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1.
A perturbation approach is used to obtain analytical expressions for the velocity, temperature distribution, and transient
Nusselt number for the problem of forced convection, in a parallel-plates channel or a circular tube occupied by a saturated
porous medium modeled by the Brinkman equation, produced by an applied pressure gradient that fluctuates with small amplitude
harmonically in time about a non-zero mean. It is shown that the fluctuating part of this Nusselt number alters in magnitude
and phase as the dimensionless frequency increases. The magnitude increases from zero, goes through a peak, and then decreases
to zero. The height of the peak decreases as the modified Prandtl number increases. The phase (relative to that of the steady
component) decreases from π/2 to − π/2. The height of the peak at first increases, goes through a maximum, and then decreases
as the Darcy number decreases. 相似文献
2.
K. A. Yih 《Heat and Mass Transfer》2001,37(1):53-57
The radiation effect on the mixed convection flow of an optically dense viscous fluid adjacent to an isothermal cone embedded
in a saturated porous medium with Rosseland diffusion approximation is numerically investigated. The entire regime of the
mixed convection is included, as the mixed convection parameter of χ varies from 0 (pure free convection) to 1 (pure forced
convection). The transformed nonlinear system of equations is solved by using an implicit finite difference method. Numerical
results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed
convection parameter χ, the cone angle parameter m, the radiation-conduction parameter R
d
and the surface temperature parameter H. The local Nusselt number decreases initially, reaches a minimum in the intermediate value of χ and then increases gradually.
It is apparent that increasing the cone angle parameter m enhances the local Nusselt number. The local Nusselt number is significantly increased for the large values of the radiation-conduction
parameter R
d
and the surface temperature parameter H, i.e., radiation effect becomes pronounced.
Received on 25 October 1999 相似文献
3.
A detailed numerical study of laminar forced convection in a porous channel which contains a fibrous medium saturated with
a power-law fluid was performed. Hydrodynamic and heat transfer results are presented for a configuration that has uniform
heat flux or uniform temperature heating at the walls. The flow in the porous medium was modeled using the modified Brinkman-Forchheimer-extended
Darcy model for power law fluids in which the non-Darcy effects of inertia and boundary were considered. Parametric studies
were conducted to examine the effects of Darcy number, power law index, inertia parameter and Prandtl number. The results
indicate that when the power law index is decreased, the velocity gradient near the walls increases but these effects are
reduced gradually as the Darcy number decreases until the Darcy regime (Da≤10−6) is reached in which case the effects of power law index become negligible. As the power law index is decreased, the thermal
boundary layer thickness decreases significantly only in the non-Darcy regime. Consequently, as the power law index decreases,
the fully developed Nusselt number increases considerably in the non-Darcy regime whereas in the Darcy regime the change in
Nusselt number is very small. As the Prandtl number increases, the local Nusselt number increases and this effect is more
significant for shear thinning fluids (n<1.0).
Received on 2 March 1998 相似文献
4.
Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local
Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically
fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations
is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on
velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn),
Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio
(K
R) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (C
f
Re
*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer
number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or
K
R increases; (2) increases as the Peclet number, Darcy number, or Biot number increases. 相似文献
5.
Natural convection in a fluid saturated porous medium has been numerically investigated using a generalized non-Darcy approach.
The governing equations are solved by using Finite Volume approach. First order upwind scheme is employed for convective formulation
and SIMPLE algorithm for pressure velocity coupling. Numerical results are presented to study the influence of parameters
such as Rayleigh number (106 ≤Ra ≤108), Darcy number (10−5 ≤ Da ≤ 10−2), porosity (0.4 ≤ ɛ ≤ 0.9) and Prandtl number (0.01 ≤ Pr ≤ 10) on the flow behavior and heat transfer. By combining the method of matched asymptotic expansions with computational
fluid dynamics (CFD), so called asymptotic computational fluid dynamics (ACFD) technique has been employed to generate correlation
for average Nusselt number. The technique is found to be an attractive option for generating correlation and also in the analysis
of natural convection in porous medium over a fairly wide range of parameters with fewer simulations for numerical solutions. 相似文献
6.
K. A. Yih 《Heat and Mass Transfer》1998,34(1):55-61
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 相似文献
7.
A linear stability analysis determining the critical Rayleigh number R
c for onset of convection in a bounded vertical cylinder containing a fluid-saturated porous medium is performed for insulated sidewalls, isothermal top surface, and bottom surface heated by forced convection. This Newtonian heating of the bottom surface involves a Biot number Bi that allows consideration of the continuum of boundary conditions ranging from constant heat flux, with global minimum R
min=27.096 found as Bi→0, to isothermal, with global minimum R
min=4π2 found as Bi→ ∞. In both cases and for most cylinder aspect ratios, incipient convection sets in as an asymmetric mode, though islands of aspect ratio exist where the onset mode is symmetric. Sample three-dimensional renderings of disturbance temperature distributions showing preferred modes at onset of convection for fixed Bi are provided and an analytical fit to R
min as a function of Bi is given. 相似文献
8.
Steady-state conjugate natural convection in a square cavity filled with a porous medium is studied numerically in this paper.
The enclosure consists of two horizontal conductive walls of finite thickness and two vertical walls at different uniform
temperatures. The focus is on the role of solid-fluid conductivity ratio, k, on the flow and heat transfer characteristics and the average Nusselt number, , over the vertical hot and cold walls of the cavity for a limited set of particular parameters. It was shown that the interface
temperature, θw, along the top of the solid wall decreases with the increase in the wall conductivity k. Also, the values of decreases with the increase of the values of the parameter k. Comparison with known results from the open literature when the wall thickness of the horizontal solid walls is neglected
(non-conjugate problem) is excellent.
Received on 4 April 2000 相似文献
9.
Natural convection in a partially filled porous square cavity is numerically investigated using SIMPLEC method. The Brinkman-Forchheimer
extended model was used to govern the flow in the porous medium region. At the porous-fluid interface, the flow boundary condition
imposed is a shear stress jump, which includes both the viscous and inertial effects, together with a continuity of normal
stress. The thermal boundary condition is continuity of temperature and heat flux. The results are presented with flow configurations
and isotherms, local and average Nusselt number along the cold wall for different Darcy numbers from 10−1 to 10−6, porosity values from 0.2 to 0.8, Rayleigh numbers from 103 to 107, and the ratio of porous layer thickness to cavity height from 0 to 0.50. The flow pattern inside the cavity is affected
with these parameters and hence the local and global heat transfer. A modified Darcy–Rayleigh number is proposed for the heat
convection intensity in porous/fluid filled domains. When its value is less than unit, global heat transfer keeps unchanged.
The interfacial stress jump coefficients β
1 and β
2 were varied from −1 to +1, and their effects on the local and average Nusselt numbers, velocity and temperature profiles
in the mid-width of the cavity are investigated. 相似文献
10.
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. 相似文献
11.
This article reports a numerical study of double-diffusive convection in a fluid-saturated vertical porous annulus subjected
to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and
concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum
equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference
technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average
Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound
influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion
of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is
placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the
average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio (λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly. 相似文献
12.
A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered
with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous
medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate
averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects
of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered.
The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly
and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds
number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with
the increase of Reynolds number. 相似文献
13.
Control of Flow and Heat Transfer in a Porous Enclosure due to an Adiabatic Thin fin on the Hot Wall
Natural convection flow in a differentially heated square enclosure filled with porous matrix with a solid adiabatic thin
fin attached at the hot left wall is studied numerically. The Brinkman–Forchheimer-extended Darcy model is used to solve the
momentum equations, in the porous medium. The numerical investigation is done through streamlines, isotherms, and heat transfer
rates. A parametric study is carried out using the following parameters: Darcy number (Da) from 10−4 to 10−2, dimensionless thin fin lengths (L
p) 0.3, 0.5, and 0.7, dimensionless positions (S
p) 0.25, 0.5, and 0.75 with Prandtl numbers (Pr) 0.7 and 100 for Ra = 106. For Da = 10−3 and Pr = 0.7, it is observed that there is a counter clock-wise secondary flow formation around the tip of the fin for S
p = 0.5 for all lengths of L
p. Moreover when Da = 10−2 the secondary circulation behavior has been observed for S
p = 0.25 and 0.75 and there is another circulation between the top wall and the fin that is separated from the primary circulation.
However, these secondary circulations features are not observed for Pr = 100. It is also found that the average Nusselt number decreases as the length of the fin increases for all locations. However,
the rate of decrease of average Nusselt number becomes slower as the location of fin moves from the bottom wall to the top
wall. The overall heat transfer rate can be controlled with a suitable selection of the fin location and length. 相似文献
14.
The present investigation deals with the numerical analysis of steady-state laminar buoyancy-driven convection in an inclined
triangular enclosure filled with fluid saturated porous media using the Darcy law equation. One wall of the enclosure is isothermally
heated and the other is cooled, while the remaining wall is adiabatic. The effect of inclination angle on natural convection
is investigated by varying the angle of inclination (φ) between 0° and 360°. The governing transformed equations are solved numerically using a finite-difference method. Obtained
results are shown in the form of streamlines, isotherms, mean Nusselt numbers and dimensionless stream function for different
values of the Rayleigh number Ra in the range 100 ≤ Ra ≤ 1,000. It is found that the values of the maximum and minimum mean Nusselt number are reached for φ = 330° and φ = 210° , respectively. However, the lowest flow strength is formed at φ = 240° for all values of Ra. 相似文献
15.
Steady mixed convection boundary layer flow from an isothermal horizontal circular cylinder embedded in a porous medium filled
with a nanofluid has been studied for both cases of a heated and cooled cylinder. The resulting system of nonlinear partial
differential equations is solved numerically using an implicit finite-difference scheme. The solutions for the flow and heat
transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle
volume fraction φ and the mixed convection parameter λ. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that for each particular nanoparticle, as the nanoparticle volume fraction φ increases, the magnitude of the skin friction coefficient decreases, and this leads to an increase in the value of the mixed
convection parameter λ which first produces no separation. On the other hand, it is also found that of all the three types
of nanoparticles considered, for any fixed values of φ and λ, the nanoparticle Cu gives the largest values of the skin friction coefficient followed by TiO2 and Al2O3. Finally, it is worth mentioning that heating the cylinder (λ > 0) delays separation of the boundary layer and if the cylinder
is hot enough (large values of λ > 0), then it is suppressed completely. On the other hand, cooling the cylinder (λ < 0) brings
the boundary layer separation point nearer to the lower stagnation point and for a sufficiently cold cylinder (large values
of λ < 0) there will not be a boundary layer on the cylinder. 相似文献
16.
The present paper focuses on the analysis of unsteady flow and heat transfer regarding an axisymmetric impinging synthetic
jet on a constant heat flux disc. Synthetic jet is a zero net mass flux jet that provides an unsteady flow without any external
source of fluid. Present results are validated against the available experimental data showing that the SST/k − ω turbulence model is more accurate and reliable than the standard and low-Re k − ε models for predicting heat transfer from an impinging synthetic jet. It is found that the time-averaged Nusselt number
enhances as the nozzle-to-plate distance is increased. As the oscillation frequency in the range of 16–400 Hz is increased,
the heat transfer is enhanced. It is shown that the instantaneous Nu distribution along the wall is influenced mainly by the interaction of produced vortex ring and wall boundary layer. Also,
the fluctuation level of Nu decreases as the frequency is raised. 相似文献
17.
Mixed convection flow in a two-sided lid-driven cavity filled with heat-generating porous medium is numerically investigated.
The top and bottom walls are moving in opposite directions at different temperatures, while the side vertical walls are considered
adiabatic. The governing equations are solved using the finite-volume method with the SIMPLE algorithm. The numerical procedure
adopted in this study yields a consistent performance over a wide range of parameters that were 10−4 ≤ Da ≤ 10−1 and 0 ≤ Ra
I
≤ 104. The effects of the parameters involved on the heat transfer characteristics are studied in detail. It is found that the
variation of the average Nusselt number is non-linear for increasing values of the Darcy number with uniform or non-uniform
heating condition. 相似文献
18.
A numerical investigation of the steady-state, laminar, axi-symmetric, mixed convection heat transfer in the annulus between
two concentric vertical cylinders using porous inserts is carried out. The inner cylinder is subjected to constant heat flux
and the outer cylinder is insulated. A finite volume code is used to numerically solve the sets of governing equations. The
Darcy–Brinkman–Forchheimer model along with Boussinesq approximation is used to solve the flow in the porous region. The Navier–Stokes
equation is used to describe the flow in the clear flow region. The dependence of the average Nusselt number on several flow
and geometric parameters is investigated. These include: convective parameter, λ, Darcy number, Da, thermal conductivity ratio,
K
r, and porous-insert thickness to gap ratio (H/D). It is found that, in general, the heat transfer enhances by the presence of porous layers of high thermal conductivity
ratios. It is also found that there is a critical thermal conductivity ratio on which if the values of Kr are higher than
the critical value the average Nusselt number starts to decrease. Also, it found that at low thermal conductivity ratio (K
r ≈ 1) and for all values of λ the porous material acts as thermal insulation. 相似文献
19.
In this study, a steady, fully developed laminar forced convection heat augmentation via porous fins in isothermal parallel-plate
duct is numerically investigated. High-thermal conductivity porous fins are attached to the inner walls of two parallel-plate
channels to enhance the heat transfer characteristics of the flow under consideration. The Darcy–Brinkman–Forchheimer model
is used to model the flow inside the porous fins. This study reports the effect of several operating parameters on the flow
hydrodynamics and thermal characteristics. This study demonstrates, mainly, the effects of porous fin thickness, Darcy number,
thermal conductivity ratio, Reynolds number, and microscopic inertial coefficient on the thermal performance of the present
flow. It is found that the highest Nusselt number is achieved at fully filled porous duct which requires the highest pumping
pressure. The results show that using porous fins requires less pumping pressure with comparable high heat augmentation weight
against fully filled porous duct. It is found that higher Nusselt numbers are achieved by increasing the microscopic inertial
coefficient (A), the Reynolds number (Re), and the thermal conductivity of the porous substrate k
2. The results show that heat transfer can be enhanced (1) with the use of high thermal conductivity fins, (2) by decreasing
the Darcy number, and (3) by increasing microscopic inertial coefficient. 相似文献
20.
Adrian Postelnicu 《Heat and Mass Transfer》2007,43(6):595-602
The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium
subjected to a chemical reaction is numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion
(Soret) effects. The transformed governing equations are solved by a very efficient numerical method, namely, a modified version
of the Keller-box method for ordinary differential equations. The parameters of the problem are Lewis, Dufour and Soret numbers,
sustentation parameter, the order of the chemical reaction n and the chemical reaction parameter γ. Local Nusselt number and local Sherwood number variations and dimensionless concentration
profiles in the boundary layer are presented graphically and in tables for various values of problem parameters and it is
concluded that γ and n play a crucial role in the solution. 相似文献