Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in unconfined flowing Newtonian fluids have been investigated numerically. The governing equations, namely, continuity, Navier–Stokes and energy, have been solved in the steady flow regime over wide ranges of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr ? 100). Prior to the investigation of drag and heat transfer phenomena, the critical values of the Reynolds number for wake formation (0.55 < Re^c < 0.6) and for the onset of vortex shedding (39.5 < Re_c < 40) have been identified. The corresponding values of the lift coefficient, drag coefficient, and Strouhal number are also presented. After establishing the limit of the steady flow regime, the influence of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr = 0.72, 1, 10, 50 and 100) on the global flow and heat transfer characteristics have been elucidated. Detailed kinematics of the flow is investigated in terms of the streamline and vorticity profiles and the variation of pressure coefficient in the vicinity of the cylinder. The functional dependence of the individual and total drag coefficients on the Reynolds number is explored. The Nusselt number shows an additional dependence on the Prandtl number. In addition, the isotherm profiles, local Nusselt number (Nu_L) and average Nusselt number (Nu) are also presented to analyze the heat transfer characteristic of a semi-circular cylinder in Newtonian media.     

Heat and fluid flow across a rotating cylinder dissipating uniform heat flux in 2D laminar flow regime

Free-stream flow and forced convection heat transfer across a rotating cylinder, dissipating uniform heat flux, are investigated numerically for Reynolds numbers of 20–160 and a Prandtl number of 0.7. The non-dimensional rotational velocity (α) is varied from 0 to 6. Finite volume based transient heatline formulation is proposed. For Re = 100, the reasons for the onset/suppression of vortex shedding at a critical rotational velocity is investigated using vorticity dynamics. At higher rotational velocity, the Nusselt number is almost independent of Reynolds number and thermal boundary conditions. Finally, a heat transfer correlation is proposed in the 2D laminar flow regime. Cylinder rotation is an efficient Nusselt number reduction or cylinder-surface temperature enhancement technique.     

Mixed convection heat transfer in horizontal,concentric annuli for transitional flow conditions

Experiments have been performed to determine mixed convection flow and heat transfer in a horizontal, concentric tube annulus for Reynolds numbers in the range 2200 < Re < 5000. Within this range, flow conditions are turbulent and laminar, respectively, in regions of the annulus above and below the heated inner tube. For Reynolds numbers less than a critical value Re₁ which depends on the Rayleigh number, diameter ratio and longitudinal position, flow along the sides of the annulus is laminar and helicoidal. For Re >Re₁, there is a breakdown in the helicoidal motion, with subsequent transition to turbulence in the top and side regions of the annular passage. The local Nusselt number at the top of the inner tube is less than, equal to, and greater than that at the bottom for Re < Re₁, Re = Re₁, and Re >Re₁, respectively. The circumferentially averaged Nusselt number is weakly dependent on longitudinal position and may be correlated in terms of the Rayleigh and Reynolds numbers and the tube diameter ratio.     

Mixed convection on jet impingement cooling of a constant heat flux horizontal porous layer

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions, and the Darcian and non-Darcian effects are evaluated. The unsteady stream function-vorticity formulation is used to solve the governing equations. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Reynolds number (1 ≤ Re ≤ 1000), modified Grashof number (10 ≤ Gr¹ ≤ 100), half jet width (0.1 ≤ D ≤ 1.0), Darcy number (1 × 10^?6 ≤ Da ≤ 1 × 10^?2), and the distance between the jet and the heated portion (0.1 ≤ H ≤ 1.0). It is found that the average Nusselt number (Nu_avg) increases with increase in either modified Grashof number or jet width for high values of Reynolds number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The average Nusselt number decreases with the increase in Da for the non-Darcy regime when Re is low whereas Nu_avg increases when Re is high. It is shown that mixed convection mode can cause minimum heat transfer unfavorably due to counteraction of jet flow against buoyancy driven flow. Minimum Nu_avg occurs more obviously at higher values of H. Hence the design of jet impingement cooling through porous medium should be carefully considered in the mixed convection regimes.     

Heat transfer from a cylinder in axial turbulent flows

Local convective heat transfer coefficients were measured on a two-diameter long cylinder in axial flows of air at conditions unexplored so far, by using thermochromic liquid crystals (TLC) coated on an electrically heated strip-foil consisting bonded to the external surfaces. The Reynolds numbers (Re) based on the cylinder diameter were between 8.9 × 10⁴ and 6.17 × 10⁵, and the flow in front of the cylinder was modified in some cases by the use of a turbulence generating grid, or by circular disc inserts of two sizes placed upstream of the cylinder. These created a major change in the local convective heat transfer coefficient distribution on the cylinder. Increase of the turbulence intensity from Tu < 0.1% to Tu = 6.7% at the same Re increased the average calculated Nusselt number Nu over the cylinder by 25%, and decreased the Nu non-uniformity over the surface. One of the flow modification inserts also reduced significantly the Nu non-uniformity. The position of flow reattachment was measured using tufts. Our heat transfer data agree well with the small amount if data published of others, when extrapolated to their conditions. Correlations between the Nu and Re in the form Nu = CRe^e were established and presented for the average Nu on the front, middle and rear cylinder surfaces, and the variation of the local exponent e was shown along the cylinder. Introducing a new technique, a TLC-coated heated flat plate mounted in the flow above the cylinder in the meridional plane was demonstrated to help visualize the flow field above the cylinder. A track of maximum convective coefficients on this plate was found similar in position to the stream line dividing the forward and backward flows in a case measured for the separated flow in a past study.     

Exergy transfer in a porous rectangular channel

Present paper is performed to investigate the heat and exergy transfer characteristics of forced convection flow through a horizontal rectangular channel where open-cell metal foams of different pore densities such as 10, 20 and 30 PPI (per pore inches) were situated. All of the bounding walls of the channel are subjected to various uniform heat fluxes. The pressure drop and heat transfer characteristics are presented by two important parametric values, Nusselt number (Nu_H) and friction factor (f), as functions of Reynolds number (Re_H) and the wall heat flux (q). The Reynolds number (Re_H) based on the channel height of the rectangular channel is varied from 600 to 33?000, while the Grashof number (Gr_Dh) ranged from approximately 10⁵–10⁷ depending on q. Based on the experimental data, new empirical correlations are constructed to link the Nu_H. The results of all cases are compared to that of the empty channel and the literature. It is found that the results are in good agreement with those cited in the references. The mean exergy transfer Nusselt number (Nu_e) based on the Re_H, Nu_H, Pr and q for a rectangular channel with constant heat flux is presented and discussed.     

Study of high temperature thermal boundary conditions on active surfaces of the cylinder shaped ultrasonic transducers

Results of an experimental and numerical research of two-dimensional unsteady flow around the butt end of the model of cylinder shaped ultrasonic transducer at zero angle attack are presented. The flow formed employing linear dc plasma torch, is turbulent with Re number between 1.8 × 10⁴ and 2.2 × 10⁴ and temperature −1200 K. At this regime the flows boundary layers at the cylinder edge separate laminar and transition takes place in the free shear layers. In the shear layer strong vortex shedding and temperature fluctuations are observed. Experimentally estimated distribution of velocities and temperatures on the flat surface of circular cylinder compared with the predicted and has been established good agreement under the results. The influence of the location to distribution and quantity of dynamic and thermal parameters was investigated.     

Characterization of sodium flow over hexagonal fuel subassemblies

Steady flow of liquid sodium over a bundle of heat generating hexagonal subassemblies has been investigated. The cross flow pressure drop and heat transfer are characterized using the general purpose CFD code STAR-CD. Analysis has been carried out for both laminar and turbulent regimes of interest to liquid metal fast reactors. Turbulence has been modeled using low Reynolds number (Re) k-ε model. The estimated pressure drop and heat transfer coefficients are compared against that of a straight parallel plate channel. It is seen that in the low Reynolds number range, the pressure drop for the hexagonal path is nearly equal to that of the parallel plate channel for the same length. However, in the high Reynolds number range, the pressure drop of the hexagonal path is much higher than that in the parallel plate channel, the ratio being 2 at Re = 2000 while it is 3.6 at Re = 20,000. Two competing factors, viz., (i) jet impingement/flow development effect and (ii) flow separation effect are found to influence the average Nusselt number (Nu). In the laminar regime, the latter effect dominates leading to a decrease of the Nusselt number with an increase in the Reynolds number. However, in the turbulent regime, the former effect dominates leading to an increase in the Nusselt number with Reynolds number. The Nusselt number in the hexagonal path is about twice that of the parallel plate channel due to under development of velocity/temperature profiles and the recirculation associated with the hexagonal path due to the changes in flow direction. Detailed correlations for both the pressure drop and the average Nusselt number have been proposed.     

Vortex shedding and heat transfer dependence on effective Reynolds number for mixed convection around a cylinder in cross flow

The influence of surface heating of a circular cylinder on the wake structure and heat transfer in the range of Reynolds number (Re) for which parallel vortex shedding occurs, is investigated numerically for different values of the buoyancy parameter, Gr. The role of buoyancy induced baroclinic vorticity on the wake formation is addressed in the present study. The variation of Strouhal number and Nusselt number with the ’effective Reynolds number’, is analyzed for different values of cylinder to free stream temperature ratio. Both Strouhal number and the rate of heat transfer increases monotonically with the increase of the effective Reynolds number. The validity of the correlations, which have been established by several authors, between the effective Reynolds number and Strouhal/ Nusselt number for forced convection, is examined in the mixed convection regime. The curves between the effective Reynolds number and the computed data for Strouhal number and Nusselt number do not collapse for the range of temperature ratio considered here. The flow field is found to be asymmetric and the cylinder experiences a negative lift. The drag coefficient increases steadily with the rise of surface temperature.     

Numerical simulation of slip flow through rhombus microchannels

Microgeometry fluid dynamics has gotten a lot interest due to the arrival of Micro-Electro-Mechanical systems (MEMS). When the mean free path of a gas and characteristic length of the channel are in the same order, continuum assumption is no longer valid. In this situation velocity slip and temperature jump occur in the duct walls. Fully developed numerical analysis for characteristic laminar slip flow and heat transfer in rhombus microchannels are performed with slip velocity, and temperature-jump boundary condition at walls. The impacts of Reynolds number (0.1 < Re < 40), velocity slip, and temperature-jump on Poiseuille number, and Nusselt number for different aspect ratio (0.15 < A < 1.0), and Knudsen number are studied in detail. The contours of non-dimensional velocity for some cases are examined as well. The results show that aspect ratio and Knudsen number have important impact on Poiseuille number, and Nusselt number in rhombus microchannels. Reynolds number has considerable influence on Nusselt number at low Reynolds number, but its influence on Poiseuille number is not very important at the studied range.     

Heat transfer and friction in the offset stripfin heat exchanger

This paper presents analytical models to predict the heat transfer coefficient and the friction factor of the offset strip-fin heat exchanger surface geometry. Two flow regimes are defined—laminar and turbulent. Based on the conditions in the wake, an equation is developed to predict transition from laminar to turbulent flow. Flow visualization experiments were performed to identify the flow structure at transition. The condition predicted by the transition equation corresponds to onset of oscillating velocities in the fin wakes. Equations are developed for the Nusselt number and friction factor by writing energy and momentum balances on a unit cell of the offset strip-fin geometry. A numerical solution is used to calculate Nu and f on the fins in the laminar regime, and a semi-empirical approach is used for the turbulent regime. Predictions are compared to data on scaled-up geometries, taken in the present study, and data on actual heat exchangers. The models predict all data within ±20%.     

Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow

An analytical solution is investigated for forced convection heat transfer from a laminar plane wall jet as conjugate case. For Re ? 1, boundary layer theory is used for the investigation. The problem has been solved for two classic cases such as Pr ? 1 and Pr ? 1. The conjugate model consists of considering the full Navier-Stokes equation in the fluid medium and coupling of energy equations in the fluid and the slab through the interface boundary conditions. Closed-form relations are found for Nusselt number (Nu), average Nusselt number and conjugate interface boundary temperature (θ_b). The effects of the Reynolds number (Re), the Prandtl number (Pr), the thermal conductivity ratio (k) between the slab and the fluid medium and the slab aspect ratio (λ) are investigated on the heat transfer characteristics. The analytical results are compared with the full numerical results.     

Three-dimensional numerical simulation of the slip flow through triangular microchannels

Three-dimensional numerical analysis for fully developed incompressible fluid flow and heat transfer through triangular microchannels over the slip flow regime is simulated in this paper. In order to study the flow through the channel, the Navier–Stokes equations are solved in conjunction with slip/jump boundary conditions. The influences of Knudsen number (0.001 < Kn < 0.1), aspect ratio (0.2 < A < 4.5), and Reynolds number (1 < Re < 15) on the fluid flow and heat transfer characteristics are extensively investigated in the paper. The numerical results reveal that the rarefaction decreases the Poiseuille number, while its effect on the Nusselt number completely depends on the interaction between velocity slip and temperature jump. It is also found that the aspect ratio has an important role in the analysis, but the variation of Reynolds number is less remarkable.     

Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli

Forced and free convective heat transfer for thermally developing and thermally fully developed laminar air flow inside horizontal concentric annuli in the thermal entrance length has been experimentally investigated. The experimental setup consists of a stainless steel annulus having a radius ratio of 2 and an inner tube with a heated length of 900 mm subjected to a constant wall heat flux boundary condition and an adiabatic outer annulus. The investigation covers Reynolds number range from 200 to 1000, the Grashof number was ranged from 6.2 × 10⁵ to 1.2 × 10⁷. The entrance sections used were long tube with length of 2520 mm (L/D_h = 63) and short tube with length of 504 mm (L/D_h = 12.6). The surface temperature distribution along the inner tube surface, and the local Nusselt number distribution versus dimensionless axial distance Z_t were presented and discussed. It is inferred that the free convection effects tended to decrease the heat transfer at low Re number while to increase the heat transfer for high Re number. This investigation reveals that the Nusselt number values were considerably greater than the corresponding values for fully developed combined convection over a significant portion of the annulus. The average heat transfer results were correlated in terms of the relevant dimensionless variables with an empirical correlation. The local Nusselt number results were compared with available literature and show similar trend and satisfactory agreement.     

Modeling of forced convective heat transfer of a non-Newtonian nanofluid in the horizontal tube under constant heat flux with computational fluid dynamics

In this paper, convective heat transfer effect on the non-Newtonian nanofluid flow in the horizontal tube with constant heat flux was investigated using computational fluid dynamics (CFD). For this purpose, non-Newtonian nanofluid containing Al₂O₃ and Xanthan aqueous solution as a liquid single phase with two average particle sizes of 45 and 150 nm and four particle concentrations of 1, 2, 4 and 6 wt.% and two concentrations of Xanthan aqueous solutions (0.6,1.0 wt.%) were used. Effect of particle size and concentration of Xanthan solution on convective heat transfer coefficient was investigated in different Reynolds numbers (500 < Re < 2500) for various axial locations of tube. The results showed that heat transfer coefficient and Nu number of non-Newtonian nanofluid increased with increasing concentration of Xanthan solution. By applying the modeling results, an equation was obtained for Nusselt number prediction using the dimensionless numbers. The results showed that the correlated data were in very good agreement with predicted data. The maximum error was around 5%.     

Investigation of dimpled fins for heat transfer enhancement in compact heat exchangers

Direct and Large-Eddy simulations are conducted in a fin bank with dimples and protrusions over a Reynolds number range of Re_H = 200 to 15,000, encompassing laminar, transitional and fully turbulent regimes. Two dimple-protrusion geometries are studied in which the same imprint pattern is investigated for two different channel heights or fin pitches, Case 1 with twice the fin pitch of Case 2. The smaller fin pitch configuration (Case 2) develops flow instabilities at Re_H = 450, whereas Case 1 undergoes transition at Re_H = 900. Case 2, exhibits higher Nusselt numbers and friction coefficients in the low Reynolds number regime before Case 1 transitions to turbulence, after which, the differences between the two decreases considerably in the fully turbulent regime. Vorticity generated within the dimple cavity and at the dimple rim contribute substantially to heat transfer augmentation on the dimple side, whereas flow impingement and acceleration between protrusions contribute substantially on the protrusion side. While friction drag dominates losses in Case 1 at low Reynolds numbers, both form and friction drag contributed equally in Case 2. As the Reynolds number increases to fully turbulent flow, form drag dominates in both cases, contributing about 80% to the total losses. While both geometries are viable and competitive with other augmentation surfaces in the turbulent regime, Case 2 with larger feature sizes with respect to the fin pitch is more appropriate in the low Reynolds number regime Re_H < 2000, which makes up most of the operating range of typical compact heat exchangers.     

Drag forces and heat transfer coefficients for spherical,cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers

This work is devoted to the numerical calculation of heat and fluid flow past spherical particles and non-spherical particles of various shapes. Although numerous works have investigated drag forces (c_d) for spherical and non-spherical particles, works about the Nusselt number (Nu) relations for non-spherical particles are rare. Motivated by this fact, as a first step we consider cuboid, spherical and ellipsoidal particles in steady-state regimes corresponding to Reynolds numbers (Re) from 10 up to 250. Due to the asymmetric flow existing when Re approaches the value of 250, all simulations are made using a three-dimensional domain. Good agreement was observed when our numerical results gained for the sphere were compared with published values for drag coefficients and Nusselt numbers. Based on the analysis of numerical results obtained for non-spherical particles we found out that in addition to the Reynolds number three geometry parameters influence particle-fluid interaction: the drag coefficient depends primarily on the normalized longitudinal length, while both the sphericity and the crosswise sphericity influence the Nusselt number. For that reason new correlations are developed for both the drag coefficient and the Nusselt number. The accuracy of the closures developed for c_d and Nu is discussed in a comparison with published models.     

Local analysis of heat transfer inside corrugated channel

Experiments are performed to study effects of hydrodynamic conditions on the enhancement of heat transfer for single phase flow. These experiments have been conducted for a wide range of Reynolds numbers, (0 < Re < 7500) in order to obtain the different regimes from steady laminar to turbulent. A two-dimensional corrugated test section which has been instrumented with thermocouples can be heated by electrical cartridges. The local temperature measurements are used to evaluate the local and global heat transfer coefficient of the wavy heat exchanger. As expected, the heat transfer is always higher than those in rectangular channel; it is essentially due to the mixing induced by the recirculation in the wake of the corrugations.     

Unsteady wake dynamics and heat transfer in forced and mixed convection past a circular cylinder in cross flow for high Prandtl numbers

This paper investigates the combined effect of Prandtl number and Richardson number on the wake dynamics and heat transfer past a circular cylinder in crossflow using a SUPG based finite element method. The computations are carried out for 80 < Re < 180, 0.7 < Pr < 100 and $0?\mathrm{Ri}?2$. The results have been presented for both forced and mixed convection flows. In the case of forced convection, crowding of temperature contours with reduced spatial spread is observed for increasing Prandtl numbers. The local and average Nusselt numbers are found to increase with increasing Reynolds number and Prandtl number. The average Nusselt number and Colburn factor are found to vary as Re^0.548 Pr ^0.373 and Re^?0.452, respectively. The extrapolated results of the average Nusselt number for low and high Reynolds numbers are found to match quite well with the available results in literature. Effect of Prandtl number shows various interesting phenomena for the mixed convective flows. Increasing the Prandtl numbers resulted in decreasing deflection and strength in the wake structures. The effect of baroclinic vorticity production during vortex shedding has been demonstrated at the vicinity of the cylinder and near wake. The Strouhal number is found to decrease with increasing Prandtl number, in the case of buoyancy induced flow. The effect of increasing Prandtl number is manifested as the stabilizing effect in the flow. This is, perhaps, the first time that such behavior for the Prandtl number is being reported. Additionally it is observed that the average Nusselt number decreases with increasing Richardson number.