Computation of buoyancy-driven flow in an eccentric centrifugal annulus with a non-orthogonal collocated finite volume algorithm

A computational study is performed on two-dimensional mixed convection in an annulus between a horizontal outer cylinder and a heated, rotating, eccentric inner cylinder. The computation has been done using a non-orthogonal grid and a fully collocated finite volume procedure. Solutions are iterated to convergence through a pressure correction scheme and the convection is treated by Van Leer's MUSCL scheme. The numerical procedure adopted here can easily eliminate the ‘Numerical leakage’ phenomenon of the mixed convection problem whereby strong buoyancy and centrifugal effects are encountered in the case of a highly eccentric annulus. Numerical results have been obtained for Rayleigh number Ra ranging from 7×10³ to 10⁷, Reynolds number Re from 0 to 1200 and Prandtl number Pr from 0.01 to 7. The mixed rotation parameter σ (=Ra/PrRe²) varies from ∞ (pure natural convection) to 0.01 with various eccentricities ε. The computational results are in good agreement with previous works which show that the mixed convection heat transfer characteristics in the annulus are significantly affected by σ and ε. The results indicate that the mean Nusselt number Nu increases with increasing Ra or Pr but decreases with increasing Re. In the case of a highly eccentric annulus the conduction effect becomes predominant in the throat gap. Hence the crucial phenomenon on whereby Nu first decreases and then increases can be found with increasing eccentricity. © 1998 John Wiley & Sons, Ltd.     

The Effects of Blowing and Suction on Double Diffusion by Mixed Convection over Inclined Permeable Surfaces

A boundary layer analysis is used to investigate the effect of lateral mass flux on mixed convection heat and mass transfer over inclined permeable surfaces in porous media. The conservation equations that govern the problem are reduced to a system of non-linear ordinary differential equations and then the resulting equations is solved by numerical method. The numerical results for heat and mass transfer in terms of Nusselt and Sherwood number are presented in x-y plots for the buoyancy ratio (N) and Lewis number (Le) with mass flux pammeter (Fw). The obtained results are validated against previously published results with on special case of the problem.     

Mixed Convection of Water at 4°C Along a Wedge with Variable Surface Flux in a Porous Medium

In this study, the mixed convection of water at 4°C along a wedge in a porous medium is investigated numerically using finite difference method. In order to explore the effect of mixed convection, both forced and free convection-dominated regimes are considered. Non-similarity solutions are obtained for the variable wall flux boundary condition. Velocity and temperature profiles as well as local dimensionless skin friction and Nusselt number are obtained and compared with the available numerical results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ are ranged from 0 to 1 in both regimes whereas different values of λ are considered for the purpose of comparison of heat transfer results.     

Experimental study of free convection in an elliptical annular enclosure in blunt and slender orientations

In this paper, free convection heat transfer between two elliptical cylinders having different elliptical ratios in blunt and slender situations was studied experimentally. Three pairs of elliptical cylinders having the same radius ratio of 2.0, the same surface area and different elliptical ratios of 0.662, 0.866 and 0.968 were cut using the computed numerically controlled wire-cut machining. The tests were carried out by keeping a constant heat flux on the inner cylinder while cooling the outer one to be isothermal. The effects of vertical eccentricity, lateral eccentricity, angle of attack of the inner cylinder on natural convection for both blunt and slender situations of each pair were investigated. Empirical correlation was deduced within an acceptable uncertainty for the experimental results. Compatible and satisfactory to the conscience agreement was found in the comparison among the results of present and previous works. In the vision of the comparison, it was found that; the vertical eccentricity can enhance free convection by about 15% than the concentric case, the horizontal eccentricity can enhance natural convection by about 10% than concentric case and slender situation offers about 40% enhancement in free convection than the blunt situation for the same elliptical ratio.     

A mixed convection in a reciprocating $$\Uppi$$ shape channel with opposite direction of gravity and inlet cooling fluids

A numerical study is executed to investigate heat transfer mechanisms of a reciprocating channel cooled by fluids. The problem of the reciprocating piston is a moving boundary problem, and the Finite Element Method and arbitrary Largragian–Eulerian Kinematics method are then utilized. Due to the high temperature of the channel, a mixed convection is taken into consideration for simulating a more realistic situation. Directions of inlet cooling fluids and gravity are opposite. Concerning important parameters of the Reynolds number and Grashof number, reciprocating frequency and amplitude are examined. Thermal stratification layers which are found firmly on the top surface are deeply dependent on the magnitude of Gr/Re ² ratio which directly affects the heat transfer mechanisms.     

Mixed convection boundary layer flow along vertical moving thin needles with variable heat flux

The problem of steady laminar mixed convection boundary layer flow of an incompressible viscous fluid along vertical moving thin needles with variable heat flux for both assisting and opposing flow cases is theoretically considered in this paper. The governing boundary layer equations are first transformed into non-dimensional forms. The curvature effects are incorporated into the analysis whereas the pressure variation in the axial direction has been neglected. These equations are then transformed into similarity equations using the similarity variables, which are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for a blunt-nosed needle (m = 0). Numerical calculations are carried out for various values of the dimensionless parameters of the problem, which include the mixed convection parameter λ, the Prandtl number Pr and the parameter a representing the needle size. It is shown from the numerical results that the skin friction coefficient, the surface (wall) temperature and the velocity and temperature profiles are significantly influenced by these parameters. The results are presented in graphical form and are discussed in detail.     

Mixed convection in non-Newtonian fluids along a vertical plate with variable surface heat flux in a porous medium

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along a vertical plate with power-law surface heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate. Received on 13 October 1998     

Modelling of the free surface with heat and mass transfer considerations on a liquid filling a porous slab heated from its sides

The position of the free surface is calculated numerically for a porous slab which is partly filled with a liquid and differentially heated from its sides. A coordinate transformation is used to transform the original problem from a physical coordinate system to a non‐orthogonal system where the free surface becomes a fixed straightline. The transformed problem is then solved using a finite difference method. Results are obtained for Rayleigh numbers up to 1000. The Nusselt numbers increase slightly with medium Rayleigh numbers (convection‐dominated region) as expected. Since at low Ra the conduction is dominant and at high Ra radiation is dominant. Hadizadeh and Tien (Int. J. Heat Mass Transfer 2004; 17 (6):799–804) studied the forced convection on the surface of porous layer. In that paper they dealt with in detail the boundary regime of liquid in the channel and modelled the flow and heat transfer. Copyright © 2007 John Wiley & Sons, Ltd.     

Mixed convection about a non-isothermal vertical surface in a porous medium

The problem of mixed convection about non-isothermal vertical surfaces in a saturated porous medium is analysed using boundary layer approximations. The analysis is made assuming that the surface temperature varies as an arbitrary function of the distance from the origin. A perturbation technique has been applied to obtain the solutions. Using the differentials of the wall temperature, which are functions of distance along the surface, as perturbation elements, universal functions are derived for various values of the governing parameter Gr/Re. Both aiding and opposing flows are considered. The universal functions obtained can be used to estimate the heat transfer and fluid velocity inside the boundary layer for any type of wall temperature variation. As a demonstration of the method, heat transfer results have been presented for the case of the wall temperature varying as a power function of the distance from the origin. The results have been studied for various combinations of the parameters Gr/Re and the power index m, taking both aiding and opposing flows into consideration. On comparing these results with those obtained by a similarity analysis, the agreement is found to be good.     

Coupled heat and mass transfer in mixed convection over a vertical flat plate embedded in saturated porous media: PST/PSC or PHF/PMF

A boundary layer analysis is used to investigate the heat and mass transfer characteristics of mixed convection about a vertical flat plate embedded in a saturated porous medium under the coupled effects of thermal and mass diffusion. The plate is maintained at prescribed surface temperature/concentration (PST/PSC) or prescribed heat/mass flux (PHF/PMF). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results for the local heat transfer rate and the local mass transfer rate are presented for various parameters. The local heat and mass transfer rates increase with increasing n and m and buoyancy parameter ξ. When buoyancy parameter ξ is very small (large) the value of local Nusselt and the local Sherwood number correspond with the pure forced (free) convection, respectively. Increasing buoyancy ratio N (or N ^*) increases the local heat and mass transfer rates. It is apparent that Lewis number has a pronounced effect on the local mass transfer rate than it does on the local heat transfer rate. Furthermore, increasing Lewis number decreases (increases) the local heat (mass) transfer rate. Received on 8 December 1997     

Nonsimilar Solutions for Mixed Convection in Non-Newtonian Fluids Along Horizontal Surfaces in Porous Media

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along horizontal surfaces with variable heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.     

Mixed convection heat transfer from a horizontal plate with variable surface heat flux in a porous medium

In this article nonsimilarity solution for mixed convection from a horizontal surface in a saturated porous medium was obtained for the case of variable surface heat flux. The entire mixed convection regime, ranging from pure forced convection to pure free convection, is considered by introducing a single nonsimilarity parameter. Heat transfer results are predicted by employing four different flow models, namely, Darcy's law, the Ergun model, and the Brinkman-Forchheimer-extended Darcy model with constant and variable porosity. The variable porosity effect is approximated by an exponential function. Effects of transverse thermal dispersion are taken into consideration in the energy equation, along with variable stagnant thermal conductivities. The formulation of the present problem shows that the flow and heat transfer characteristics depend on five parameters, that is, the power in the variation of surface heat flux, the nonsimilarity mixed-convection parameter, the inertia effect parameter, the boundary effect parameter, and the ratio of thermal conductivity of the fluid phase to that of the solid phase. Numerical results for the local Nusselt number variations, based on the various flow models, are presented for the entire mixed convection regime. The impacts␣of different governing parameters on the heat transfer results are thoroughly investigated. Received on 7 August 1997     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

Analytical Solution for the Effect of Viscous Dissipation on Mixed Convection in Saturated Porous Media

A new analytical solution is introduced for the effect of viscous dissipation on mixed convection flow and heat transfer about an isothermal vertical wall embedded in Darcy and non-Darcy porous media with uniform free stream velocity. The effect of viscous dissipation on mixed convection in both regimes has been analyzed for both the aiding and opposing flows using Gebhart number, Ge _x =gx/c _p. The governing parameters are Re, Ra, Pe and Ge _x . The case of Re=0 corresponds to Darcy mixed convection region and Re/Pe is identified as the mixed convection governing parameter, Ra=0 leading to pure forced convection. A good agreement was found between the numerical and analytical solutions. It was found from the Nusselt number results that viscous dissipation lowers the heat transfer rate in both Darcy and Forchheimer flow regimes for aiding as well as opposing flows.     

Combined Laminar Mixed Convection and Surface Radiation using Asymptotic Computational Fluid Dynamics (ACFD)

This paper reports the use of the technique of combining asymptotics with computational fluid dynamics (CFD), known as asymptotic computational fluid dynamics (ACFD), to handle the problem of combined laminar mixed convection and surface radiation from a two dimensional, differentially heated lid driven cavity. The fluid under consideration is air, which is radiatively transparent, and all the walls are assumed to be gray and diffuse and having the same hemispherical, total emissivity (ɛ). The computations have been performed on FLUENT 6.2. The full radiation problem (i.e. all the walls are radiatively black corresponding to ɛ = 1) is first taken up and the method of “perturbing and blending” is used wherein, first, limiting solutions of natural and forced convection are perturbed, to obtain correlations for the weighted average convective Nusselt numbers for the full radiation case. These correlations are then blended suitably in order to obtain a composite correlation for the weighted average convective Nusselt number that is valid for the entire mixed convection range, i.e., 0 ≤ Ri ≤ ∞. This correlation is then expanded in terms of ɛ to obtain an expression for the average convective Nusselt number that is valid for any ɛ in the range 0 ≤ ɛ ≤ 1. In so far as radiation heat transfer is concerned, using asymptotic arguments, a new weighted average radiation Nusselt number is defined such that this quantity can be expanded just in terms of ɛ. Hence, by the use of ACFD, the number of solutions required to obtain reasonably accurate correlations for both the convective and radiative heat transfer rates and hence the total heat transfer rate (Nu _total = Nu _C + Nu _R), is substantially reduced. More importantly, the correlations for convection and radiation are asymptotically correct at their ends. The effect of secondary variables like aspect ratio and the case of unequal wall emissivities can also be included without significant additional effort.     

Transient responses of magnetostrictive plates by using the GDQ method

We used the generalized differential quadrature (GDQ) method to compute the transient response of thermal stresses and center displacement in laminated magnetostrictive plates under thermal vibration. We obtained the GDQ solutions in a three-layer (0°^m/90°/0) and a 10-layer (0°^m/90°/0°/90°/0)_s laminated magnetostrictive plate with four simply supported edges. We presented the transient responses of thermal stress and center displacement with and without velocity feedback control, respectively. The advantage of the GDQ method used provide us with an efficient method to compute the results including shear deformation effect with a few grid points. These GDQ results had its potential that could be used and considered as basic data in the future magnetostrictive laminate studies.     

MHD mixed convective heat transfer flow about an inclined plate

Mixed convection heat transfer about a semi-infinite inclined plate in the presence of magneto and thermal radiation effects is studied. The fluid is assumed to be incompressible and dense. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the non-similar boundary layer equations, which are then solved numerically using the Keller box method. The effects of the mixed convection parameter R _i, the angle of inclination α, the magnetic parameter M and the radiation–conduction parameter R _d on the velocity and temperature profiles as well as on the local skin friction and local heat transfer parameters. For some specific values of the governing parameters, the results are compared with those available in the literature and a fairly good agreement is obtained.     

Development of mixed convection flow over a vertical plate due to an impulsive motion

The development of the mixed convection flow of an incompressible laminar viscous fluid over a semi-infinite vertical plate has been investigated when the fluid in the external stream is set into motion impulsively, and at the same the surface temperature is suddenly raised from its ambient temperature. The problem is formulated in such a way that at time t = 0, it reduces to Rayleigh type of equation and as time t , it tends to Blasius type of equation. The scale of time has been selected such that the traditional infinite region of integration becomes finite which significantly reduces the computational time. The nonlinear coupled singular parabolic partial differential equations governing the unsteady mixed convection flow have been solved numerically by using an implicit finite-difference scheme. The surface shear stress and the heat transfer increase or decrease with time when the buoyancy parameter is greater or less than a certain valve. There is a smooth transition from the initial steady state to the final steady state. The skin friction and heat transfer for the constant heat flux case are more than those of the constant wall temperature case. Also they increase with the buoyancy force.     

Similarity analysis of axisymmetric free convection on a horizontal infinite plate subject to a mixed thermal boundary condition in a micropolar fluid

Similarity analysis of the problem of axisymmetric free convection on a horizontal infinite plate of a micropolar fluid is considered assuming that the plate is subjected to a mixed thermal boundary condition. It is shown that the thermal boundary condition is characterized by a positive parameter m and the two cases of m = 0 and m = 1 correspond to prescribed plate temperature and prescribed surface heat flux respectively. If one has to compute the heat transfer coefficient for various values of m, there is no need to solve the boundary value problem every time; it is enough to solve a certain polynomial equation provided the solution is known for any particular value of m. Received on 3 November 1998     

Laminar film condensation from downward flowing superheated vapors onto a non-isothermal sphere

 A model is developed for the study of mixed convection film condensation from downward flowing superheated vapors onto a sphere with variable wall temperature. The model combined natural convection dominated and forced convection dominated film condensation, including effects of superheated vapor, pressure gradient and wall temperature variation can be solved numerically by the fourth-order Runge–Kutta technique. By the present numerical approach, the mean heat transfer is evaluated up to the critical angle of the condensate layer, φ_c. In general, the result of mean heat transfer shows that, as A, the wall-temperature amplitude, increases, the value of with inclusion of P, the pressure gradient effect, goes down slightly, however, the value of with the pressure gradient effect ignored will remain almost uniform. Further, for P=2.0, the mean heat transfer coefficient increases significantly, by 8.6–23.9%, depending on A, as the superheat parameter, S p, increases within a practical range. Received on 7 September 2000