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In this paper, turbulent airflow and heat transfer are studied numerically in a square sectioned channel which is rotating about a parallel axis. Channel rotation may create secondary flows as a result of centrifugal buoyancy and Coriolis forces which may increase the heat transfer coefficient and wall friction. Under certain conditions that the axial flow is dominant over the rotation, the effects of rotation can simply be ignored which means that friction factor and Nusselt number can be calculated regardless of rotation. This paper explores a novel criterion to demonstrate how the rotation affects the fluid flow and heat transfer. Rotational Grashof number ( Gr Ω ) and Reynolds number ( Re Ω ) are chosen to describe the rotation effects in addition to Reynolds number (Re) taking the axial flow into account. The results show that at a given Gr Ω and, Re Ω a specific Reynolds number ( Re ∗ ) in which the effects of rotation vanishes can be defined. It is revealed that Re ∗ may be presented as a function of Gr Ω only. With this regards, a non- dimensional group as Gr Ω a 1 / R e is obtained which is utilized to judge the rotational effects. It is shown that for Gr Ω a 1 / R e > 0.0167 the rotation starts to become important while for Gr Ω a 1 / R e 0.0167 the Nusselt number is approximately equal to stationary counterpart.

This paper analyzes the effects of input uncertainties on the outputs of a three dimensional natural convection problem in a differentially heated cubical enclosure. Two different cases are considered for parameter uncertainty propagation and global sensitivity analysis. In case A, stochastic variation is introduced in the two non-dimensional parameters (Rayleigh and Prandtl numbers) with an assumption that the boundary temperature is uniform. Being a two dimensional stochastic problem, the polynomial chaos expansion (PCE) method is used as a surrogate model. Case B deals with non-uniform stochasticity in the boundary temperature. Instead of the traditional Gaussian process model with the Karhunen-Lo e ve expansion, a novel approach is successfully implemented to model uncertainty in the boundary condition. The boundary is divided into multiple domains and the temperature imposed on each domain is assumed to be an independent and identically distributed (i.i.d) random variable. Deep neural networks are trained with the boundary temperatures as inputs and Nusselt number, internal temperature or velocities as outputs. The number of domains which is essentially the stochastic dimension is 4, 8, 16 or 32. Rigorous training and testing process shows that the neural network is able to approximate the outputs to a reasonable accuracy. For a high stochastic dimension such as 32, it is computationally expensive to fit the PCE. This paper demonstrates a novel way of using the deep neural network as a surrogate modeling method for uncertainty quantification with the number of simulations much fewer than that required for fitting the PCE, thus, saving the computational cost.

The paper investigates numerical results of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. The case with the thermal Rayleigh number, Ra T = 10 5 , the Prandtl number, Pr = 1 , the Lewis number, Le = 2 and height-to-width aspect ratio, A = 4 is considered. Effects of the buoyancy ratio of composition to temperature, N, on dynamical behavior, flow structure and heat and mass transfer efficiency are investigated carefully. The present results suggest that with the buoyancy ratio N increasing from 1 to 2, the flow of transition is a complex series of changes from the periodic to quasi-periodic, chaotic, periodic, and finally to laminar with concentration dominated. There are three types of periodic flows, the first one is simple periodic flow with single fundamental frequency (FF), the second one is periodic flow with FF and its integer multiple of frequencies (INTMF), the last one is the more complex periodic flow with FF, INTMF and its sub-harmonic frequency multiple (SFM). A new type periodical solution with reverse central symmetrical structure is captured in the present paper. Multi cells structures traversing between two vertical walls will produce salt figure phenomenon and benefit to enhance heat and mass transfer efficiency.

The main objectives were to develop a method for designing an effective finned heat exchanger through changing the configuration to ensure the tubes be streamlined shape. Kinds of inserts including, vortex generator, louver fin, and serrated fin in the heat transfer was used to increase the effect of thermal performance, but also was harmful to the flow characteristics. Consequently, the comprehensive performance was obviously lower than the heat exchangers with no inserts. In order to solve this problem, streamlined tube configuration was adopted in this paper to search a new method to enhance the comprehensive performance by reducing the Karman vortex street effect. Two modified configurations of tube were investigated in this paper. The modified configurations were both made of semicircular tube and semielliptical tube. The simulation was validated by Wang’s experiment and Arafat’s simulation. The numerical data were presented at Reynolds number in the range between 1300 and 2000. Based on the numerical results, the effect of elliptical axis ratio on the thermal hydraulic performance was discussed. The results showed that the comprehensive performance of the modified configurations was greater than that of the circular tube. In addition, the velocity vector, flow streamline and temperature contour of the configurations were displayed. The Karman vortex street effect was adopted to explain the reason of wake region formation. It can be concluded that long and thin section of heat transfer tube, which was coincident with streamlined design, was beneficial to improve the comprehension performance of the heat exchanger.

This paper reports a numerical investigation of fluid flow and heat transfer in a rectangular channel with delta-shaped winglet longitudinal vortex generators (LVGs) under different configurations. In addition to the conventional common-flow-down configuration and the common-flow-up configuration, a unique mixed configuration is suggested. The “method of images” is successfully adopted to analyze the dynamics of the longitudinal vortices due to wall interference. The Nusselt number, friction factor and overall performance coefficient for the three configurations are compared at various Reynolds numbers (all less than 2200), LVG row numbers, channel heights, and LVG aspect ratios. It is found that the channel height and LVG aspect ratio are the two most critical factors influencing the effectiveness of the different LVG configurations, which may explain why inconsistent conclusions have been presented by previous studies comparing the performance of the common-flow-down and common-flow-up configurations. When the channel height is relatively small, the unique mixed configuration is found to be the most effective at enhancing fluid mixing (and therefore improving heat transfer) at streamwise cross sections. When the LVG aspect ratio becomes large, the common-flow-down configuration outperforms the common-flow-up configuration. This paper sheds some insight on how to design the optimal LVG configuration for enhancing heat transfer performance.

This paper main goal is aimed at a paradigm shift in the enhancement of heat transfer rate between finned surfaces and surrounding fluid by presenting a novel approach in composite fins. This approach consists in using high thermally conductive coatings on top of the finned substrate in order to increase the local temperature along the fin washed surface. In the present paper a high thermal conductivity coating has been applied to an aeroengine vane of different shape and dimensions subject to icing conditions at high Reynolds numbers and where the main aim was to keep the vane warm as to avoid icing in aerospace applications. Numerical simulations have been carried out to ascertain the range of thickness of the coatings to be used to maximise the wanted effect. Both short Engine Section Stator (ESS) and longer fan Outlet Guide Vane (OGV) have been modelled, having different final goals. In the case of longer OGV, an additional novel design modification has been suggested to enhance further the heat transfer along the vane length by the use of the internal webs. The experimental validation also carried out at much higher Reynolds numbers than that reported in Buffone et al. (2005), demonstrate that the novel concept of heat transfer enhancement in composite fins is a simple and yet powerful strategy in a wide range of Reynolds numbers. A fin analysis has been performed of both the present ESS vane the fins tested in Buffone et al. (2005) at much lower Reynolds numbers and shows that the improvement obtained with the coated fins tested in Buffone et al. (2005) is much larger than the coated ESS vanes investigated in the present study. This said, the present study demonstrates that the use of high conductive coatings in composite fins can keep the ESS vanes ice free, something that was not possible with uncoated vanes. It is important to note that the actual optimal thickness of the thermally conductive coatings is a function of Biot number, fin shape, dimensions and thermal conductivities of fin substrate and coating; depending on the application, a proper design of the fin substrate and coating should be carried out.

In this paper, a weighted meshless spectral radial point interpolation method (MSRPIM) is implemented for the numerical solutions of a class of multi-term time fractional advection-diffusion problems with spatial and temporal dispersion. In the proposed methodology, meshless shape functions are used for discretization in space. These functions are generated via radial basis functions (RBFs) and point interpolation method. Weighted θ -scheme and first order finite differences together with a simple quadrature rule are employed for the discretization of time fractional derivatives. Efficiency and accuracy of the formulated method is validated in terms of number of nodal points N, time-step size τ and weight parameter θ ∈ [ 0 , 1 ] . Quality of the computed solutions are checked using E ∞ , E 2 and E rms error norms. Stability of the proposed method is analyzed theocratically and validated computationally, which is an important task of the current paper. Simulations reveal very good accuracy for both 1D and 2D test problems having constants and variable coefficients.

In this paper, a numerical method is developed to simulate the effect of an external magnetic field on convection heat transfer of a ferrofluid flow inside a rectangular duct. This model is two-dimensional, steady-state, laminar and incompressible. Simple finite volume method is used to couple and solve continuity, momentum and energy equations. In the first part of this paper, it is observed that ferrofluid particles movement along the magnetic field of a line dipole changes the streamline patterns and enhances heat transfer. In the second part of this paper, a sensitivity analysis is performed to investigate the effects of Reynolds number, magnetic field strength, location, and number of line dipoles on the convection heat transfer. It is observed that cooling rate is higher at larger Reynolds numbers while increasing magnetic field strength would not necessarily result in noticeable improvement in heat transfer. It is also noticed that magnetic field strength should be large enough to merge small vortexes and to create large circulation zones inside the duct. Our simulation also revealed that heat transfer could be augmented by adding line dipoles on high-temperature regions closer to the duct inlet.

According to the force balance analysis on a bubble, the bubble departure diameter in horizontal subcooled flow boiling is mainly influenced by quasi-steady drag force, surface tension force and bubble growth force while an additional force, buoyancy force, plays an important role in vertical flow boiling. In this paper, the effects of these forces can be concluded by a series of dimensionless parameters including density ratio of vapor and liquid, Prandtl number, Jacob number and bubble Reynolds number. Based on the different forces, two different characteristic lengths are adopted to non-dimensionlize bubble departure diameters in horizontal flow boiling and vertical flow boiling, respectively. Finally, the semi-empirical correlations for bubble departure diameters in both horizontal and vertical subcooled flow boiling are proposed in this paper based on the force balance analysis and available experimental data from literature. The predicted results using the present correlations agree fairly well with the experimentally measured values with a mean relative error of 19.72%.

The aim of the present paper is to study experimentally the enhancement of heat transfer, due to the presence of a layer of aluminum foam covering a smooth circular cylinder. The measurements are carried on with the impingement of a rectangular jet of air, which has a transversal dimension equal or smaller than the cylinder diameter, or jet flow, and full flow (or uniform flow, which has a greater dimension than the cylinder diameter). Literature does not report any paper dealing with this multiple problem. Experimental heat transfer and fluid dynamics measurements are carried out at Reynolds number ranging from ReD=2200 to ReD=24,750. The layer of the aluminum foam, 8 mm thick, is glued onto the smooth cylinder, with an external diameter of D = 10 mm. The height of the slot jet is H = 10 mm, with a width of W = 135 mm. Jet flow visualizations are performed for the smooth and the foam-covered cylinder to explain the heat transfer results from the fluid dynamics point of view. The flow visualizations show that the jet flow always penetrates into the foam, wetting it completely, while the reattachment never occurs downstream. In the smooth cylinder, the jet completely envelops the cylinder, at greater Reynolds numbers and a distance of x/H = 7, with a small recirculation zone, showing that the rear surface also participates in the heat transfer. The heat transfer on the foam-covered cylinder increases, mainly, because of the large increase in the exchange surface, while it is somewhat penalized, at the higher Reynolds values and at the greater distance from the slot exit, because the rear surface is little involved in the heat transfer.

In this paper, we experimentally investigated the effect of turbulent intensity on heat transfer in a square rotating channel. The grid generated turbulence is measured by hot-wire, and the heat transfer coefficient is measured by TLCs. In the experiment, the Reynolds number, based on the channel hydraulic diameter ( D = 80 mm ) and the bulk mean velocity ( V m = 1.82 m / s ), is 10,000, and the rotation number ranges from 0 to 0.52. The mean density ratio ( d . r . = ( T w - T b ) / T w ) is about 0.1 in the current work using transparent heater glass (Indium Tin Oxide) to provide uniform heat flux. Two different turbulent intensity of inlet air (0.6% and 5.5%) are taken into consideration to investigate the heat transfer distribution on the leading and trailing side. The results show that turbulent intensity has an effect on heat transfer on both leading and trailing side, especially at rotating conditions. At static conditions, the effect of turbulent intensity on heat transfer is not obvious. However, with the increase of rotation number, in case B with a medium turbulent intensity (Tu) of 5.5%, the Nu/Nu0 is about 10% higher than that in the case A with low turbulent intensity of 0.6% with the rotation number of 0.52 at X/D = 2 on trailing side. The enhancement of case B decreases along X/D directions. On the leading side, the turbulent intensity has same effect on heat transfer with that on trailing side, but not as prominent as that on the trailing side. In current work, the turbulent intensities at different X/D directions are also presented to explain the phenomenon of heat transfer in the channel. More detail of results will be presented in this paper.

The discharging process causes the multiple physical field coupling problem, which make it complicated to analyze the heat effect of discharging arc. The heat effect of the arc can be divided two parts including the heat effect of the arc column and the heat effect on the cathode surface. Therefore, this paper proposes an equivalent heat source to be equivalent to the two parts heat effect of the arc and simplifies the process for thermal analysis of the arc. Firstly, this paper analyzes the heat source characteristics of the arc based on MHD model. According to the heat source characteristics of the arc, this paper proposes respectively using ellipsoid heat source and Gaussian surface heat source to be equivalent to the two parts of the heat effect of the arc. Then the equivalent heat source is used to calculate the temperature distribution of tip-plane electrode under discharging. Comparing with the numerical results in MHD model, the error between the two models is within 0.5%, which proofs that the equivalent heat source can be used to equivalent to the heat effect of the arc. Moreover, this paper discusses the method to determine the parameters of the equivalent heat source. Finally, an experiment is carried out to verify the accuracy of the MHD model and the equivalent heat source of the arc.

This paper presents a detailed numerical study regarding the influence of Reynolds and Richardson numbers in T-junctions with circular cross-section. The numerical investigation is based on the wall-resolved Large-Eddy Simulation (LES), which has been experimentally validated. The Reynolds number in the main pipe covers a range from R e = 78400 to R e = 235200 , which is high enough to approach the engineering applications. This also belongs to the primary contribution of the current study. Furthermore, the temperature difference between the main pipe and branch pipe ( T m − T b ) is 180 K and the mass flow rate ratio ( m ˙ m / m ˙ b ) is 3. The primary focus is on thermal mixing characteristics in the downstream as well as on the evolution of the flow by consideration of gravity and buoyancy effects. Additionally, our study considers the thermal field and its corresponding fluctuations in the near-wall region. In addition, this paper also includes simulations with different T-junction configurations therefore we can examine the influence of the entrance orientation of the heavier cold branch pipe fluid on the mixing process and heat transfer. The analysis of our results indicates that gravity effects can be neglected in cases with increased Reynolds number and simultaneously decreased Richardson number. The area with high fluctuation intensities becomes larger by the higher Reynolds number and lower Richardson number of the mixing flow therefore they shows a higher potential for High Cycle Thermal Fatigue (HCTF). Furthermore, the highest near-wall thermal fluctuations are 40 % of the temperature difference between the mixing flows.

This paper presents a novel configuration suitable for latent-heat thermal energy storage systems based on the use of phase-change materials (PCMs). It is a double-pipe unit with a helical fin attached to the inner tube in which a heat-transfer fluid (HTF) flows. Experiments in the unit are performed both for regular conditions, when its shell is exposed to ambient air, and for a slightly heated shell which allows to achieve close-contact melting (CCM). It is clearly shown that CCM in the suggested unit is possible and shortens the melting time by a factor of three. In addition to the experimental demonstration, the paper includes comprehensive modeling of the unit. Both analytical and numerical models are included, describing the phenomenon of close-contact melting on a helical surface. The analytical model, made possible under the assumption that the fin is isothermal, accounts for other main features of the process and also reveals its governing dimensionless parameters, including the Fourier, Stefan, Archimedes and Prandtl numbers, along with the group representing the unit geometry. The numerical model includes a complete solution for the time-dependent fin temperature distribution, and can account also for the sensible heat of the PCM. A very good agreement of the numerical predictions and experimental findings is achieved. Then, a dimensional analysis, based on the analytical model, is applied to the numerical results. Generalized behavior is obtained for such parameters as the temperature difference between the heat-transfer fluid and the PCM, and the helical fin pitch. The analysis is then extended to a non-isothermal fin, suggesting an additional physically-meaningful dimensionless group which completely generalizes the results for different fin radii, fin thicknesses and fin-to-PCM volume ratios. It is argued that the suggested configuration may have a number of advantages in comparison with the existing fin-array systems. These advantages include enhanced melting, prevention of increased pressures in melting (or solidification if the material is anomalous like water) and voids in solidification, and highly-convenient handling and maintenance of the system. Also, the helical fin might be attached to the outer tube (shell), and a configuration in which the HTF flows across the shell is possible while preserving all important features of the unit explored.

The paper presents results of an investigation into mixed convection in a vertically oriented microchannel with slip boundary conditions. Solutions of the problem were obtained analytically and using a numerical approach based on the Lattice Boltzmann method (LBM). The solution yields relations, which enable estimating velocity and temperature profiles and the Nusselt number as functions of the Knudsen, Rayleigh and Prandtl numbers. It was shown that Knudsen number effects are prevailing in the vicinity of the wall, whereas near the centerline of the channel effects of the Rayleigh number are stronger. If the Rayleigh numbers are high, velocity profiles demonstrate M-shapes with a point of minimum at the channel centerline, whereas temperature profiles flatten so that the fluid temperature in the channel cross-section tends to the wall temperature. The temperature jump magnitude on the wall is dependent on the Prandtl number value and decreases with the increasing Prandtl numbers. For almost all combinations of the parameters considered in this paper, higher Knudsen numbers entail heat transfer deterioration except for the case of Pr = 10 and Ra = 100. Increasing the Knudsen number diminishes hydraulic resistance for low Rayleigh numbers, but for high values of the Rayleigh numbers the trend is reversed. It was shown that mixed convection in microchannels can be successfully simulated using the LBM methodology, whose deviation from the analytical solution and is less than 1%.

This paper numerically studied the Re-independence of turbulent flow and pollutant dispersion around five scaled building models. The RANS-based CFD model, hereafter called numerical wind tunnel (NWT) model, was validated by wind-tunnel experiments and applied to investigate the flow-structure independence on building Reynolds number (ReH) and roughness Reynolds number (Rer). The ratio of relative change (RRC) was used to evaluate the Re-independence with 5% selected as the threshold. The results show that the critical ReH (ReH,crit) is strongly affected by the building structure, particularly the building height. However, the value of the critical Rer (Rer,crit) in the pedestrian level plane changes very little with the different building models, which is suggested to be 25 in terms of the RRC criterion. Distributions of dimensionless velocity and concentration in the pedestrian level planes validated this suggested value. For the RANS turbulence models tested in this paper (high Reynolds number model and low Reynolds number model) the predicted value of Rer,crit is independent on the model. This work improves the understanding of Re-independence in the investigation of the flow and pollutant dispersion by using wind-tunnel experiment.

Heat transfer enhancement technology has been widely used in heat exchangers. The six-start spirally corrugated tube is a novel heat transfer tube, and its flow resistance characteristics have not been studied. In this paper, the flow resistance characteristics of the six-start spirally corrugated tube are studied. Specifically, the effect of influencing factors such as geometric parameters (pitch and corrugation depth), fluid properties and Reynolds number on flow resistance of the six-start spirally corrugated tube are studied. The results show that, firstly, the six-start spirally corrugated tube has a better heat transfer performance than both the circular tube and four-start spirally corrugated tube, and its flow resistance is situated between circular tube and four-start spirally corrugated tube. Secondly, with the increasing of the pitch p of the six-start spirally corrugated tube, both the pressure drop ΔP and resistance coefficient f are decreasing gradually. Thirdly, the increase of corrugation depth e can lead to a large flow resistance, so it is not recommended to adopt an excessive increase in the corrugation depth e. The effect of fluid properties on flow resistance in tube is not obvious, and the changing rate of ratio fe/fs of all working media are almost the same. Moreover, with the increasing of Reynolds number Re, resistance coefficient f both in the six-start spirally corrugated tube and circular tube are decreasing gradually. Finally, based on the above research data, the criterion correlation for flow resistance calculation in the six-start spirally corrugated tube is obtained. It can be concluded that the six-start spirally corrugated tube studied in this paper has a smaller flow resistance than the commonly used four-start spirally corrugated tube. This work can provide some advices for the future research of reducing flow resistance in spirally corrugated tube or other related devices.

Motivated by applications in concentrating solar power plants, the paper presents direct numerical simulations of the turbulent upward-directed flow of a liquid metal in a vertical channel. One of the walls features a backward-facing step with the vertical wall behind the step being heated. The paper addresses the impact of buoyancy effects by comparing two simulations, one with the buoyancy term removed from the equations, the other one with a Richardson number of 0.338. After a thorough validation detailed statistical data for both cases are provided. Due to the buoyancy forces acting on the fluid at the heated wall, the flow field is substantially altered and recirculation is considerably diminished. The altered flow field and the increased advection of temperature increase heat transfer at the heated wall. The differences in the turbulent heat fluxes are thoroughly discussed and related to the altered flow conditions. The results contribute to the physical understanding of buoyancy effects on turbulent heat transfer in the considered regime. Furthermore, the generated data allows the validation and improvement of turbulence models for turbulent heat transfer in the range of low Prandtl numbers.

Structured non-wetting surfaces provide alternating no-slip and partial slip boundary conditions to the fluid flow which, in turn, affects the convective heat transfer performance over the surfaces. In this paper, an analytical model is developed for the interfacial Nusselt number, the overall Nusselt number and a thermal hydraulic performance factor for fluid flow in a cylinder patterned with structured non-wetting surfaces, for the two cases of uniform wall heat flux and uniform wall temperature. In addition, by considering the stability of the Cassie state of wettability and its transition to the Wenzel state for flow over superhydrophobic surfaces, the present model overcomes certain limitations of the previously reported studies in the literature. Based on the analytical formulations and the stability constraints, the present paper provides optimum design maps for tailoring structured non-wetting surfaces for maximizing convective heat transfer and the combined thermal-hydraulic performance in applications. Use of the design maps on example cases is also discussed. It is shown that the use of structured non-wetting surfaces is most effective for low Reynolds numbers and/or small cylinder radius.

Turbulent heat transfer attracts continuous attention from researchers due to the high convective heat transfer performance. In the mini-channel heat sink, turbulent heat transfer enhancement measures may improve the heat transfer coefficient further and reduce the mass flow rate. However, there is lack of turbulent heat transfer enhancement researches in the mini-channel heat sink due to the difficulty caused by entrance effect. In this paper, a novel heat transfer enhancement concept of enhancing the original flow pattern was successfully applied to enhance the turbulent heat transfer in the mini-channel heat sink. The investigation was carried out in a mini-channel heat sink whose substrate size was 50mm × 50mm with Reynolds number ranging from 3600 to 6800. The original flow pattern in the conventional heat sink was revealed firstly. Subsequently, the v-ribs roughness was applied to generate multi-longitudinal swirls flow so as to enhance the original flow pattern. The numerical results indicated that the variation ranges of Nu/Nu0, f/f0, EEC, and R3 were 1.71–3.55, 2.76–7.99, 0.32–0.89, and 1.12–2.06, respectively, in the mini-channel. Besides, the maximum average heat flux of the substrate could achieve 5.79 W/mm2 within a temperature difference of 60 K. In addition, this paper also investigated the thermal resistance and irreversibility in the mini-channel heat sink. This work may promote the development of heat transfer enhancement.

To study the heat transfer and flow characteristic of supercritical CO2 cooling in the spirally fluted tubes, this paper presents numerically investigation of heat transfer performance of various cases within different geometric parameters (the radius of the groove r1, the radius of the fillet r2, the depth of the groove e1, the distance between the main tube and the outer sleeve e2 and the helix angle w). Based on the verified turbulent model at an inlet temperature of 323.15 K, an operating pressure of 8.0 MPa, an inlet Reynolds number of 35,000 and a total heat of 4200 W, the optimal structure is obtained (r1 = 6.5 mm, r2 = 2.0 mm, e1 = 5.5 mm, e2 = 1.0 mm, w = 0.70 rad) according to the evaluation factors proposed in the paper. The representative parameters (e1 and w) are employed to investigate the variation of the local heat transfer coefficient and turbulent kinetic energy, and mechanisms underlying the effect of parameters on heat transfer are revealed. Furthermore, the buoyancy effect is also discussed. Results show that the buoyancy force has an improvement effect on the heat transfer performance. However, as w increases, the influence of buoyancy will be weakened.

In this paper, conjugate gradient method (CGM) considering variations in material properties with temperature is developed to solve transient inverse heat conduction problems. With CGM, the measured outer wall temperatures of supersonic combustor are used as input data to recover the heat flux and temperature on the inner wall. Numerical test has been done to study the effect of temperature measurement noises on accuracy of the inversion result. It indicates that the inversion results are very close to the exact heat flux with a maximum error of less than 5% when the measurement noise is less than +/- 3 K. At the same time, a series of experiments are conducted on a Mach 3 supersonic combustor test facility with varied fuel injection conditions. The heat fluxes on the inner wall are recovered by measured outer wall temperatures via CGM. The inversion results of heat flux agree satisfactorily with the values measured by heat flux sensors and a maximum difference of less than 5% is found. The present comparison results prove the validity and accuracy of the CGM developed in the paper for estimation of the wall heat flux of supersonic combustor. (C) 2016 Elsevier Ltd. All rights reserved.

Experimental investigations on heat transfer in a circular pipe for laminar, transitional and turbulent flow are presented. Reliable prediction of heat transfer coefficients for transitional flows is still a challenging task. While methods for predicting laminar and turbulent heat transfer coefficients are widely established in literature, the proposed methods and the validity for calculating according values for the transition region and even the definition of this region itself remains a field of ongoing development. One aspect in this picture is the scarce availability of experimental data on heat transfer coefficients in circular pipe flow for Reynolds numbers in the range of 1000 Re 4000 , especially for higher Prandtl numbers, i.e. 10 Pr 90 . Thus, this paper focuses on providing experimental results for heat transfer in circular pipe flow for Reynolds ( Re ) numbers in the range of 500 Re 23000 and 7 Pr 41 . The test fluid is a water–glycol mixture with a mass fraction of water of x m = 0.477 . The results presented in this paper show good agreement with the widely used calculation methods proposed by Gnielinski in 2013 for laminar, transitional and turbulent flow. The results also confirm the presence of the transition region to occur between 2300 Re 4000 . 184 data points in the range of 1000 Re 4000 are shown, since in this range scarce data are available in literature. In summary 261 heat transfer coefficients for 500 Re 23000 and 7 Pr 41 are presented, which show good agreement (80.8% are within ±15%) to the cited literature.

In this paper the non axisymmetric longwave instability of a thin viscoelastic liquid film flowing down a vertical heated cylinder is investigated. The stability of the film coating a cylinder in the absence of gravity is also investigated. In a previous paper it is found that viscoelasticity stimulates the appearance of azimuthal modes but the axial mode is the most unstable one. Other calculations in a former paper show that for flow outside a heated cylinder azimuthal modes can be the more unstable when the Marangoni number is large and, in particular, when the Reynolds number and wavenumber are small. Therefore, the small wavenumber and large cylinder radius approximation is assumed with the simultaneous action of viscoelasticity and thermocapillarity on the stability of azimuthal modes. In the presence and in the absence of gravity, it is found that, in comparison with the Newtonian case, it is easier to excite the azimuthal modes when viscoelasticity and thermocapillarity destabilize at the same time. Moreover, it is shown that, despite the axial mode is the most unstable one, there are wide wavenumber ranges where higher modes are the more unstable and they can show up by means of a periodic time dependent perturbation.

This paper focuses on the application of the Generalized Leveque Equation (GLE) to circular pipe flow with hydrodynamic and thermal developing flow describing the analogy between heat and momentum transfer. As shown theoretically by other authors, this analogy should be applicable to laminar and turbulent developing flow, in which the hydrodynamic exceeds the thermal boundary layer, i.e. for high Prandtl numbers. The question is, whether this fact can be proven experimentally, and above which Prandtl number is this applicable to a hydrodynamic and thermal developing circular pipe flow. Thus, this paper presents results of an experimental investigation on pressure drop and heat transfer for laminar, turbulent and transition flows in a circular pipe to check the applicability of the GLE for a wide range of Prandtl numbers. Experimental data for heat transfer coefficients are compared to heat transfer coefficients calculated from pressure drop data with the GLE. Reynolds numbers range between 500 x m = 0.477 . The results show that the GLE is applicable to hydrodynamic and thermal developing laminar and turbulent flow in a circular pipe for Pr > 30. It is also shown that as soon as the hydrodynamic boundary layer thickness is triple the thermal one, the analogy between momentum and heat transfer according to the GLE is suitable for laminar circular pipe flow.

This paper presents geometric optimization and flow parameters modelling for subcooled flow boiling (two-phase flow). The objective of the paper was to minimize the thermal resistance of the microchannel heat exchanger subject to fixed volume constraints of heat sink and microchannel. The geometric and flow parameters were allowed to morph, according to the constructal design principles to obtain their optimized values. The flow was highly subcooled at inlet temperature of 25 °C using deionized water as the cooling fluid and aluminium as the heat sink material. Velocities between 0.1 and 4.5 m/s and heat fluxes between 100 and 1200 W/cm2 (1 × 106 W/m2 and 1.2 × 107 W/m2) were used in the modelling and optimization. Computational fluid dynamics code, ANSYS was used for both the simulations and the optimization of the configurations. The numerical code used for the simulations was validated by available experimental data in the literature and the agreement showed the capability of CFD (ANSYS) to predict accurately, subcooled flow boiling (two-phase flow) in rectangular microchannel heat exchangers for cooling of microelectronic devices. Comparisons were made between two-phase flow and single-phase flow by using their optimized geometric and flow parameters, and the results clearly demonstrated the superiority of two-phase flow regime in rectangular microchannels for removal of high heat fluxes at low Reynolds numbers. As the optimized Reynolds number increases, the minimized thermal resistance (peak temperature) decreases which is consistent with previous results obtained in the open literature. Results further show the aspect ratio, the optimized diameter and axial length of the microchannel as a function of the dimensionless pressure drop number (Bejan number).

In this paper, three-dimensional Green’s functions for transient heat conduction problems in general anisotropic bimaterial are obtained based on two-dimensional Fourier transform and Laplace transform, and are separated as a sum of a full-space Green’s function and a complementary part. We can get the bimaterial Green's functions in the transformed domain by boundary conditions, and then in the physical domain by the inverse Fourier and Laplace transform. Although the present paper aims to develop Green's function in anisotropic bimaterial, the derived solutions can be reduced to simple cases, such as in isotropic or orthotropic materials, and in half-space or full-space. Moreover, this method can be extended to derivation of new Green’s functions in multi-layer materials. Numerical examples are presented to verify the validity and applicability of present solutions. When the source is constant and time extends to infinity, the present transient solution approaches the steady one. Besides, the anisotropic solution indicates high correlation with the properties of material.

The determination of the effectiveness of large heat wheels using standard measured data and test conditions can be very expensive and time consuming. The main contribution of this paper is that it tests heat wheel components rather than the wheel itself. In addition, this paper deals directly with the question of what accuracy can be achieved for the determination of sensible energy effectiveness by using a transient step change method for the exchanger matrix materials in a test cell. In this study, the sensible effectiveness of heat wheels is predicted by performing a number of cyclic and single step change transient experiments on a parallel-plate heat exchanger. A new experimental facility is developed to cause a step change for the inlet air temperature of the exchanger. In the cyclic tests, the heat exchanger is exposed to a periodic inlet temperature steps; afterward, the sensible effectiveness of parallel-flow and counter-flow heat wheel, comprised of the same material as parallel-plate exchanger, is determined using the obtained temperature profiles. It is find that this method can be used to determine the sensible effectiveness of parallel-flow heat wheel. However, the high uncertainty found in the sensible effectiveness of counter-flow heat wheel, ±32%, makes the results unreliable. In the single step-change test, a time constant is assigned to the exchanger response when it is subjected to a step change in inlet temperature. The time constant is obtained by fitting the experimental data to a first order exponential time response curve. An analytical solution posits that the effectiveness of the heat wheel depends only on the product of the time constant and the wheel angular speed, or angle ratio. Comparing values of the sensible effectiveness calculated through available empirical correlations and the ones obtained by single step change experiment showed less than 3% difference in results when the heat capacity rate ratio is greater than 5. It is concluded that due to simplicity, accuracy, and low cost of the single step change experiments, it is the preferred method to determine the effectiveness of heat wheels operating at a specified rotary speeds, provided the flow channel geometries and Reynolds numbers for both the wheel and the small-scale test cell.

In this paper, the MRT (Multiple Relaxation Time)-D2Q9 model and the MRT-D2Q5 are employed to simulate the flow and heat transfer of laminar confined impinging jet flow. For impinging jet flows, the paper considers the effect of Reynolds numbers and jet-impingement surface distance ratio (H/W) on the flow and temperature fields. As for the investigation of heat transfer behaviors on stagnation Nusselt number, it is evident that the effect of H/W is not significant. The Nu number increases dramatically with increasing Reynolds number. And what’s more, this study presents flow and heat transfer predictions of slot jets impinging on cylinder and obtains distribution of Nusselt numbers around the cylinder for different Reynolds number.

This paper is the second part of our study on the behavior of the interaction between twin transitional round fountains with equal power in a homogeneous fluid. In the first part (Mahmud et al., 2015), an experimental study using PIV techniques and flow visualization was carried out over the ranges 1⩽Fr⩽5 and 25⩽Re⩽400, where Re and Fr are the Reynolds and Froude numbers, respectively. In the current paper, this work is extended to wider ranges, i.e., 1⩽Fr⩽10 and 25⩽Re⩽1000, by a series of three-dimensional direct numerical simulation (DNS). In addition, a preliminary study on the effect of the distance between the two fountain sources is also carried out for three representative cases. The DNS results are found to capture all the major features of the steady, and unsteady weakly multi-modal and strongly multi-modal interaction behavior, which is dominated by bobbing and flapping motions, as found by the experimental study (Mahmud et al., 2015), but over wider ranges of Fr and Re. Furthermore, the maximum fountain penetration height and the maximum thickness of the interaction region, obtained with the DNS, together with the experimental results of (Mahmud et al., 2015), are quantified and compared to the available scalings for single fountains in a homogeneous fluid at comparable Fr and Re values, and several scaling relations are then developed for these parameters over the ranges of Fr and Re considered in the current study.

This paper reports thermal performance of porous latent heat thermal energy storage (or LHTES) system filled with nano-phase change material (or nano-PCM). In the first part of the paper, scale analysis is executed to estimate the extent of the complete phase change process which is a key factor of designing LHTES systems. The scale analysis results in simplified relationships among different non-dimensional parameters (i.e., Fourier number, Stefan number, Rayleigh number, Nusselt number, porosity of the porous medium, and nano particle volume fraction). In the second part, the natural convection melting process of nano-PCM inside the porous medium is solved numerically. For the porous medium the Darcy model is employed. The numerical simulation serves two purposes: (i) it verifies the correctness of the relationships proposed by scale analysis in the first part of the paper and (ii) it identifies the effects of nano-particle volume fraction, time, and Rayleigh number, on flow field, thermal field, and heat transfer process during the melting of nano-PCM inside the thermal energy storage system. The proposed scaling relationships can be applied to predict the progress and execution of LHTES system filled with porous medium saturated by nano-PCM.

In this paper, we compare the Marangoni effect and the effect of the Prandtl number variation on features of the liquid film rupture under the action of a thermal load and show a principal difference between these two effects. Results of computational analysis allow us to make the following conclusions. When affecting on the free surface of the plane liquid film by thermal beam, in order to obtain the initial holes of the same size in films with various thermal physical properties, one should apply a thermal load of a certain well-defined type, more specifically, concentrated thermal load, which provides the predetermined temperature at least on one of the film boundaries. In this case the size of the holes will depend only on the width of a thermal beam applied to the film free surface. Paper presents the solutions of the model problems.

In the paper, being the first part out of two (the second one is focused on processes of heat transfer), results of the computer simulations of the flow in a circular pipe with a ball inserts turbulising the flow are presented. An influence of the diameter of balls and their longitudinal distance on a pressure drop in the turbulent flow as a function of the Reynolds number (for Re = 10,000 ÷ 300,000) was analyzed. The investigations were carried out for different diameters of the balls (Db = 7, 10, 13, 16 and 19 mm) and different distances between them (L = 20, 24, 28, 32, 36, 40, 48, 60 and 85 mm) at a constant inner diameter of the tube (Dp = 26 mm). The results indicate that for the whole tested range of ball diameters and their longitudinal arrangements, there is an analytical dependency which allows for expressing a friction factor by the relationship: f = A⋅ReB. The constants A and B were functions of two variables: a dimensionless diameter of the ball (X = Db/Dp) and a dimensionless longitudinal distance between balls (Y = L/Dp). These two constants are closely related. They can be calculated analytically for the entire range of X and Y using a formula of the fourth order surface polynomial (15 coefficients of that polynomial are presented in the paper). The paper presents also experimental investigations carried out using a PIV (Particle Image Velocimetry) apparatus. A comparative analysis of selected inserts and numerical calculations was the goal. The obtained results show a good correlation between the experiment and computer modelling.

In this paper calculations are done of the flow instability of a shallow horizontal fluid layer under an inclined temperature gradient for Prandtl numbers of magnitudes Pr > 1. In a previous paper (Ortiz-Perez and Davalos-Orozco, 2011 [17]), the range of values investigated were Pr ⩽ 1. There, the magnitudes of the horizontal Rayleigh number investigated were far larger than those used in the literature and it was found the new oblique oscillatory mode Obo . In the present paper it is found that this oblique oscillatory mode still appears for Pr = 2. Further, it is also shown that some modes become irrelevant when the Prandtl number is increased, and different modes become the first to go unstable. An important result is that above a large enough Prandtl number, the curves of criticality remain almost the same. Therefore, the limit Pr → ∞ is employed to calculate useful analytical expressions for the longitudinal modes of criticality which cover almost all the range of horizontal Rayleigh numbers. In contrast to the authors previous results, in this paper it is shown that for Pr > 1 the transversal oscillatory mode has a range, in the horizontal Rayleigh number, as the first unstable one which first increases and then decreases with Pr, but never disappears.

The steady laminar boundary layer flow over a perforated plate, in the presence of suction, moving in a parallel stream with constant velocity is investigated in this paper. The temperature boundary condition on the plate is a convective condition. In contrast to the majority of the previous works, in the present paper the heat transfer coefficient and the suction velocity are constant and the problem is non-similar. The results are obtained with the direct numerical solution of the governing equations. The problem is governed by Prandtl number, the Biot number, the velocity ratio parameter and a streamwise parameter and the influence of these parameters on the results are presented in tables and figures. It was found that the temperature reaches an asymptotic state and an analytical solution has been found for the calculation of wall temperature at the asymptotic state.

This paper focuses on temperature rise due to the viscous dissipation in liquids flowing through micro-channels. In the past, equations for the prediction of the temperature rise have been obtained as a function of the friction factor, Reynolds number and Eckert number or a similar form, starting from Navier–Stokes equation and energy equation under the assumption of fully developed laminar flow by researchers. The temperature rises calculated from the equations have been compared with experimental data and the equations have been validated. However, in this paper, a new equation for the prediction of the temperature rise is simply obtained from the first law of thermodynamics without restriction of fully developed laminar flow.

The present paper investigates heat and mass transfer over a moving porous plate with hydrodynamic slip and thermal convective boundary conditions and concentration dependent diffusivity. The similarity representation of the system of partial differential equations of the problem is obtained through Lie group analysis. The resulting equations are solved numerically by Maple with Runge–Kutta–Fehlberg fourth–fifth order method. A representative set of results for the physical problem is displayed to illustrate the influence of parameters (velocity slip parameter, convective heat transfer parameter, concentration diffusivity parameter, Prandtl number and Schmidt number) on the dimensionless axial velocity, temperature and concentration field as well as the wall shear stress, the rate of heat transfer and the rate of mass transfer. The analytical solutions for velocity and temperature are obtained. Very good agreements are found between the analytical and numerical results of the present paper with published results.

Transient heat or mass transfer to a spherical drop of a dielectric fluid suspended in another dielectric fluid in the presence of steady and time periodic electric fields (both uniform and non-uniform) is investigated in this paper. The internal problem or the heat (mass) transfer limit that corresponds to the bulk of the resistance being in the dispersed phase is addressed. Using a finite volume formulation, the energy conservation equation is solved to obtain the transient temperature distribution and the overall Nusselt number for the drop Peclet numbers from 0 to 10,000 and the dimensionless frequency (ω∗) from 0 to 50,000 using a fully implicit method. Application of steady and time-periodic fields leads to fluid circulation in the drop which provides an increase in the heat (mass) transfer rate. At first glance one might expect that the time-periodic field, which gives rise to a continuously varying flow field, might provide better mixing and improved heat (mass) transfer enhancement compared to time invariant one which gives rise to a steady flow field. However results show that for low to moderate Peclet numbers, the steady electric field is more effective in heat transfer enhancement compared to non-uniform time periodic field which in turn is more effective than the uniform time-periodic field. This counterintuitive heat (mass) transfer behavior is explained in detail in the paper. On the other hand, at high Peclet numbers, the non-uniform time periodic field provides significant improvement in heat (mass) transfer relative to steady uniform electric field. We show that at high Peclet numbers the maximum heat (mass) transfer enhancement is obtained when the dimensionless electric field frequency is of the order of Peclet number or ω∗ ∼ O(Pe). By tracking Lagrangian fluid particles, it is revealed that application of non-uniform unsteady electric field results in chaotic advection at high Pe whereas steady and unsteady uniform electric fields do not.

The development of efficient solar thermal receivers has received significant interest for solar to electrical power conversion and heating applications. Volumetric flow receivers, where the incoming solar radiation is absorbed in the volume of a heat transfer fluid (HTF), promise reduced heat loss at the surface compared to surface absorbers. In order to efficiently store the thermal energy in the volume, nanoparticles can be suspended in the HTF to absorb the incoming radiation. In such systems, compact models are needed to design and optimize the performance. This paper presents an analytical model that investigates the effect of heat loss, particle loading, solar concentration and channel height on receiver efficiency. The analytical model was formulated by modeling the absorption of solar radiation by the suspended nanoparticles as a volumetric heat release inside the flowing HTF. The energy equation was solved with the surface heat losses modeled using a combined radiative and convective heat loss coefficient. The analytical solution provides a convenient tool for predicting the effect of different parameters, in terms of dimensionless numbers (Pe, NuE, G ¯ , and θamb), on two-dimensional temperature profiles and system performance. By combining the receiver efficiency with a power generation efficiency, idealized by the Carnot efficiency, an optimum receiver length where the total efficiency is maximized is determined. However, in practice, the maximum efficiency depends on the maximum allowable temperature of the working HTF. As a case study, predictions were made for Therminol® VP-1 with suspended graphite nanoparticles in a 1 cm deep channel with a solar concentration of 10. The model predicts an optimum total system efficiency of 0.35 for a dimensionless receiver length of 0.86. Finally, the analytical model was used to estimate the optimum efficiency and the corresponding optimum receiver length for different design configurations with varying NuE and G ¯ . The results from this paper will help guide experimental design of volumetric flow receivers for solar thermal based power systems.

This paper presents the new development on the turbulent Prandtl number distribution models which are used to improve the computation accuracy of film cooling effectiveness distribution in the frame of the isotropic turbulence models. In the new developed turbulent Prandtl number distribution models, the turbulent Prandtl number varies with some characteristic quantity of the film cooling to make the models applicable for more film cooling cases effectively. A new VTG-Pr t model is developed for the computation of film cooling cases in which the wall is mainly influenced by the mixing layer region between the jet core and the mainstream. The Pr t value in this model varies with dimensionless temperature gradient which is suggested to be the characteristic quantity of the mixing layer region. The VTG-Pr t model has been used in the computations of long cylindrical hole film cooling, short cylindrical hole film cooling, compound angle cylindrical hole film cooling and expansion shaped hole film cooling in the present paper. And it is validated to be an effective and easy way to obtain accurate film cooling effectiveness distributions for this kind of film cooling. But for the kind of film cooling, in which the wall is mainly influenced by the jet core region and the influence of heat diffusion in the mixing layer region on the cooling effectiveness is very small, the VTG-Pr t model is disabled. Another turbulent Prandtl number distribution model, named VT-Pr t model, is developed for this kind of film cooling in the present paper. The Pr t value in this model varies with dimensionless temperature which is suggested to be the characteristic quantity of the jet core region. Good agreement between the computed and measured results is obtained through the use of VT-Pr t model in the computation of converging slot hole film cooling.

Power optimization approaches are unified for various energy converters, such like: thermal, solar, chemical, and electrochemical engines. Thermodynamics leads to converter’s efficiency and limiting power. Efficiency equations serve to solve problems of upgrading and downgrading of resources. While optimization of steady systems applies the differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. In reacting systems chemical affinity constitutes a prevailing component of an overall efficiency, so that power is analyzed in terms of an active part of chemical affinity. The main novelty of the present paper in the energy yield context consists in showing that the generalized heat flux Q (involving the traditional heat flux q plus the product of temperature and the sum products of partial entropies and fluxes of species) plays in complex cases (solar, chemical and electrochemical) the same role as the traditional heat q in pure heat engines. The presented methodology is also applied to power limits in fuel cells as to systems which are electrochemical flow engines propelled by chemical reactions. The performance of fuel cells is determined by magnitudes and directions of participating streams and mechanism of electric current generation. Voltage lowering below the so-called idle run voltage is a proper measure of cells imperfection. The voltage losses, called polarization, include three main sources: activation, ohmic and concentration polarization. Examples show power maxima in fuel cells and prove the suitability of the thermal machine theory to chemical and electrochemical systems. The main novelty of the present paper in the FC context consists in introducing the effective or reduced Gibbs free energy change between products p and reactants s which take into account the decrease of voltage and power decrease caused by the incomplete conversion of the overall electrochemical reaction.

Paper presents an idea of utilization infinite regular polyhedrons for designing heat exchange devices. The investigated prototype of the heat exchanger was consisted of twenty identical solids. Each of them was composed from eight regular hexagons. CFD simulations, reported in this paper, were used to obtain an influence of the flow domain modification on the intensification of the forced convection heat transfer in the developed device. Computational analyses clearly showed that the experimental testing of the heat exchanger prototype should be realized with include of cuboid turbulence inserts. Heat transfer performance and pressure drop obtained by experimental investigations are presented, too. The average Nusselt number and Fanning friction factor were expressed in terms of the Reynolds number.

In this paper, experiments are performed to determine the convective mass transfer coefficient for evaporation in a horizontal rectangular duct with an aspect ratio of 14.5:1. In the test facility, a short pan of water forms the lower panel of a long duct where a hydrodynamically fully developed laminar or turbulent airflow passes over the surface of the water. The measured convective mass transfer coefficients have uncertainties that are typically less than ±10% and are presented for Reynolds numbers (Re) between 570 and 8100, Rayleigh numbers (Ra) between 6300 and 83,000, inverse Graetz numbers (Gz) between 0.003 and 0.04, and operating conditions factors (H∗) between −3.6 and −1.4. The measured convective mass transfer coefficients are found to increase as Re, Ra, Gz and H∗ increase and these effects are included in the Sherwood number correlations presented in this paper, which summarize the experimental data.

In this paper, spray absorber in absorption chillers, a new technique is proposed. This concept of atomization increases the heat and mass transfer rates due to the increases of the expose area of the brine solution compared to falling film technique used in the conventional absorber. Results presented in this paper show the great enhancement of water absorption property by having a pressure atomization. The experimental set up was included a single nozzle adiabatic spray chamber operating at the design pressure, a solution circulating and tempering system, a Laser measurement system to measure the size and the velocity of the droplets, and data acquisition and control system. Based on a first principle “Newman model”, an analytical model was developed to predict the enhance transfer rates. These analytical results were compared with the experimental results that showed good agreement. The experiments were conducted by varying the differential pressure across the nozzle and the liquid desiccant flow rate. The dimensionless viscosity ratio, k , of this disperse/continuous phase flow was around 1300. The nozzles tested were able to produce the expected drop sizes and mean drop velocities. The droplet Reynolds number and Peclet number varied from 10 to 1500 and 0.005 to 0.5, respectively.

An analysis is given for fully developed thermal transport through a wall-bounded turbulent fluid flow with constant heat flux supplied at the boundary. The analysis proceeds from the averaged heat equation and utilizes, as principal tools, various scaling considerations. The paper first provides an accounting of the relative dominance of the three terms in that averaged equation, based on existing DNS data. The results show a clear decomposition of the turbulent layer into zones, each with its characteristic transport mechanisms. There follows a theoretical treatment based on the concept of a scaling patch that justifies and greatly extends these empirical results. The primary hypothesis in this development is the monotone and limiting Peclet number dependence (at fixed Reynolds number) of the difference between the specially scaled centerline and wall temperatures. This fact is well corroborated by DNS data. A fairly complete qualitative and order-of-magnitude quantitative picture emerges for a complete range in Peclet numbers. It agrees with known empirical information. In a manner similar to previous analyses of turbulent fluid flow in a channel, conditions for the existence or nonexistence of logarithmic-like mean temperature profiles are established. Throughout the paper, the classical arguments based on an assumed overlapping of regions where the inner and outer scalings are valid are avoided.

Measurements of heat transfer coefficient (h) are presented for rows of round holes at streamwise angles of 30°, 60° and 90° with a short but engine representative hole length (L/D = 4). The study began with a single row of holes with pitch-to-diameter ratios of 3 and 6, followed by two inline and staggered rows for each hole spacing and streamwise inclination, which amount to 105 different test cases in addition to the 21 test cases presented on the single hole [C.H.N. Yuen, R.F. Martinez-Botas, Film cooling characteristics of a single round hole at various angles in a crossflow: Part I. Effectiveness, Int. J. Heat Mass Transfer, in press; C.H.N. Yuen, R.F. Martinez-Botas, Film cooling characteristics of a single round hole at various angles in a crossflow: Part II. Heat transfer coefficients, Int. J. Heat Mass Transfer, in press]. The present investigation is a continuation of the previous work [Yuen and Martinez-Botas, Parts I and II, in press] with the same test facility, operating conditions (freestream Reynolds number, ReD of 8563, and blowing ratio, 0.33 ⩽ M ⩽ 2), and measurement technique of liquid crystal thermography and the steady-state heat transfer method, therefore the results presented in the form of h/h0, which is the ratio of heat transfer coefficient with film cooling to that without, are directly comparable. Both local values and laterally averaged ones are presented, the latter refers to the averaged value across the central hole. The corresponding measurements of effectiveness for the rows of holes are presented in a companion paper [C.H.N. Yuen, R.F. Martinez-Botas, Film cooling characteristics of rows of round holes at various angles in a crossflow: Part I. Effectiveness, Int. J. Heat Mass Transfer, submitted for publication]. The low effectiveness observed with the 90° holes in the companion paper [Yuen and Martinez-Botas, submitted for publication] and the relatively large heat transfer coefficient presented here, suggest that the normal injection should only be used in situations where shallower holes are not feasible. The combined performance of effectiveness and heat transfer coefficient suggests that the two inline rows are likely to be advantageous in the film cooling of turbine blades with good coverage per unit mass flow of cooling air and lower thermal stresses due to the smaller heat load.

The classical problem of the fully developed mixed convection flow with frictional heat generation in a vertical channel bounded by isothermal plane walls having the same temperature is revisited in this paper. The existence of dual solutions of the local balance equations is pointed out. They are either columnar upflows or cellular down–up–down flows. Below a maximum value Ξ max of the governing parameter Ξ = Ge Pr Re (the product of the Gebhart, Prandtl and Reynolds numbers), for any given Ξ a pair of different solutions occurs. The value Ξ max corresponds to a maximum value of the Reynolds number above which no laminar solution can be found. At this maximum value, the two solution branches bifurcate from each other. In the neighborhood of the bifurcation point Ξ max even small perturbations can cause transitions from one flow regime to the other. In the paper, the mechanical and thermal characteristics of the dual flow regimes are discussed in detail both analytically and numerically.

This paper presents a collection of numerical simulation data which provides a reference for the assessment of various statistical/stochastic models in incompressible homogeneous particle-laden turbulent flows. Four different homogeneous flow configurations are studied, namely, homogeneous shear flow, homogeneous plane strain flow, homogeneous axisymmetric expansion and contraction. An Eulerian–Lagrangian formulation is used for the two-phase flow simulation. A Fourier pseudospectral method is used for the solution of the Eulerian carrier-phase equations without resorting to any turbulence model. The Lagrangian equations for the dispersed phase are integrated using a modified Stokes drag. For the shear flow, both monodispersed and polydispersed particles have been considered. In this paper, only the results that are relevant for assessment of various statistical models for both the fluid and dispersed phases are presented.

The paper presents results of the calculations of the average temperature variations of model rotor of a high-speed rotating heat exchanger in the course of thermal start up. A model rotor adopted for the calculations has a porous structure formed by radially oriented ducts of a constant circular cross-section. The scope of this paper covers numerical calculations of temperature distribution in the material of the rotor versus its rotational speed, temperature difference of the gases at the inlet, and types of the rotor material. With the use of these results, graphs are elaborated representing the dependence of the rotor’s dimensionless temperature on the Fourier number, with the Biot number used as a parameter.

The paper is an investigation of turbulent film condensation on a half oval body. The high tangential velocity of the vapor flow at the boundary layer is determined from potential flow theory. The Colburn analogy is used to define the local liquid–vapor interfacial shear which occurs when the high velocity vapor flows across the body surface. The paper then presents a discussion of the results obtained for the local dimensionless film thickness and heat transfer characteristics. Furthermore, the present paper discusses the influence of Froude number, sub-cooling temperature and system pressure on mean Nusselt number.