Showing papers on "Nusselt number published in 1986"

A numerical study of non-darcian natural convection in a vertical enclosure filled with a porous medium

Abstract: A numerical study of non-Darcian natural convection in a vertical enclosure filled with a porous medium is performed. The flow is modeled using the Brinkman-Forchheimer-extended Darcy equations. The governing equations are solved with the SIMPLER algorithm and good agreement with previously reported numerical and experimental results is found. An order of magnitude analysis and the numerical results demonstrate the importance of non-Darcian effects. For high Darcy numbers (Da > 10−4), both extensions are of the same order of magnitude and must be used simultaneously. In addition, Forch-heimer's extension must be included for Pr ≤ 1.0 and all Darcy numbers. Finally, Nusselt number correlations are presented for three different ranges of the Darcy number covering wide ranges of the governing parameters.

Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement

Abstract: Modulatory heat-transfer enhancement in grooved channels is investigated by direct numerical simulation of the Navier–Stokes and energy equations using the spectral element method. It is shown that oscillatory perturbation of the flow at the frequency of the least-stable mode of the linearized system results in subcritical resonant excitation and associated transport enhancement as the critical Reynolds number of the flow is approached. The Tollmien–Schlichting frequency theory that was presented in Part 1 of this paper is shown to accurately predict the optimal frequency for transport augmentation for small values of the modulatory amplitude, and the effect of the excited travelling-wave channel modes on the resulting temperature distribution is described. The importance of (non-trivial) geometry in the forced response of a flow is discussed, and grooved-channel flow is compared to (straight-channel) plane Poiseuille flow, for which no resonance excitation occurs owing to a zero projection of the forcing inhomogeneity on the dangerous modes of the system. For the particular grooved-channel geometry investigated, resonant oscillatory forcing at modulatory amplitudes as small as 20% of the mean flow results in a doubling of transport as measured by a time, space-averaged Nusselt number.

Route to chaos in porous-medium thermal convection

Abstract: A pseudo-spectral numerical scheme is used to study two-dimensional, single-cell, time-dependent convection in a square cross-section of fluid saturated porous material heated from below. With increasing Rayleigh number R convection evolves from steady S to chaotic NP through the sequence of bifurcations S→P(1)→QP2→P(2)→NP, where P(1) and P(2) are simply periodic regimes and QP2 is a quasi-periodic state with two basic frequencies. The transitions (from onset of convection to chaos) occur at Rayleigh numbers of 4π2, 380–400, 500–520, 560–570, and 850–1000. In the first simply periodic regime the fundamental frequency f1 varies as . The chaotic states are characterized by spectral peaks with at least 3 fundamental frequencies superimposed on a broadband background noise. The time dependence of these states arises from the random generation of tongue-like disturbances within the horizontal thermal boundary layers. Transition to the chaotic regime is accompanied by the growth of spectral components that destroy the centre-symmetry of convection in the other states. Over-truncation can lead to spurious transitions and bifurcation sequences; in general it produces overly complex flows.

Heat Transfer Around Sharp 180-deg Turns in Smooth Rectangular Channels

Abstract: Measured Nusselt numbers are presented for forced convection within and around sharp 180 degree turns in smooth channels of rectangular cross section. Separately determined top wall, bottom wall, and side wall values are presented individually along with azimuthal averages. The geometry of the channels and connecting turn is characterized by parameters W*, the ratio of upstream and downstream channel widths; 0*, the non-dimensional channel depth; and H*, the nondimensional clearance at the tip of the turn. Results from nine combinations of these parameters are presented at several values of channel Reynolds number to illustrate the effect of turn geometry on the heat transfer distributions.

Correlations for laminar mixed convection flows on vertical, inclined, and horizontal flat plates

Abstract: Local Nusselt numbers for laminar mixed convection flows along isothermal vertical, inclined, and horizontal flat plates are presented for the entire mixed convection regime for a wide range of Prandtl numbers, 0.1 ≤ Pr ≤ 100. Simple correlation equations for the local and average mixed convection Nusselt numbers are developed, which are found to agree well with the numerically predicted values and available experimental data for both buoyancy assisting and opposing flow conditions. The threshold values of significant buoyancy effects on forced convection and forced flow effects on free convection, as well as the maximum increase in the local mixed convection Nusselt number from the respective pure convection limits, are also presented for all flow configurations. It is found that the buoyancy or forced flow effect can increase the surface heat transfer rate from pure forced or pure free convection by about 20 percent.

Rayleigh-Bénard convection in an intermediate-aspect-ratio rectangular container

Abstract: We report a study of the flow patterns associated with Rayleigh—Benard convection in rectangular containers of approximate proportions 10 × 5 × 1 at Prandtl numbers σ between 2 and 20. The flow is studied at Rayleigh numbers ranging from the onset of convective flow to the onset of time dependence; Nusselt-number measurements are also presented. The results are discussed in the content of the theory for the stability of a laterally infinite system of parallel rolls. We observed transitions between time-independent flow patterns which depend on roll wavenumber, Rayleigh number and Prandtl number in a manner that is reasonably well described by this theory. For σ [lsim ] 10, the skewed-varicose instability (which leads directly to time dependence in much larger containers) is found to initiate transitions between time-independent patterns. We are then able to study the approach to time dependence in a regime of larger Rayleigh number where the instabilities in the flow are found to have an intrinsic time dependence. In this regime, the onset of time dependence appears to be explained by the recent predictions of Bolton, Busse & Clever for a new set of time-dependent instabilities.

Melting from a flat plate embedded in a porous medium in the presence of steady natural convection

Abstract: The problem of melting from a flat plate embedded in a porous medium is studied. The main focus is to determine the effect of natural convection flow in the liquid phase on the melting phenomenon. Two configurations an considered and modeled mathematically: a vertical plate and a horizontal plate. The final similarity equations art integrated numerically by use of the fourth-order Runge-Kutta method. Systematic “shooting” is required to satisfy the boundary conditions at infinity. Results are reported for the temperature and flow fields in the melt region. The melting phenomenon decreases the local Nusselt number at the solid-liquid interface.

Laminar Mixed Convection in a Symmetrically or Asymmetrically Heated Vertical Channel

Abstract: A numerical investigation is made of laminar mixed convection of air in a vertical channel. The thermal boundary conditions considered are symmetric heating, where both plates are heated, and asymmetric heating, where one plate is heated and the other is adiabatic. Results are obtained for Rayleigh numbers of 10 3 , 10 5 , and 10 6 and Gr/Re 2 values of 0.1, 1, 3, and 5. The temperatures are observed to increase with increasing Gr/Re 2 and decreasing Rayleigh number. The velocity profile peaks near the hot plates and exhibits a concavity, which, in the symmetric heating case, occurs around the centerline. With increasing Gr/Re 2 the velocity near the hot wall increases while the velocity near the centerline decreases. The Nusselt number attains its maximum value near the inlet of the channel and increases with decreasing Gr/Re 2 values.

Constant heat flux solutions for natural convection between concentric and eccentric horizontal cylinders

Abstract: Numerical solutions are presented for steady laminar two-dimensional natural convection in annuli between concentric and vertically eccentric horizontal circular cylinders with specified (constant) heat flux at the boundaries. The results encompass streamline and isotherm contours, temperature distributions on both cylinder boundaries, and average Nusselt numbers as functions of the modified Rayleigh number.

Thermal convection in a porous layer: Effects of anisotropy and surface boundary conditions

Abstract: The theory describing the onset of convection in a homogeneous porous layer bounded above and below by isothermal surfaces is extended to consider an upper boundary which is partly permeable. The general boundary condition p + λ ∂p/∂n = constant is applied at the top surface and the flow is investigated for various λ in the range 0 ⩽ λ < ∞. Estimates of the magnitude and horizontal distribution of the vertical mass and heat fluxes at the surface, the horizontally-averaged heat flux (Nusselt number) and the fraction of the fluid which recirculates within the layer are found for slightly supercritical conditions. Comparisons are made with the two limiting cases λ → ∞, where the surface is completely impermeable, and λ = 0, where the surface is at constant pressure. Also studied are the effects of anisotropy in permeability, ξ = K H /K V , and anisotropy is thermal conductivity, η = k H /k V , both parameters being ratios of horizontal to vertical quantities. Quantitative results are given for a wide variety of the parameters λ, ξ and η. In the limit ξ/η → 0 there is no recirculation, all fluid being converted out of the top surface, while in the limit ξ/η → ∞ there is full recirculation.

Effects of crossflow temperature on heat transfer within an array of impinging jets

Abstract: On considere des reseaux bidimensionnels de jets d'air circulaires heurtant une surface de transfert de chaleur parallele a la plaque d'ou sortent les jets. Apres la collision le jet est contraint de sortir le long du canal forme par la plaque a orifices et la plaque de transfert de chaleur

Prandtl Number Effect on Bénard Convection in Porous Media

Abstract: A numerical study of buoyance-driven two-dimensional convection in a fluid-saturated horizontal porous layer is reported emphasizing the nonlinear inerital effect on heat transport. The Forchheimer-Brinkman-Darcy-Boussinesq formulation and a single energy equation for the volume-average temperature are used. Closure to the wavenumber selection problem is sought through a criterion based on the Glansdorff and Prigogine theory of nonequilibrium thermodynamics. Good agreement with laboratory data and the analogy with th Rayleigh-Benard problem are corroborative facts which justify smililar non-Darcian formulations and demonstrate the role of the quadratic inertial terms in decreasing the mean convective heat transfer across the layer.

Mixed convection in horizontal porous layers heated from below.

Abstract: Numerical studies are reported for steady, mixed convection in two-dimensional horizontal porous layer with localized heating from below. The interaction mechanism between the forced flow and the buoyant effects is examined for wide ranges of Rayleigh number Ra* and Peclet number Pe*. The external flow significantly perturbs the buoyancy-induced temperature and flow fields when Pe* is increased beyond unity. For a fixed Peclet number, an increase in Rayleigh number produces multicellular recirculating flows in a domain close to the heat source. This enhances heat transfer by free convection. However, for a fixed Ra*, an increase in forced flow or Peclet number does not necessarily increase the heat transfer rate. Hence, there exists a critical Peclet number as a function of Ra* for which the overall Nusselt number is minimum. The heat transfer is, generally, dominated by the buoyant flows for Pe* < 1 whereas the contribution of free convection is small for Pe* 10 when Ra* {le} 10.

Laminar forced convection of power-law non-Newtonian fluids inside ducts

Abstract: Thermal entrance region heat transfer for laminar forced convection of power-law fluids inside a circular tube and parallel plate channel for uniform wall temperature is solved exactly, and as many eigenvalues and eigenfunctions as needed for the solution are determined automatically and with high accuracy by using the recently advanced Sign-Count method. Results are presented for the local and average Nusselt number over a wide range of the Graetz number in both graphical and tabular forms. The present benchmark results are utilized to critically examine the accuracy of the approximate Leveque solution.

Influence of baffle location on natural convection in a partially divided enclosure

Abstract: A numerical study has been made of natural convection in a square partitioned enclosure with two offset baffles and perfectly conducting horizontal end walls. The study is made for three different baffle locations and two different conductivities at Rayleigh numbers of 104, 105, and 3.55 × 105. The results clearly demonstrate that baffle position has a significant effect on the heat transfer. As the top baffle is moved toward the cold wall and the bottom baffle toward the hot wall the average Nusselt number value decreases, as does the tendency of the flow to separate behind the baffles. At high Rayleigh numbers the tendency for separation increases and the average Nusselt number value decreases with increasing baffle conductivity. The influence of baffle conductivity on the local Nusselt number distribution increases as the top baffle is moved toward the cold wall and the bottom baffle toward the hot wall. For all baffle locations, the average Nusselt number is smaller than the corresponding value in an ...

Laminar forced convective heat transfer in a two-dimensional 90° bifurcation

Abstract: Laminar forced convective heat transfer in a two-dimensional 90° bifurcation is studied numerically. The governing elliptic equations are solved by a finite-difference numerical scheme utilizing primitive dependent variables. A wide range of Reynolds numbers and dividing flow rates is studied with air at constant properties as the working fluid, which is heated by the constant-temperature walls of the bifurcation. The locations of the separation and reattachment points corresponding to the two recirculatian zones that form in the bifurcation are quantified as a function of the Reynolds number and dividing flow rate. For a given dividing flaw rate, the sizes of the two recirculation zones increase as the inlet Reynolds number is increased. On the other hand, for a given Reynolds number, the sizes of the two recirculation zones increase as the dividing flow rate increases, but they reach maxima after which a higher dividing flow rate results in smaller recirculation zones. The variation of the local Nusselt...

Penalty finite-element analysis of coupled fluid flow and heat transfer for in-line bundle of cylinders in cross flow

Abstract: The two-dimensional steady state Navier-Stokes equations and the energy equation governing laminar incompressible flow are solved using a penalty finite-element model for the case of flow across an in-line bundle of cylinders. Two cases of in-line cylinder bundles, one five rows deep and the other an infinite bundle, are considered with pitch-diameter ratios of 1.25, 1.5 and 1.8 Reynolds numbers studied range from 100 to 600 and Prandtl number is taken as 0.7. Velocity field vectors, stream lines, vorticity, pressure and temperature contours, local and average Nusselt numbers, pressure and shear stress distribution around the cylinder walls and drag coefficients are presented. The results obtained agree well with available experimental and numerical data.