Nusselt Number

Numerical investigations on the turbulent fluid flow and the local heat transfer from rectangular bars for three different aspect ratios were carried out with Re=22000 and Pr=-0.71. The standard k-e turbulence model and a modified version were used in conjunction with the Reynolds-averaged momentum and energy equations for the simulations. The predictions of drag, lift, local and global heat transfer coefficients on the front, side and on the rear face of the rectangular bars are compared with available experimental results.

A numerical study has been carried out to understand and highlight the effects of axial wall conduction in a conjugate heat transfer situation involving simultaneously developing laminar flow and heat transfer in a square microchannel with constant flux boundary condition imposed on bottom of the substrate wall. All the remaining walls of the substrate exposed to the surroundings are kept adiabatic. Simulations have been carried out for a wide range of substrate wall to fluid conductivity ratio (k sf $ 0.17-703), substrate thickness to channel depth (d sf $ 1-24), and flow rate (Re $ 100-1000). These parametric variations cover the typical range of applications encountered in microfluids/microscale heat transfer domains. The results show that the conductivity ratio, k sf is the key factor in affecting the extent of axial conduction on the heat transport characteristics at the fluid-solid interface. Higher k sf leads to severe axial back conduction, thus decreasing the average Nusselt number (Nu). Very low k sf leads to a situation which is qualitatively similar to the case of zero-thickness substrate with constant heat flux applied to only one side, all the three remaining sides being kept adiabatic; this again leads to lower the average Nusselt number (Nu). Between these two asymptotic limits of k sf , it is shown that, all other parameters remaining the same (d sf and Re), there exists an optimum value of k sf which maximizes the average Nusselt number (Nu). Such a phenomenon also exists for the case of circular microtubes.

Accurate computation of heat flux is a primary motivation for convection calculations, yet heat fluxes have generally been calculated to substantially less than optimal accuracy, given the accompanying temperature and velocity fields. We analyse this problem in the context of the finite element method, using bilinear shape functions to interpolate the nodal values of velocity and temperature throughout the medium. Our method, however, is general and also applies to finite difference and higher order finite elements. Consider (dimensionless) vertical heat flux qz = wT -dT/dz, with w vertical velocity and T temperature. The first term is quadratic within (bilinear) elements and continuous at nodes, while the second term is constant within elements and discontinuous at nodes. Usual practice is to evaluate qz at element centres. We instead assign to each element the volume average of qz over that element. Element values are then projected to nodes using a modification of a technique used for pressure smoothing (Hughes et al.) Our approach reduces the calculated depth variation in horizontallyaveraged flux by more than a factor of 10 and shows more rapid convergence of Nusselt number Nu as a function of grid size. It also eliminates the artificial diffusion of heat out of supposed insulating side walls.

The nonlinear flow and heat transfer characteristics for a slot-jet impinging on slightly-curved surfaces are experimentally studied here. The effects of curved surface geometry and jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. Two different slightly-curved surface geometries of convex and concave are used as target surfaces. The nozzle geometry is a rectangular slot, and the dimensionless nozzle-to-surface distance equals to L * = 8. The constant heat fluxes are accordingly applied to the surfaces to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of Re = 8617, Re = 13 350 and Re = 15 415 for both curved surfaces. The velocity distributions of issuing jet from the nozzle exit to the target surface are obtained by a highly sensitive hot-wire anemometer. The T-type thermocouples are used to measure local temperatures of both the air jet and the plates. Two-dimensional velocity measurements show that the surfaces are remained out of the potential core region for all Re tested here. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported. The correlations reveal that the impinging cooling rate is higher with the concave surface and increase with increasing Re.

Natural convection effects of the numerical solution for unsteady, laminar, free convection flow over an incompressible viscous fluid past a no n-isothermal vertical cone with surface temperature T ' w(x) = T ' ∞ + ax n varying as power function of distance from the apex (x = 0) is presented here. The dimensionless governing equations of the flow that

A series of experiments was conducted to study the effect of twisted-tape width on the heat transfer and pressure drop with laminar flow in tubes. Data for three twisted-tape wavelengths, each with five different widths, have been collected with constant wall temperature boundary condition. Correlations for the friction factor and Nusselt number are also available. The correlations predict the experimental data to within 10 to 15 percent for the heat transfer and friction factor, respectively. The presence of the twisted tape has caused the friction factor to increase by a factor of 3 to 7 depending on Reynolds number and the twisted-tape geometry. Heat transfer results have shown an increase of 1.5 to 3 times that of plain tubes depending on the flow conditions and the twisted-tape geometry. The width shows no effect on friction factor and heat transfer in the low range of Reynolds number but has a more pronounced effect on heat transfer at the higher range of Reynolds number. It i...

The problem of heat convection from a sphere placed in an oscillating viscous free stream is considered for the two cases of forced and mixed convection regimes[ The sphere surface is assumed isothermal and the free!stream oscillations are always in the vertical direction resulting in axisymmetric~ow and thermal _elds for both regimes[ The study is based on the solution of the unsteady NavierÐStokes and energy equations for a Boussinesq~uid of constant Prandtl number "Pr 9[60#[ The main parameters considered are the Reynolds number\ Grashof number\ and Strouhal number[ Comparison of results with published data shows a good agreement for the special case of steady forced and mixed convection[ The details of the resulting thermal _elds are presented in the form of isotherm patterns and the local Nusselt number distribution[ Þ 0887 Elsevier Science Ltd[ All rights reserved[ Nomenclature a radius of the sphere f n functions de_ned in eq[ "6# gravitational acceleratioǹ n functions de_ned in eq[ "7# Gr Grashof number\`b"T s −T # "1a# 2 :n 1 h n functions de_ned in eq[ "8# N u local Nusselt number N u overall Nusselt number N time!averaged Nusselt number P n Legendre polynomials of order n P 0 n

Steady two-dimensional free convection heat transfer from a horizontal, isothermal cylinder located underneath an adiabatic ceiling is studied experimentally using a Mach-Zehnder interferometer. Effects of the ratio of cylinder spacing from the adiabatic ceiling to its diameter (L/D) on heat transfer from the cylinder are investigated for various Rayleigh numbers. Experiments are performed for L/D = 0.1, 0.3, 0.5, 0.7, 1.0, 1.5 and 2.4, and the Rayleigh number ranging from 1000 to 40,000. For each experiment thermal and flow fields are illustrated. Results indicate that the adiabatic ceiling has no influence on free convection heat transfer from the cylinder for L/D P 1.5. But by reducing this ratio from 1.5 to 0.5, Nusselt number decreases considerably. For close spacing of (L/D < 0.5), average Nusselt number again increases due to the vortex formation at the top of the cylinder where its effect is present as a sharp increase in the magnitude of local Nusselt number around circumferential position 130 6 h 6 180. Flow visualization by smoke is done to exhibit the existence and the location of the vortices. A correlation based on the experimental data for the average Nusselt number of the cylinder as a function of Ra and L/D is presented in the aforementioned ranges.

Heat transfer enhancement technology has the aim of developing more efficient systems as demanded in many applications. An available passive method is represented by the employ of rough surfaces. Transversal turbulators enhance the heat transfer rate by reducing the thermal resistance near surfaces, because of the improved local turbulence; on the other hand, higher losses are expected. In this paper, a numerical investigation is carried out on turbulent water forced convection in a ribbed channel. Its external walls are heated by a constant heat flux. Several arrangements of ribs in terms of height, width, and shape are analyzed. The aim is to find the optimal configuration in terms of high heat transfer coefficients and low losses. The maximum average Nusselt numbers are evaluated for dimensionless pitches of 6, 8, and 10 according to the shape while the maximum friction factors are in the range of pitches from 8 to 10.

The purpose of the present work is to investigate the effect of magnetic field on laminar natural-convection heat transfer inside a partitioned enclosure. In our formulation of non linear governing equations, mass, momentum, and energy are applied to the partitioned enclosure. A finite volume code based on PATANKAR's SIMPLER method is utilized. Results are obtained for different Rayleigh numbers (Ra), Hartmann numbers (Ha) and baffle positions while the Prandtl number is constant (Pr = 0 733). Results show that as Ra increases the maximum absolute value of the stream function increases and causes the flow to move faster. Also, as Hartman number increases (magnetic field intensifies) the natural convection suppresses and therefore the maximum absolute value of the stream function and Nusselt number reduces. Furthermore the partition causes the flow to separate and to form two vortexes inside the enclosure.

The paper analytically investigated the double-diffusive natural convective boundarylayer flow of a nanofluid past a vertical plate with heat flux condition. The diffusive model used for nanofluid included the effects of Brownian motion and Thermophoresis. A similarity solution was presented and numerical calculations were performed by Maple software. The reduced Nusselt number as a function of a buoyancy-ratio number Nr, a Brownian motion number Nb, and a Thermophoresis number Nt was found with a various values of Prandtl number Pr and Lewis number Le.

A 3D numerical study was carried out to analyze flow, heat and mass transfer first in a single half-cell cathode channel of proton exchange membrane (PEM) fuel cell. From practical point of view, it is necessary to put the appropriate number of cells in a stack. Hence, the above study on a single half-cell is extended to a stack of channels. Due to stacking, the assumption of uniform flow distribution would no longer hold true. Therefore, the channel flow-maldistribution is considered. The water formed at the active surface due to the electrochemical reaction diffuses through the porous layer and eventually enters the gas flow duct. The higher gas velocities in the duct result in faster water vapour removal which leads to a lower value of water vapour into the duct and hence a lower Nusselt number.

This paper addresses the impact of adding insulated plate extensions at the entrance of a vertical parallel-plate channel. The plates receive a uniform heat flux and the cooling occurs by natural convection air flow. The model relies on the full elliptic conservation equations which are solved numerically in a composite three-part computational domain. The pertinent results are reported in terms of wall temperatures, induced mass flow rates, as well as velocity, pressure and temperature profiles of the air for various thermal and geometric 0 bare channel w wall w 1 left wall w 2 right wall ∞ free stream condition

In this paper, roughness was modelled as a pattern of parallelepipedic elements of height k periodically distributed on the plane walls of a microchannel of height H and of infinite span. Two different approaches were used to predict the influence of roughness on heat transfer in laminar flows through this microchannel. Three-dimensional numerical simulations were conducted in a computational domain based on the wavelength l. A one-dimensional model (RLM model) was also developed on the basis of a discrete-element approach and the volume averaging technique. The numerical simulations and the rough-layer model agree to show that the Poiseuille number Po and the Nusselt number Nu increase with the relative roughness. The RLM model shows that the roughness effect may be interpreted by using effective roughness heights k eff and k effq for predicting Po and Nu respectively. k eff and k effq depend on two dimensionless local parameters: the porosity of the rough-layer and the roughness height normalized with the distance between the rough elements. The present results show that roughness increases the friction factor more than the heat transfer coefficient (performance evaluation criteria < 1), for a relative roughness height expected in the fabrication of microchannels (k/(H/2) < 0.46) or k/D h < 0.11).

An experimental investigation on natural convection in air in vertical convergent channels with wall uniform heat flux is presented. Wall temperatures show that by increasing the spacing the effect of the convergence angle decreases. For the lowest spacing, a significant decrease of maximum wall temperature occurs passing from the parallel vertical plate configurations to convergence angles h P 2 .

The paper considers a problem in which a steady-state sonic wave is propagated in the longitudinal direction in a fluid enclosed between two horizontal parallel plates which are kept at different temperatures;. The distance between the plates is much smaller than the sound wavelength. Rayleigh's vortical acou~stic streaming that appears in the region between the plates as a result of the sound wave leads to forced heat convection. The effect of that forced convection on heat transferred between the plates is analyzed theoretically. An acoustic Peclet number, which represents the interaction between heat conduction and #orced convection is introduced, and asymptotic relations expressing the mean Nusselt number in terms of this dimensionless group are derived. The results obtained demonstrate that acoustic streaming results in a marked enhancement of heat transfer between the plates.

The current study investigates the augmentation in the laminar forced convection characteristics of the backward-facing step flow in a two-dimensional channel by means of introducing an adiabatic circular cylinder in the domain. The effects of various cross-stream positions (i.e., y c ¼ 0e1.5) of the circular cylinder on the flow and heat transfer characteristics of the backward-facing step flow has been numerically explored for the Reynolds number range 1e200 and Prandtl number of 0.71 (air). The governing continuity, NaviereStokes and energy equations along with appropriate boundary conditions are solved by using FLUENT. The flow and thermal fields have been explained by streamline and isotherm profiles, respectively; however, no temperature dependency effects are considered for the flow viscosity and thermal conductivity. The engineering parameters like wake/recirculation length, total drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions. The present results show an enhancement in the peak Nusselt value of up to 155% using a circular cylinder as compared to the unobstructed case (i.e., without cylinder). Finally, simple correlations for total drag coefficient and peak Nusselt number are obtained for the above range of conditions.

A numerical simulation has been carried out to investigate the buoyancy induced flow and heat transfer characteristics inside a wavy walled enclosure. The enclosure consists of two parallel wavy and two straight walls. The top and the bottom walls are wavy and kept isothermal. Two straight-vertical sidewalls are considered adiabatic. Governing equations are discretized using the control volume based Finite-Volume method with collocated variable arrangement. Simulation was carried out for a range of surface waviness ratios, =0.00-0.25; aspect ratios, A=0.25-0.5; and Rayleigh numbers Ra=100-107 for a fluid having Prandtl number equal to 1.0. Results are presented in the form of local and global Nusselt number distributions, streamlines, and isothermal lines for different values of surface waviness and aspect ratios. For a special case of =0 and A=1.0, the average Nusselt number distribution is compared with available reference. The results suggest that natural convection heat transfer is changed considerably when surface waviness changes and also depends on the aspect ratio of the domain. In addition to the heat transfer results, the heat transfer irreversibility (HTI) in terms of Bejan number (Be) was measured. For a set of selected values of the parameters (, A, and Ra), a contour of the Bejan number is presented at the end of this paper.

Reçu le 15 juillet 2004 ; accepté après révision le 19 octobre 2004 Présenté par Michel Combarnous Résumé Dans cette étude, on s'intéresse au transfert de chaleur d'un fluide non newtonien fortement thermodépendant en écoulement non isotherme entre deux plaques parallèles chauffées. On étudie, par voie numérique, l'influence des différents paramètres sur les évolutions de la couche limite thermique et du nombre de Nusselt. Les corrélations sont proposées pour calculer le transfert de chaleur dans deux cas de chauffage pariétal à densité de flux ou à température constante. Pour citer cet article : N. Van Tuan, M. Lebouche, C. R. Mecanique 333 (2005).  2004 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés. Abstract Numerical study of a thermodependent non Newtonian fluid flow between two parallel plates. In this study, the heat transfer of a non Newtonian thermodependent fluid flowing between two parallel plates is considered. The effects of different parameters on the evolutions of thermal boundary layer and of Nusselt number are numerically investigated in two heating cases and correlations are proposed to compute the heat transfer. To cite this article: N. Van Tuan, M. Lebouche, C. R. Mecanique 333 (2005).  2004 Académie des sciences. Publié par Elsevier SAS. Tous droits réservés.

This paper addresses the natural convection behavior of air when heated in single vertical, parallel-plate channels. To enhance the heat transfer two passive schemes are combined: (1) an equidistant short plate is inserted at the inlet and (2) two parallel, colinear insulated plates are appended at the exit. The channel plates are symmetrically heated with a uniform heat flux. The computational procedure is made by solving the full elliptic Navier-Stokes and energy equations with the finite-volume methodology in an I-type computational domain that is much larger than the physical domain. Within the framework of a "proof-of-concept" the controlling Grashof number based on the heated plate height ranges between 10 3 and 10 6 . The numerical velocity, pressure and temperature fields are post-processed to compute the quantities of engineering interest such as the induced mass flow rate, the pressure at the channel mid-plane and the temperature along the plates. In addition, the Nusselt number and the average Nusselt number, both based on the heated plate height, are presented in graphical form. At the end, optimal channel configurations expressed in terms of the highest average Nusselt number are obtained for the pair of pre-assigned Grashof numbers.

Mixed convection heat transfer in a lid-driven cavity along with a heated circular hollow cylinder positioned at the center of the cavity has been analyzed numerically. The present study simulates a realistic system such as air-cooled electronic equipment with a heat component or an oven with heater. A Galerkin weighted residual finite element method with a Newton-Raphson iterative algorithm is adopted to solve the governing equations. The computation is carried out for wide ranges of the Richardson numbers, cylinder diameter and solid fluid thermal conductivity ratio. Results are presented in the form of streamlines, isothermal lines, average Nusselt number at the heated surface and fluid temperature in the cavity for the mentioned parameters. It is found that the flow field and temperature distribution strongly depend on the cylinder diameter and also the solid-fluid thermal conductivity ratio at the three convective regimes.

Pulsation effect on heat transfer in laminar incompressible flow, which led to contradictory results in previous studies, is theoretically investigated in this work starting from basic principles in an attempt to eliminate existing confusion at various levels. First, the analytical solution of the fully developed thermal and hydraulic profiles under constant wall heat flux is obtained. It eliminates the confusion resulting from a previously published erroneous solution. The physical implications of the solution are discussed. Also, a new time average heat transfer coefficient for pulsating flow is carefully defined such as to produce results that are both useful from the engineering point of view, and compliant with the energy balance. This rationally derived average is compared with intuitive averages used in the literature. New results are numerically obtained for the thermally developing region with a fully developed velocity profile. Different types of thermal boundary conditions are considered, including the effect of wall thermal inertia. The effects of Reynold and Prandtl numbers, as well as pulsation amplitude and frequency on heat transfer are investigated. The mechanism by which pulsation affects the developing region, by creating damped oscillations along the tube length of the time average Nusselt number, is explained. Ó

Rotary desiccant wheels are widely used in dehumidification and energy recovery applications. In this work, we have developed a 2D, steady state model of a rotary desiccant wheel. Mass and energy balance equations for the air streams and the desiccant wheels were developed. The hydraulic diameter and surface area for heat and mass transfer were calculated based on knowledge of the flute geometry. Appropriate correlations for the Sherwood number and Nusselt number were used to estimate heat and mass transfer coefficients. The model is capable of predicting steady state behavior of desiccant wheels having at the most three sections (process, purge, and regeneration). The mathematical model was validated using a real desiccant wheel, and the calculation results are in reasonable agreement with the experimental data. Based on this model, the temperature and humidity profiles in the wheel during both the dehumidification and the regeneration processes are analyzed. The simulated results were used to gain an insight into the operation of desiccant wheels. The model and the presented results will be useful for optimizing dehumidification and energy recovery applications.

A numerical simulation of two-dimensional laminar steady-state natural convection in a square tilt open cavity has been numerically studied. The opposite wall to the aperture is placed at either isothermal heat source or isoflux heat source, while the surrounding fluid interacting with the aperture is maintained at an ambient temperature. The two remaining walls are assumed to be adiabatic. The fluid concerned is air with Prandtl number fixed at 0.71. The governing mass, momentum and energy equations are expressed in a normalized primitive variables formulation. In this paper, a finite element method for steady-state incompressible natural convection flows has been developed. The streamlines and isotherms are produced, heat transfer characteristics is obtained for Rayleigh numbers from 10 3 to 10 6 and for an inclination angles of the cavity ranges from 0º to 60º. The results show that the Nusselt numbers increases with the Rayleigh numbers. Also the average Nusselt number changes substantially with the inclination angle of the cavity while better thermal performance is also sensitive to the boundary condition of the heated wall.

A numerical investigation of the airside performance of a plain fin-and-tube heat exchanger having 4 row configurations has been presented in this study. Fluid flow is steady, incompressible and three dimensional. Laminar (400&lt;Re H &lt;1200) and transitional (1300&lt;Re H &lt;2000) flow conditions are considered for both in-line and staggered tube arrangements. For transitional flow calculations, the k-ω turbulence model is used. Uniform flow with constant velocity and temperature are considered at inlet and no-slip boundary condition and constant wall temperature is assumed at fin and tube surfaces. In this study the geometrical parameters such as fin pitches, longitudinal pitches and transverse pitches of tube spacing are studied. The results are compared with previous experimental data of Wang et al. [1]. Results are presented in the form of friction factor (f) and Colburn factor (j). For both laminar and transitional flow conditions heat transfer and friction factor decrease ...

The purpose of this study is to investigate the influence of indentations on the parameters of fluid flow and heat of water-silver nanofluid in a rectangular two-dimensional micro channel. It includes heat transfer water silver nano fluid in an indented micro channel under the constant temperature. The system is numerically modeled, by Finite Volume Method. After solving the governing equations for U, V and θ, other useful quantities such as Nusselt number and friction factor can be determined. The hot fluid inlet exits after cooling by the cold walls of the micro channel. Calculations are done for the two ranges of Reynolds number (Re). It was observed that at times the fluid has more indentations; it has a greater temperature drop that is at the output cross section of the micro channel. With increasing Reynolds number (Re), number of the indentations and the increasing volume fraction of the nanoparticles, greater temperature drop occurs. The presence of indentation in the micro channel increases the speed and the dimensionless temperature at the center line. Finally, the results are provided in the form of the contour of flow and isothermal lines, the coefficient of friction, Nusselt number, temperature and velocity profiles in different micro channel sections. The results of the numerical simulation indicate that the heat transfer rate is significantly affected by the solid volume fraction and Reynolds number.

A numerical analysis of the entropy production has been performed due to natural convection heat transfer and fluid flow in isosceles triangular enclosures with partially heated from below and symmetrically cooled from sloping walls. Governing equations are solved by finite difference method. Governing parameters on flow and temperature fields are Rayleigh number (10 3 6 Ra 6 8.8 · 10 5 ), dimensionless length of heater (0.25 6 (' 0 = '/L) 6 1.0), dimensionless location of heater (0.25 6 (c 0 = c/L) 6 0.75) and inclination angle of slopping walls (30°6 b 6 60°). Heat transfer results are presented in terms of local and mean Nusselt numbers (Nu) while entropy production results are shown with entropy production number (N s ) and Bejan number (Be). Isotherms, streamlines, contours of entropy production due to heat transfer and fluid friction irreversibility are plotted. It is observed that entropy production number increases but Bejan number decreases with increasing of Rayleigh number. However, both entropy production due to heat transfer and fluid friction irreversibility are affected by higher inclination angle of triangle and length of heater.

An experimental study has been performed on single-phase heat transfer, boiling inception, and pressure drop of R-123 over a bank of shrouded micro pin fins 243 lm long with hydraulic diameter of 99.5 lm. Heat transfer coefficients and Nusselt numbers have been obtained over effective heat fluxes ranging from 3.5 to 65.5 W/cm 2 and Reynolds numbers from 134 to 314. A delay in boiling incipience has been observed and a meta-stable single-phase region was apparent at liquid exit temperatures noticeably exceeding the saturation temperature. Once boiling was initiated, vapor burst instabilities resembling the compound relaxation instabilities were attained. It has also been found that endwalls effects on heat transfer diminished for Re > 100.

Numerical simulation of an air and water two-phase flow in a micro tube is carried out. The focus is laid upon bubbly and slug flows with dry-out. An axisymmetric two-dimensional flow is assumed. The Phase-Field method is adopted to capture the interface, as well as to resolve the singularities arising at the rupture of liquid film and the consequent contact

In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette-Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement.

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic j-e turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra m . Computations covered the range 10 < Ra m < 10 6 and 10 À7 < Da < 10 À10 and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra m , merging to the laminar branch for a reducing Ra m and for Ra m less than a certain critical Rayleigh number, Ra cr . This convergence of results as Ra m decreases can be seen as a characterization of the laminarization phenomenon. For Ra m values less than around 10 4 , both laminar and turbulent flow solutions merge, indicating that such critical value for Ra m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.

Heat transfer to an obliquely impinging air jet is investigated experimentally. Distributions of the mean and the fluctuating component of the surface heat transfer are reported for a jet Reynolds number of 10,000, nozzle to impingement surface distance, H/D, from 2 to 8 and angle of impingement, a, from 30°to 90°(normal impingement). Flow velocity measurements along the impingement surface are related to heat transfer distributions. At specific locations the surface heat transfer and the local fluid velocity are measured simultaneously and coherence and phase difference information between the signals are reported. The vortical characteristic of the flow is shown to vary considerably with the angle of impingement; depending on the distance between the near nozzle edge and the impingement surface, vortices at different stages of development impact with the target surface. The influence of naturally occurring vortices in an impinging jet flow on the magnitude of heat transfer in the near wall jet is reported.

An experimental investigation of steady-state natural convection heat transfer was carried out in finite rectangular air layers heated from above. Two different aspect ratios, namely A = 20 and 80, and perfectly conducting boundary conditions on the end walls were used. The angle of inclination was varied from ~b = 0 (heated from below) to ~b = 180 ° (heated from above). A total of 226 test points were taken for heat transfer measurements in air layers heated from above at four different orientations in the range 120 ~< tp ~< 180 ° for Rayleigh numbers between 102 and 2 x 10 6. Additional test points have been carried out to show the effect of the angle of tilt in the range 0 ~< ~b ~< 180 ° on the average Nusselt number for fixed values of the Rayleigh number. Local measurements of the Nusselt number over discrete portions of the air layer are reported to show the Nusselt number distribution over different flow regimes. Copyright

Whereas the heat transfer mechanisms in steady impinging jets are well understood, the available knowledge of heat transfer to impinging synthetic jets remains inconsistent. This paper provides an objective comparison of the stagnation point heat transfer performance of axisymmetric impinging synthetic jets versus established steady jet correlations. Furthermore, a general correlation for the stagnation point Nusselt number is proposed including the effect of all appropriate scaling parameters: Reynolds number (500 6 Re 6 1500), jet-to-surface spacing (2 6 H/D 6 16) and stroke length (2 6 L 0 /D 6 40). Based on the ratio of stroke length to jet-to-surface spacing L 0 /H, four heat transfer regimes are identified.

A liquid crystal based experimental investigation of the heat transfer enhancement supplied by ribs on a vertical plate, has been presented. Since the ribs were adiabatic, they did not work as extended heat transfer surfaces but by redirecting the flow, were used to enhance the heat transfer. Four different rib heights (H = 10, 20, 30, 40 mm) and five different angles of inclination (θ = 0°, 10°, 20°, 30°, 45°) are considered. Local heat transfer coefficients and the mean Nusselt numbers for the considered experimental cases are compared to those of the flat plate without ribs. The enhanced flow is always found to have higher heat transfer values. On the other hand, both the rib height and the angle of inclination affect the magnitude of the local and total heat transfer coefficients. To reach a reasonable correlation between the geometrical parameters and the heat transfer values, three-dimensional numerical simulations of the natural convection flow along a vertical plate with ribs were performed.

An analysis is performed to study the laminar boundary layer flow over a porous flat plate with injection or suction imposed at the wall. Two different analyses techniques are used for the solution of boundary layer equations: similarity solution and numerical solution. The effect of uniform suction/injection on the heat transfer is discussed. The constant surface temperature thermal boundary condition is used for the horizontal flat plate. The effect of Prandtl number on heat transfer is also investigated. A scale analysis is performed to get more insight into the Prandtl effect. Friction coefficients and Nusselt numbers are calculated for constant fluid injection/suction along the plate. The results indicate that the suction enhances the heat transfer coefficient while injection causes a decrease in heat transfer.

The transient cooling of a fluid initially at rest inside a storage tank submitted to heat losses to the ambient is studied. The study is restricted to laminar flow conditions. In order to identify the relevant non-dimensional groups that define the transient natural convection phenomenon that occurs, a non-dimensional analysis is carried out. The long-term behaviour of the fluid is modeled by formulating a prediction model based on global balances. A parametric study by means of several multidimensional numerical simulations led to correlate the Nusselt number and the transient mean fluid temperature, to feed the global model proposed. Special attention is given to the appropriateness of the spatial and time discretisation adopted, the verification of the numerical solutions and the post-processing tasks in order to obtain the correlations. The most relevant particularities of the numerical model developed are also pointed out.

Turbulent flow and heat transfer of three different nanofluids (CuO, Al 2 O 3 and SiO 2 ) in an ethylene glycol and water mixture flowing through a circular tube under constant heat flux condition have been numerically analyzed. New correlations for viscosity up to 10% volume concentration for these nanofluids as a function of volume concentration and temperature are developed from the experiments and are summarized in the present paper. In our numerical study, all the thermophysical properties of nanofluids are temperature dependent. Computed results are validated with existing well established correlations. Nusselt number prediction for nanofluids agrees well with Gnielinski correlation. It is found that nanofluids containing smaller diameter nanoparticles have higher viscosity and Nusselt number. Comparison of convective heat transfer coefficient of CuO, Al 2 O 3 and SiO 2 nanofluids have been presented. At a constant Reynolds number, Nusselt number increases by 35% for 6% CuO nanofluids over the base fluid.

The problem of buoyancy driven turbulent flow in parallel-plate channels is investigated. The investigation is limited to vertical channels of uniform crosssection with different modes of heating. The details of the flow and thermal fields are obtained from the solution of the conservation equations of mass, momentum, and energy in addition to equations of the low Reynolds number turbulence model. The study covers Rayleigh number ranging from 10 5 to 10 7 and focuses on the effect of channel geometry on the characteristic of the flow and thermal fields as well as the local and average Nusselt number variation. A Nusselt number correlation has been developed in terms of a modified Rayleigh number and channel aspect ratio for the cases of symmetrically heated isothermal and isoflux conditions.

The rates of heat transfer for flow through a periodic array of wavy passages are studied with an accurate numerical scheme. The flow was observed to be steady until Re around 180 after which self-sustained oscillatory flow was observed. The self-sustained oscillations lead to the destabilization of laminar thermal boundary layers, replenish the near-wall fluid with the fluid in the core region, and thus provide a natural mechanism of heat and mass transfer enhancement. In the steady-flow regime, the average Nusselt numbers for the wavy wall channel were only slightly larger than those for a parallel-plate channel. On the other hand, in the transitional-flow regime, the enhancement of heat transfer was about a factor of 2.5. Friction factors for the wavy channel were about twice those for the parallel-plate channel in the steady-flow region, and remained almost constant in the transitional regime.

The various techniques for achieving improved heat transfer are usually referred to as "heat transfer augmentation" or "heat transfer enhancement" and the heat exchanger provided with heat transfer enhancement techniques as "Augmented Heat Exchanger". The objective is to reduce as many of the factors as possible: Capital Cost, Power Cost, Maintenance Cost, Space and Weight, Consistent with safety and reliability. Present work describes the principal techniques of industrial importance for the augmentation of single phase heat transfer on the inside of tubes namely twisted tapes. So twisted tape should be used in heat exchanger when high heat transfer rate is required and pressure drop is of no significance.

A numerical experiment has been conducted to determine the interfacial convective heat transfer coecient in the two-energy equation model for convection in porous media, which is needed when the local thermal equilibrium between the¯uid and solid phases breaks down. The similarity of periodically fully developed temperature pro®les allows one to perform a numerical experiment using only a single structural unit for determining the fully developed heat transfer coecient without any empiricism. A universal correlation for the Nusselt number, which agrees well with available experimental data, has been established using the results obtained for a wide range of porosity, Prandtl and Reynolds numbers. Ó