values of buoyancy parameter, whereas for opposing flow, they exist only if the magnitude of the buoyancy parameter is small. Comparison with known results for steady-state flow is excellent.     

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.     

Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium

Unsteady laminar mixed convection flow (combined free and forced convection flow) along a vertical slender cylinder embedded in a porous medium under the combined buoyancy effect of thermal and species diffusion has been studied. The effect of the permeability of the medium as well as the magnetic field has been included in the analysis. The partial differential equations with three independent variables governing the flow have been solved numerically using a implicit finite difference scheme in combination with the quasilinearization technique. Computations have been carried out for accelerating, decelerating and oscillatory free stream velocity distributions. The effects of the permeability of the medium, buoyancy forces, transverse curvature and magnetic field on skin friction, heat transfer and mass transfer have been studied. It is found that the effect of free stream velocity distribution is more pronounced on the skin friction than on the heat and mass transfer. The permeability and magnetic parameters increase the skin friction, but reduce the heat and mass transfer. The skin friction, heat transfer and mass transfer are enhanced due to the buoyancy forces and curvature parameter. The heat transfer is strongly dependent on the viscous dissipation parameter and the Prandtl number, and the mass transfer on the Schmidt number.     

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd.     

Combined heat and mass transfer in natural convection between vertical parallel plates

This study purposes to examine the effects of latent heat transfer associated with the liquid films vaporization on the heat transfer in the natural convection flows driven by the simultaneous presence of combined buoyancy forces of thermal and mass diffusion. Results are especially presented for an air-water system under various conditions. The influence of channel length and system temperatures on the momentum, heat and mass transfer in the flow are investigated in great detail. The important role of transport of latent heat of vaporization under the situations of buoyancy-aiding and opposing flows is clearly demonstrated.     

The effects of transpiration on the boundary layer flow and heat transfer over a vertical slender cylinder

This paper deals with a theoretical (numerical) analysis of the effects that blowing/injection and suction have on the steady mixed convection or combined forced and free convection boundary layer flows over a vertical slender cylinder with a mainstream velocity and a wall surface temperature proportional to the axial distance along the surface of the cylinder. Both cases of buoyancy forces aid and oppose the development of the boundary layer are considered. Similarity equations are derived and their solutions are dependent upon the mixed convection parameter, the non-dimensional transpiration parameter and the curvature parameter, as well as of the Prandtl number. Dual solutions for the previously studied mixed convection boundary layer flows over an impermeable surface of the cylinder are shown to exist also in the present problem for aiding and opposing flow situations.     

Numerical study on mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows

Fluid flow and heat transfer of mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows have been simulated based on the projection method with two dimensional exponential stretched staggered cylindrical meshes. Cycle mean temperature and secondary streaming are obtained by the method of partial sums of the Fourier series. Present numerical results are validated by comparing the heat transfer results of free convection and the secondary streaming of pure oscillating flow over a circular cylinder to published experimental and numerical results. The complete structures of the cycle mean temperature and secondary streaming patterns are provided by numerical simulations over wide ranges of the Reynolds number, the Keulegan–Carpenter number and the Richardson number. Based on turning points of the curves of the overall Nusselt numbers versus Reynolds numbers and the characteristics of the cycle averaged temperature and flow patterns, the heat transfer can be divided into three linear regimes (conduction, laminar convection, and turbulent convection dominated regimes) and two non-linear transition regimes. The effects of wave directions, amplitudes, frequencies, and buoyancy forces on the enhancement of heat transfer are also investigated. The effective ranges of the governing parameters for heat transfer enhancement are identified.     

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

Convective heat transfer from a rotating or nonrotating axisymmetric body

An analysis of steady laminar mixed-convection heat transfer from a rotating or nonrotating axisymmetric body is presented. A mixed-convection parameter is proposed to serve as a controlling parameter that determines the relative importance of the forced and the free convection. In addition, a rotation parameter is introduced to indicate the relative contributions of the flow forced convection and the rotational forced convection. The values of both these two parameters lie between 0 and 1. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection from the forced-convection limit (rotating or nonrotating bodies) to the pure free-convection limit (non-rotating bodies) and the entire regime of forced convection from the pure flow forced-convection limit (nonrotating bodies) to pure rotational forced-convection limit (rotating bodies). The effects of mixed-convection intensity, body rotation, fluid suction or injection, and fluid Prandtl number on the velocity profiles, the temperature profiles, the skin-friction parameter, and heat transfer parameter are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.     

Buoyancy effects on mixed convection heat and mass transfer in a duct with sudden expansions

The present paper deals with the study of heat and mass transfer by mixed convection in an inclined duct preceded with a double step expansion. The control volume based finite element method was used to solve the set of non-dimensional equations for the vorticity, stream function, energy and species conservation. Numerical simulations are carried out for different combinations of the Lewis number, thermal and mass diffusion Grashof numbers for different inclinations. Streamlines, temperature and concentration distributions are presented and discussed. The results show the effect of the secondary flow induced by buoyancy forces and the presence of the double step expansion on the heat and mass transfer mechanism. It is found that the recirculation vortices induced by the expansion can be present along the channel and the flow structure can be wavy. For the vertical orientation, asymmetric fields are observed for the different simulated cases.     

3D Numerical study of the effect of aspect ratio on mixed convection air flow in upward solar air heater

A 3D Numerical study of mixed convection air flow in upward solar air heater with large spanwise aspect ratio (A = 10 to 40) was performed using CFD commercial code Fluent 14.5 (ANSYS). The main objective of this study is to investigate the channel height's effect (aspect ratio) on flow pattern and heat transfer in upward solar air heater in the particular case of low Re and high aspect ratio. The bottom plate (absorber) was submitted to Constant Heat Flux (CHF) in the range of 200 to 1000 W/m² and Reynolds number was varied from 50 to 1000. Our results are in concordance with most of authors conclusions about Poiseuille–Rayleigh–Benard flows. In mixed convection, increasing heat flux enhances heat transfer unlike forced convection flows. Simulation results of flow visualizations and Nusselt number calculations have shown that depending on Ri*, the velocity and temperature distributions in SAH vary greatly with the channel's height. The obtained results were different from previous studies. Indeed, our investigation of channel's height was achieved for the same heat flux but different Grashof numbers. For low channel's heights (high aspect ratio), increasing heat flux has not a significant effect but for higher channel's heights, an augmentation of heat flux enhances buoyancy effects in the flow and causes high turbulence. Also, increasing Reynolds number in low channel's heights (high A), can enhance substantially heat transfer. For higher channel's heights (low A), increasing Reynolds number decreases Ri* and thus buoyancy forces. Heat transfer is reduced and so Nusselt number. The obtained results may be very useful for engineers in designing and testing solar collectors.     

A numerical study based on a weakly compressible formulation for thermosolutal convection in vertical cavities

Laminar thermosolutal convection in cavities with uniform, constant temperature and mass fraction profiles at the vertical side is studied numerically. The study is conducted in the case where an inert carrier gas (species “1”) present in the cavity is not soluble in species “2”, and do not diffuse into the walls. A mass flux of species “2” into the cavity occurs at the hot vertical wall and a mass flux out of the cavity occurs at the opposite cold wall. The weakly compressible model proposed in this work was used to investigate the flow fields, and heat and mass transfer in cavities filled with binary mixtures of ideal gases. The dimensionless form of the seven governing equations for constant thermophysical properties, except density, show that the problem formulation involves ten dimensionless parameters. The results were validated against numerical results published in the literature for purely thermal convection, and thermodynamic predictions for transient thermosolutal flows. A parametric study has been performed to investigate the effects of the initial conditions, molecular weight ratio, Lewis number, and aspect ratio of the cavity for aiding or opposing buoyancy forces. For the range of parameters considered, the results show that variations in the density field have larger effects on mass transfer than on heat transfer. For opposing buoyancy forces, the numerical simulations predict complex flow structures and possible chaotic behavior for rectangular vertical cavities according to the value of the molecular weight ratio.     

Combined radiation and natural convection effects on graetz problem in horizontal isothermal circular tubes

A numerical analysis is performed on the combined thermal radiation and mixed convection for a gray fluid flow in a horizontal isothermally-heated circular tube. The governing equations of vorticity-velocity form are employed and solved by DuFort-Frankel method. The contribution of radiation is formulated by integral expression and solved by finite element nodal approximation. The effects of radiation and convection on local Nusselt number and the developing of bulk temperature are presented. The result shows that the heat transfer can be significantly enhanced by the effects of radiation and secondary flow induced by buoyancy. Besides, the fluctuation in local Nusselt number curve which is caused by the existence of secondary flow is reduced by the effect of thermal radiation.     

Turbulence Budgets in Buoyancy-affected Vertical Backward-facing Step Flow at Low Prandtl Number

The paper investigates buoyancy impact on the vertical flow over a backward-facing step at low Prandtl number by Direct Numerical Simulation. In particular, the very low Prandtl number of liquid sodium, 0.0088, is considered in the regime of mixed convection, i.e. for Richardson numbers below unity. The effects of buoyancy on mean flow, heat transfer and turbulence are assessed. Buoyancy is found to attenuate recirculation and, consequently, increase heat transfer. Turbulence is decreased in the attached boundary layer for moderate buoyancy impact but surpasses the levels found in forced convection at the largest Richardson number investigated. Beyond the mean flow and second moments, the budgets of turbulent kinetic energy, Reynolds shear stress, temperature variance, and turbulent heat flux components are studied and related to the alterations in the mean field quantities. Due to scale separation, production and dissipation nearly balance for temperature variance while this is not the case for turbulent kinetic energy. Similar findings for the turbulent heat fluxes show that the correlation between temperature and pressure gradient is the most important contribution to the budget aside from production and dissipation. In addition to the physical insight into this flow, the data presented may be used for the validation and improvement of turbulence models for liquid metal flows.