Numerical analysis of transient laminar forced convection of nanofluids in circular ducts

In this study, forced convection heat transfer characteristics of nanofluids are investigated by numerical analysis of incompressible transient laminar flow in a circular duct under step change in wall temperature and wall heat flux. The thermal responses of the system are obtained by solving energy equation under both transient and steady-state conditions for hydro-dynamically fully-developed flow. In the analyses, temperature dependent thermo-physical properties are also considered. In the numerical analysis, Al₂O₃/water nanofluid is assumed as a homogenous single-phase fluid. For the effective thermal conductivity of nanofluids, Hamilton–Crosser model is used together with a model for Brownian motion in the analysis which takes the effects of temperature and the particle diameter into account. Temperature distributions across the tube for a step jump of wall temperature and also wall heat flux are obtained for various times during the transient calculations at a given location for a constant value of Peclet number and a particle diameter. Variations of thermal conductivity in turn, heat transfer enhancement is obtained at various times as a function of nanoparticle volume fractions, at a given nanoparticle diameter and Peclet number. The results are given under transient and steady-state conditions; steady-state conditions are obtained at larger times and enhancements are found by comparison to the base fluid heat transfer coefficient under the same conditions.     

Experimental and numerical investigation of dynamic heat transfer parameters in packed bed

Dynamic experiments in a nonadiabatic packed bed were carried out to evaluate the response to disturbances in wall temperature and inlet airflow rate and temperature. A two-dimensional, pseudo-homogeneous, axially dispersed plug-flow model was numerically solved and used to interpret the results. The model parameters were fitted in distinct stages: effective radial thermal conductivity (K _r) and wall heat transfer coefficient (h _w) were estimated from steady-state data and the characteristic packed bed time constant (τ) from transient data. A new correlation for the K _r in packed beds of cylindrical particles was proposed. It was experimentally proved that temperature measurements using radially inserted thermocouples and a ring-shaped sensor were not distorted by heat conduction across the thermocouple or by the thermal inertia effect of the temperature sensors.     

Pre-Chamber Ignition Mechanism: Simulations of Transient Autoignition in a Mixing Layer Between Reactants and Partially-Burnt Products

The structure of autoignition in a mixing layer between fully-burnt or partially-burnt combustion products from a methane-air flame at ? = 0.85 and a methane-air mixture of a leaner equivalence ratio has been studied with transient diffusion flamelet calculations. This configuration is relevant to scavenged pre-chamber natural-gas engines, where the turbulent jet ejected from the pre-chamber may be quenched or may be composed of fully-burnt products. The degree of reaction in the jet fluid is described by a progress variable c (c = taking values 0.5, 0.8, and 1.0) and the mixing by a mixture fraction ξ (ξ = 1 in the jet fluid and 0 in the CH₄-air mixture to be ignited). At high scalar dissipation rates, N₀, ignition does not occur and a chemically-frozen steady-state condition emerges at long times. At scalar dissipation rates below a critical value, ignition occurs at a time that increases with N₀. The flame reaches the ξ = 0 boundary at a finite time that decreases with N₀. The results help identify overall timescales of the jet-ignition problem and suggest a methodology by which estimates of ignition times in real engines may be made.     

Wall Heat Flux and Thermal Stratification Investigations during the Compression Stroke of an engine-like Geometry: A comparison between LES and DNS

The near wall regions in internal combustion engines contain a significant amount of the gaseous mass in the cylinder and thus have a high relevance for the amount of unburned hydrocarbons, the wall heat transfer and the thermal stratification in the cylinder. In this context in the following study the predictive capability of Large Eddy Simulation (LES) with respect to wall heat flux and thermal stratification during the compression stroke i.e. under non-reactive conditions in an Internal Combustion Engine (ICE) are investigated based on a comparison with Direct Numerical Simulations (DNS). Two different modeling approaches for the near wall region, the low Reynolds damping approach and the LES adapted model from Plengsaard and Rutland, have been tested. During the first half of the compression stroke the low Reynolds damping approach agreed well with the DNS data, but increasing deviations were observed after 270° CA (piston halfway up). The underprediction of the wall heat flux at later stages was found to stem from the underestimation of the y ₊ values of the first cell centroid, compared to values obtained by evaluating the DNS data at the same location, and originates from the model used to determine the friction velocity. As a consequence of the underpredicted y ₊ value, the cell is not located in the viscous sublayer as expected, and the temperature gradient which is needed for the heat flux calculation is underpredicted. The results of the LES wall heat transfer model from Plengsaard and Rutland on the other hand showed overall reasonable agreement with the DNS data, but the model strongly depended on the modeling constants. With respect to the increasing thermal stratification during the compression both methods were found to significantly under predict the DNS results. These findings are especially relevant for LES of auto ignition phenomena in engines, since ignition timing and location are known to strongly depend on the temperature distribution.     

High temperature and pressure reactive flows through porous media

Large heat load are encountered in hypersonic and space flight applications due to the high vehicle speed (over Mach 5, i.e. 5000 km h⁻¹) and to the combustion heat release. If passive and ablative protections are a way to ensure the thermal management, the active cooling is probably the most efficient way to enable the structures withstanding of such large heat load. In some conditions, transpiration cooling will be used. In this paper, the permeation of fuels and other fluids through porous media is studied up to 1150 K and 60 bars. A dedicated experimental bench has been established to ensure the monitoring of temperature, pressure, mass flow rate and chemical composition (Gas Chromatograph, Mass Spectrometer, Infra Red spectrometer) in stationary and transient conditions. The tests on metallic and composite samples have been conducted with N₂, CH₄, H₂ + CH₄ mixtures and synthetic fuels (n-C₁₂H₂₆). The pressure losses comparison with the mass flow rate has enabled the determination depending on the temperature of the Darcian permeability, K_D the linear contribution, and of the Forchheimer’s term, K_F the quadratic one. The fuel pyrolysis in such low Reynolds flow has been investigated. The blockage effect due to coking activity has been estimated.     

Preparation and characterization of core-shell Al@PFHP with improving the combustion and ignition properties of aluminum powder

The dense alumina shell on the surface of aluminum powder will hinder the combustion of aluminum powder and increase its ignition temperature. In this study, the aluminum oxide shell layer on the surface of aluminum powder was removed with hydrofluoric acid by one-pot method, and 3-Perfluorohexyl-1, 2-epoxypropane (PFHP) (F₃C(CF₂)₅CH₂C₂H₃O) was coated to form a uniform and controllable core-shell Al@PFHP. The core-shell Al@PFHP showed better thermal reaction and ignition performance. The exothermic enthalpy of Al@0.15 PFHP was increased by about 1.9 times, with lower ignition temperature (reduced by about 140 °C) and longer burning duration (increased by about 1.5 times) after coating with PFHP, compared with raw aluminum powder. In addition, the formation of PFHP coating shell can effectively improve the hydrophobicity and corrosion resistance of aluminum powder.     

Determination of thermal conductivity and interfacial energy of solid Zn solution in the Zn-Al-Bi eutectic system

The equilibrated grain boundary groove shapes for solid Zn solution (Zn-3.0 at.% Al-0.3 at.% Bi) in equilibrium with the Zn-Al-Bi eutectic liquid (Zn-12.7 at.% Al-1.6 at.% Bi) have been observed from quenched sample with a radial heat flow apparatus. Gibbs-Thomson coefficient, solid-liquid interfacial energy and grain boundary energy for solid Zn solution in equilibrium with Al-Bi-Zn eutectic liquid have been determined to be (5.1 ± 0.4) × 10⁻⁸ K m, (80.1 ± 9.6) × 10⁻³ and (158.6 ± 20.6) × 10⁻³ J m⁻² from the observed grain boundary groove shapes, respectively. The thermal conductivity variation with temperature for solid Zn solution has been measure with radial heat flow apparatus and the value of thermal conductivity for solid Zn solution has been determined to be 135.68 W/km at the eutectic melting temperature. The thermal conductivity ratio of equilibrated eutectic liquid to solid Zn solution, R = K_L(Zn)/K_S(Zn) has also been measured to be 0.85 with Bridgman type solidification apparatus.     

Conjugate Natural Convection in a Porous Enclosure with Non-Uniform Heat Generation

Effects of a conductive wall on natural convection in a square porous enclosure having internal heating at a rate proportional to a power of temperature difference is studied numerically in this article. The horizontal heating is considered, where the vertical walls heated isothermally at different temperatures while the horizontal walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and finite difference method is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (0 ???Ra ???1000), the internal heating and the local exponent parameters (0 ????? ???5), (1 ????? ???3), the wall to porous thermal conductivity ratio (0.44 ???Kr ???9.9) and the ratio of wall thickness to its width (0.02 ???D ???0.5). The results are presented to show the effect of these parameters on the fluid flow and heat transfer characteristics. It is found a strong internal heating can generate significant maximum fluid temperature more than the conductive solid wall. Increasing value thermal conductivity ratio and/or decreasing the thickness of solid wall can increase the maximum fluid temperature. It is also found that at very low Rayleigh number, the heat transfer across the porous enclosure remain stable for any values of the thermal conductivity ratio.     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

Mixed Convection Heat Transfer in the Annulus Between Two Concentric Vertical Cylinders Using Porous Layers

A numerical investigation of the steady-state, laminar, axi-symmetric, mixed convection heat transfer in the annulus between two concentric vertical cylinders using porous inserts is carried out. The inner cylinder is subjected to constant heat flux and the outer cylinder is insulated. A finite volume code is used to numerically solve the sets of governing equations. The Darcy–Brinkman–Forchheimer model along with Boussinesq approximation is used to solve the flow in the porous region. The Navier–Stokes equation is used to describe the flow in the clear flow region. The dependence of the average Nusselt number on several flow and geometric parameters is investigated. These include: convective parameter, λ, Darcy number, Da, thermal conductivity ratio, K _r, and porous-insert thickness to gap ratio (H/D). It is found that, in general, the heat transfer enhances by the presence of porous layers of high thermal conductivity ratios. It is also found that there is a critical thermal conductivity ratio on which if the values of Kr are higher than the critical value the average Nusselt number starts to decrease. Also, it found that at low thermal conductivity ratio (K _r ≈ 1) and for all values of λ the porous material acts as thermal insulation.     

Flame-Flow Interaction in Premixed Turbulent Flames During Transient Head-On Quenching

This paper reports on experimental investigations of turbulent flame-wall interaction (FWI) during transient head-on quenching (HOQ) of premixed flames. The entire process, including flame-wall approach and flame quenching, was analyzed using high repetition rate particle image velocimetry (PIV) and simultaneous flame front tracking based on laser-induced fluorescence (LIF) of the OH molecule. The influence of convection upon flame structures and flow fields was analyzed qualitatively and quantitatively for the fuels methane (CH₄) and ethylene (C₂H₄) at ? = 1. For this transient FWI, flames were initialized by laser spark ignition 5 mm above the burner nozzle. Subsequently, flames propagated against a steel wall, located 32 mm above the burner nozzle, where they were eventually quenched in the HOQ regime due to enthalpy losses. Twenty ignition events were recorded and analyzed for each fuel. Quenching distances were 179 μm for CH₄ and 159 μm for C₂H₄, which lead by nondimensionalization with flame thickness to Peclet numbers of 3.1 and 5.5, respectively. Flame wrinkling and fresh gas velocity fluctuations proved flame and flow laminarization during wall approach. Velocity fluctuations cause flame wrinkling, which is higher for CH₄ than C₂H₄ despite lower velocity fluctuations. Lewis number effects explained this phenomenon. Results from flame propagation showed that convection dominates propagation far from the wall and differences in flame propagation are related to the different laminar flame speeds of the fuels. Close to the wall flames of both fuels propagate similarly, but experimental results clearly indicate a decrease in intrinsic flame speed. In general, the experimental results are in good agreement with other experimental studies and several numerical studies, which are mainly based on direct numerical simulations.     

Effect of Conduction in Bottom Wall on Darcy–Bénard Convection in a Porous Enclosure

Conjugate natural convection-conduction heat transfer in a square porous enclosure with a finite-wall thickness is studied numerically in this article. The bottom wall is heated and the upper wall is cooled while the verticals walls are kept adiabatic. The Darcy model is used in the mathematical formulation for the porous layer and the COMSOL Multiphysics software is applied to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (100 ≤ Ra ≤ 1000), the wall to porous thermal conductivity ratio (0.44 ≤ K _r ≤ 9.90) and the ratio of wall thickness to its height (0.02 ≤ D ≤ 0.4). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. It is found that the number of contrarotative cells and the strength circulation of each cell can be controlled by the thickness of the bottom wall, the thermal conductivity ratio and the Rayleigh number. It is also observed that increasing either the Rayleigh number or the thermal conductivity ratio or both, and decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure.     

Unsteady entrance heat transfer in laminar pipe flows with convection from the ambient

The characteristics of unsteady entrance heat transfer in the combined entrance heat transfer region of laminar pipe flows resulting from time-varying inlet temperature are numerically investigated. Three non-dimensional parameters,Nu ₀, a^*, andf are identified in the study. Also, their effects on the non-dimensional duct wall temperature, fluid bulk temperature, and duct wall heat flux are discussed in great detail. Comparisons are made with the zero thermal capacity wall solution.     

Transient heat transfer in a functionally graded convecting longitudinal fin

The study investigates the transient thermal performance of a constant area longitudinal fin made of a functionally graded material. Such a fin offers advantages that are not attainable with a traditional fin made of a homogeneous material. A numerical approach has been used to study the transient response of the fin with a step change in its base temperature. The fin is assumed to have an adiabatic tip. Three types of variations in the thermal conductivity with the longitudinal distance along the fin are considered: (a) linear, (b) quadratic, and (c) exponential. New analytical solutions for the steady state performance of the fin are derived in terms of the Bessel functions for cases (a) and (c) and in terms of the Legendre functions for case (b). These solutions provide a check on the accuracy of the transient numerical predictions for large times. The thermal performance of the fin is governed by the classical fin parameter, N _c, and the fin thermal conductivity grading parameter, a. Results are presented for the transient temperature distribution, base heat flow, convective heat loss, the energy stored in the fin and the fin efficiency for representative values of N _c and a. It is found that the transient, as well the steady state performance of the fin, is significantly affected by the functional grading of the fin material. The results presented are not only of fundamental interest but can also be used to design a functionally graded fin with the desirable steady and transient thermal characteristics.     

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k _s), thermal conductivity of flush-mounted discrete heat source (k _c), Reynolds number of fluid flow (Re _s), modified Richardson number (Ri ⁺) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T ^*) using the asymptotic computational fluid dynamics (ACFD) technique.     

Thermal fracture of a functionally graded/homogeneous bimaterial with system of cracks

The thermal fracture of a bimaterial consisting of a homogeneous material and a functionally graded material (FGM) with a system of internal cracks and an interface crack is investigated. The bimaterial is subjected to a heat flux. The thermal properties of FGM are assumed to be continues functions of the thickness coordinate, while the elastic properties are constants. The method of the solution is based on the singular integral equations. For a special case where the interface crack is much larger than the internal cracks in the FGM the asymptotic analytical solution of the problem is obtained as series in a small parameter (the ratio between sizes of the internal and interface crack) and the thermal stress intensity factors (TSIFs) are derived as functions of geometry of the problem and material characteristics. A parametric analysis of the effects of the location and orientation of the cracks and of the inhomogeneity parameter of FGM’s thermal conductivity on the TSIFs is performed. The results are applicable to such kinds FGMs as ceramic/ceramic FGMs, e.g., TiC/SiC, MoSi₂/Al₂O₃ and MoSi₂/SiC, and also some ceramic/metal FGMs.     

Measuring the thermal conducitivity of uranin

A convenient experimental method for measuring the thermal conductivity of uranin (fluorecein sodium, C₂₀H₁₀O₅Na₂) is described. Two similar blocks of uranin, produced from a strong uranin/water solution, were exposed to one-dimensional steady-state conduction. It was found that, for a mean bulk temperature ranging from ambient up to 55°C, the uranin has a constant thermal conductivity of 0.43 W/mK. Above these temperatures, the material begins to soften and the thermal conductivity is seen to decrease     

Study on premixed combustion in cylindrical micro combustors: Transient flame behavior and wall heat flux

The micro combustor is a key component of the micro thermophotovoltaic (TPV) system. Improving the wall temperature of the micro combustor is an effective way to elevate the system efficiency. An experimental study on the wall temperature and radiation heat flux of a series of cylindrical micro combustors (with a backward-facing step) was carried out. For the micro combustors with d = 2 mm, the regime of successful ignition (under the cold wall condition) was identified for different combustor lengths. Acoustic emission was detected for some cases and the emitted sound was recorded and analyzed. Under the steady-state condition, the effects of the combustor diameter (d), combustor length (L), flow velocity (u₀) and fuel–air equivalence ratio (Ф) on the wall temperature distribution were investigated by measuring the detailed wall temperature profiles. In the case that the micro combustor is working as an emitter, the optimum efficiency was found at Ф ≈ 0.8, independent of the combustor dimensions (d and L) and the flow velocity. Under the experimental conditions employed in the present study, the positions of the peak wall temperature were found to be about 8–11 mm and 4–6 mm from the step for the d = 3 mm and d = 2 mm micro combustors, respectively, which are 8–11 and 8–12 times of their respective step heights. This result suggests that the backward-facing step employed in the combustor design is effective in stabilizing the flame position.     

Transient conjugated mixed-convective heat transfer in a vertical plate channel with one wall heated discretely

 This study presents a numerical solution of the unsteady conjugated mixed-convection heat transfer in a vertical plate channel with one wall suddenly subjected to either isoflux or isothermal discrete heat sources. The effects of the dimensionless heat source length H ₁, the dimensionless spacing between heat sources H ₂, the dimensionless channel length L, the dimensionless heated-plate thickness B _l, the wall-to-fluid conductivity ratio K and the ratio of Grashof number to Reynolds number Gr/Re on the interface heat flux, Nusselt number and bulk fluid temperature are discussed in detail. Results show that the discrete heating can cause the heat transfer direction conversely from the fluid to the heated plate during the transient period, which is more significant for the cases with larger L and H ₂. For the system with isoflux discrete heat sources, the time required to reach the steady-state is shorter for larger H ₂. While the trend is reverse for system with isothermal discrete heat sources. Additionally, a higher ratio of the input energy is axially conducted through the plate wall from heated sections to unheated regions for a larger H ₂ and B _l or smaller L. Received on 9 November 1998     

Numerical Study of Ignition Process in Turbulent Shear-less Methane-air Mixing Layer

In this work, ignition process in a turbulent shear-less methane-air mixing layer is numerically investigated. A compressible large eddy simulation method with Smagorinsky sub-grid scale model is used to solve the flow field. Also, a thickened flame combustion model and DRM-19 reduced mechanism are used to compute species distribution and the heat release. Non-reacting mean and RMS axial velocity profiles and mean mixture fraction are validated against experimental data. Instantaneous mixture fraction contours show that the large bursts penetrate from the fuel stream into that of the oxidizer and vice versa and a random behaviour in the cross-stream direction. Flame kernel initiation, growth and propagation are analysed and compared with the experimental data. The ignition results show that the flame is not stable and blow-off occurs, but a more detailed investigation shows that local and short time flame stabilization exist during blow-off. During these local stabilization, heat release increased at the upstream edge of the flame. Most_upstream flame edge scalar analysis shows that the methane mass fraction has a dominant role in the local flame stabilization. OH, HO₂, CH₂O and heat release contours demonstration reveal that HO₂ and CH₂O mass fraction as well as the heat release reach a maximum on the border of the flame, but the maximum OH concentration is located in the middle of flame kernel.