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This paper mainly analyzes the heat transfer of Carreau fluid over an infinite rotating disk, and two models with variable thermal conductivity are considered. Firstly, the governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by similarity transformation. Then, the boundary value problem is solved by improved bvp4c method, which reduced sensitivity to the initial values. For shear-thinning and shear-thickening fluids, the effects of Carreau fluid index n and Prandtl number Pr on velocity and temperature fields are shown and analyzed when 0.5 ≤ n ≤ 1.5 , 1 ≤ P r ≤ 10. Furthermore, the thermal conductivity is computed under two cases. [ABSTRACT FROM AUTHOR]

The flow induced by a simultaneously rotating and radially stretching disk is revisited in this paper. The steady solution is given by a power-series of exponentials including the governing parameter of the problem c = Ω ∕ s , which is the ratio of the angular velocity of rotation Ω and the strain rate of stretching s. Since the series satisfy the far field conditions automatically, the boundary value problem reduces to an initial value problem and this guarantees the uniqueness of the solutions. Based on the exponential series solution, the features of the flow in the stretching dominated the subcritical regime 0 < c < c c r i t = 2. 384895 and in the rotation dominated overcritical regime c > c c r i t are discussed in detail. Further features of engineering interest, as the pumping performance of the "rotating and stretching viscous pump", as well as its heat transfer characteristics are also considered in the paper. [ABSTRACT FROM AUTHOR]

Abstract The main aim of this paper is to present the methodology for calculating the applicability range of the Dual-Phase-Lag model in integrated circuits (IC) made of different materials. Furthermore, analyses of requirements for using the Dual-Phase-Lag instead of the Fourier-Kirchhoff heat transfer model are described. All considerations are based on a transistor elementary cell including FinFETs in modern ICs. The obtained results have been analyzed in detail and compared. Moreover, the paper shows an important correction to the Neumann boundary condition required for consistency with the Dual-Phase-Lag equation. In addition, the simplified Dual-Phase-Lag model has also been presented in this paper. It is based on both the classical Fourier-Kirchhoff methodology and Dual-Phase-Lag approach. However, significant improvements related to time lags approximation have been proposed. This simplified model can be implemented in Finite Difference Method and Finite Element Method simulators based on two conjugate diffusion equations. Finally, the temperature distribution inside one- and three-dimensional FinFET structures has been determined based on Fourier-Kirchhoff and Dual-Phase-Lag models. Highlights • The applicability range of Dual-Phase-Lag (DPL) model for different materials is presented. • The 1-D and 3-D DPL model of 12 nm FinFET cell is delivered. • The simplified as well as harmonic conjugate diffusion DPL model is proposed. • The important correction to the Neumann boundary condition is proposed. • The cut-off frequency (bandwidth) estimation procedure is presented. [ABSTRACT FROM AUTHOR]

The paper addresses the problem of coupled heat and moisture transfer in porous materials with the time-periodic boundary conditions applied. The solution of Luikov equations [1] , which describe coupled heat and moisture transfer, is presented. Laplace transform is used, where some terms of the inverse Laplace transform ought to be solved by Gaussian quadrature, meaning that the solution is semi-analytical. The time-periodic boundary conditions are applied to simulate the humidity and temperature oscillations of natural environment. Therefore, the proposed solution is appropriate to evaluate the distribution of moisture and temperature within the porous material exposed to everyday natural cycles. The paper presents convergence tests, validation of semi-analytical solution and application to different building materials are presented in the paper. [ABSTRACT FROM AUTHOR]

With the increasing demand for oil storage, storage tanks are developing towards large-scale tanks better adaptability to extreme working conditions. The variation law of the oil temperature field and the flow field inside the tank should be accurately understood to guarantee safe and economical operation of an oil depot. Aimed at understanding the periodic variation in the ambient environment of the tank’s location and the physical properties of the crude oil, the theoretical model of unsteady heat transfer flow in a large floating roof tank was established by using the relative heat transfer theory in this paper. The numerical solution technique for the crude oil temperature field and the flow field was studied. This paper thoroughly analyzed the effect of heat transfer and flow coupling characteristics on the tank static storage process under the influences of the atmospheric temperature, solar radiation, etc. The results show that according to the variation law of the temperature field, the static storage cooling process was divided into a partial rapid cooling stage, overall rapid cooling stage, condensate reservoir growth stage and overall low-speed cooling stage. The heating process was divided into a partial low-speed heating stage and partial rapid heating stage. The solar radiation has a great influence on the temperature fluctuation, and the atmospheric temperature has a great influence on the rate of temperature decrease. The results can provide theoretical support for optimizing the design of the storage process and managing the manufacturing of a large floating roof tank. [ABSTRACT FROM AUTHOR]

The paper shows application of the method of fundamental solutions in combination with the radial basis functions for analysis of fluid flow and heat transfer in an internally corrugated tube. Cross-section of such a tube is mathematically described by a cosine function and it can potentially represent a natural duct with internal corrugations, e.g. inside arteries. The boundary value problem is described by two partial differential equations (one for fluid flow problem and one for heat transfer problem) and appropriate boundary conditions. During solving this boundary value problem the average fluid velocity and average fluid temperature are calculated numerically. In the paper the Nusselt number and the product of friction factor and Reynolds number are presented for some selected geometrical parameters (the number and amplitude of corrugations). It is shown that for a given number of corrugations a minimal value of the product of friction factor and Reynolds number can be found. As it was expected the Nusselt number increases with increasing amplitude and number of corrugations. [ABSTRACT FROM AUTHOR]

This paper and its future companion papers, were aimed to develop a set of efficient and accurate enough modular tools to build a simulation test bed for the stability analysis of interacting VAV (variable air volume air-conditioning system) control loops. By providing the correlation equations between the heat flow and temperature of the two opposite surfaces, the wall model was expected to link adjacent zones effectively and efficiently. In part 1, the development of an optimal simplified 3R2C (composed of three resistances and two capacitances) thermal network model of building envelope, i.e., the wall model, was descripted. The verification showed that the simplification of one-dimensional heat conduction through a typical wall of heavy construction was acceptable. The accuracy of the optimal simplified 3R2Cmodel was satisfying, and outperformed that of the optimal 4R3C model as well as two 3R2C models which were normally used in practical applications. First and foremost, the room dimensions of the test bed with the boundary conditions in numerical scheme were designed under the principle of similarity. After validation of the numerical scheme with the high-cited scaled experiment, a series of numerical test cases simulating the potential oscillations in practical applications, were conducted. Then, the long neglected concerned frequency range within which heat flow transfer through extern wall, was determined. Finally, the part of solid wall was separated with the part of indoor air, and was developed into a flexible wall module of 3R2C model based on frequency domain regression. [ABSTRACT FROM AUTHOR]

The paper presents analysis of displacement of a propulsion system shaft line and a crankshaft axis caused by temperature of marine, slow-speed main engine. Detailed information of thermal displacement of a power transmission system axis is significant during a shaft line alignment and a crankshaft springing analysis and during designing of structural health monitoring (SHM) system. A warmed-up main engine is a source of deformations of an engine body as well as a ship hull in the area of an engine room and hence axis of a crankshaft and a shaft line. Engines' producers recommend the model of parallel displacement of the crankshaft axis under the influence of an engine heat. This model may be too simple in some cases (especially for SHM systems). The paper presents computations of MAN B&W K98MC type engine mounted on 3000 TEU container ship. The engine body is much stiffer than its foundation pads and ship hull (double bottom) - boundary conditions of the engine. Especially for the high power marine engines correct model of the boundary conditions plays a key role during the analyses. Presented numerical analyses are based on temperature measurements of the main engine body and the ship hull during a sea voyage. Numerical analyses were performed using Nastran software based on Finite Element Method. The FEM model of the engine body comprised over 800 thousand degree of freedom (dof); the model of the ship hull contains over 200 thousand dof. Both models are analysed separately; the mutually interaction between them is taken into account by heat transfer and special model of boundary conditions. The specialized SHM system dedicated to marine propulsion systems working in very bad environmental conditions is the future aim of the research. [ABSTRACT FROM AUTHOR]

Smoke and Heat Exhaust Ventilation Systems (SHEVS) are technical solutions used to limit the consequences of a fire in a building, related to the spread of the smoke. Currently, the design methodologies follow an assumption, that if a system constantly exhausts amount of the smoke estimated with a calculation method based on an onerous steady-state fire scenario, the building should be safe. This paper introduces a different approach to optimal system design, based on the transient characteristic of the fire. The main idea is that a system can adapt to the momentary density of the removed smoke, to benefit from the thermal expansion of gases in the fire. As the fire grows, the temperature does rise, and the pressure within installation falls down, and so do the forces acting on ducts, dampers and other elements. This behaviour is observed in high-temperature furnace tests of exhaust fans, during which the change of pressure and power-supply requirement in changing temperature can be measured. The author presents results of 9 high-temperature tests that are a proof of the concept. The practical implementation of the idea presented in this paper could mean, that a system designed with an existing methodology for ambient conditions, could work with a higher capacity in high-temperature, without additional strain on the elements of the system. This shift in thinking allows using higher capacity systems, in place of currently used, by artificially limiting the capacity of an oversized fan in ambient conditions and increasing it, following the measurements of the temperature of the exhausted air or pressure in the shafts. Beside the theoretical introduction to a new concept, the paper presents results of 8 numerical analysis (CFD) of airflow in an enclosed car park during a fire, performed in ANSYS® Fluent® solver. The author created an User Defined Function (UDF) to automate the transient change of the fan boundary condition, dependant on the exhausted smoke temperature – following the assumptions of the adaptive solution presented in the paper. Four CFD analysis were performed for each traditional and new solution, and their results were compared in with qualitative and quantitative approach. Results of the CFD analysis show a possible gain of 25–41% of system capacity, using the same ductwork and reaching the same design goal, as contemporary SHEVS. The pressure within the ductwork and at fans is almost constant in the adaptive analysis. The paper is closed with a discussion of legal aspects, possible limitations in the design and the further research necessary to establish the new method of the design. [ABSTRACT FROM AUTHOR]

Heat transfer simulation in thermoplastics processing is crucial to predict the quality of parts in terms of geometry and mechanical properties. The results accuracy depends on the knowledge of thermo-physical properties, crystallization kinetics and boundary conditions, which have to be determined in representative process conditions. In this work, we focus on the impact of high cooling rate on heat transfer and crystallization at the surface of a thermoplastic part. For this purpose, a home-made device named “Lagardère apparatus” is presented. It can reproduce cooling rate encountered in injection moulding by the sudden contact between a cold surface and a molten polymer. The first objective of this paper is the direct measurement of the thermal contact resistance used to model the imperfect contact between the polymer and the mould. The mould surface temperature and the heat flux at the interface were provided by a heat flux sensor. The specificity of this methodology was to obtain the polymer surface temperature with an optical fibre associated with a photodetector. A particular attention was made to avoid the invasiveness of the sensors on heat transfer. The second objective of the paper is the crystallization study at the surface of the polypropylene part. The experimental heat flux was compared with computed ones for which crystallization kinetics comes from Fast Scanning Calorimetry measurement and a standard model commonly used in the literature. It seemed that a very fast crystallization occurred at the surface of the part with a lower released enthalpy compared to the bulk. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Fully resolved simulations of heat transfer problems in tubular fluid-particle systems. • Handles mixed boundary conditions, i.e. isothermal and isoflux, consistently. • Investigation of the influence of particle sizes and passive particles. • Comparison between two classes of immersed boundary method, i.e. CFM and DFM. Abstract In this paper two immersed boundary methods (IBM), specifically a continuous forcing method (CFM) and a discrete forcing method (DFM), are applied to perform direct numerical simulations (DNSs) of heat transfer problems in tubular fluid-particle systems. Both IBM models are built on the well-developed models utilized in momentum transfer studies, and have the capability to handle mixed boundary conditions at the particle surface as encountered in industrial applications with both active and passive particles. Following a thorough verification of both models for the classical Graetz-Nusselt problem, we subsequently apply them to study a much more advanced Graetz-Nusselt problem of more practical importance with a dense stationary array consisting of hundreds of particles randomly positioned inside a tube with adiabatic wall. The influence of particle sizes and fractional amount of passive particles is analyzed at varying Reynolds numbers, and the simulation results are compared between the two IBM models, finding good agreement. Our results thus qualify the two employed IBM modules for more complex applications. [ABSTRACT FROM AUTHOR]

Highlights • The aero-thermal performance of slanted-pins on a vertical wall are examined. • The mixed convection heat transfer is studied numerically. • The modified Richardson number is varied in a laminar flow regime. • The fin-inclination angle showing the best performance is captured. • Differences from the forced- and natural- convection results are assessed. Abstract This paper presents a numerical study on the mixed convection heat transfer of slanted-pin fins mounted on a vertical heated wall for the laminar flow regime, which is an extension of the authors' accompanying study (Oh et al. 2018) on the natural convection. Using the ideal gas assumption for the air, three-dimensional governing equations for fluid flow and heat transfer were calculated by imposing a periodic boundary condition in the horizontal lateral direction with the SIMPLE algorithm. The discrete ordinate method was also included to calculate the effect of radiation. The effects of the fin-inclination angle were investigated in a modified Richardson number range of 500–2500 by varying the Reynolds number at a fixed Grashof number. It was found that as the forced convection increases, the fin-inclination angle showing the best heat transfer performance changes from negative to positive fin angles. The critical Richardson number for this transition and the corresponding flow and heat-transfer characteristics in the mixed convection regime are summarized. [ABSTRACT FROM AUTHOR]

Highlights • The optimal pitch ratio of the ribs mounted in a channel is provided based on inverse analysis. • The entransy dissipation was taken as the objective function in the inverse method. • Taking entransy dissipation as objective function leads to a fast and stable convergence process. Abstract The ribbed surface is a widely used convection heat transfer enhancement technology. The geometric parameters of the ribbed surface have great influences on its heat transfer performance. It is crucial to determine the optimum geometric parameters. In the present work, the optimal arrangement of ribs mounted in a rectangular channel is provided by solving the inverse optimization problem with the entransy dissipation as the objective function. The parameter analysis based on the direct solution is firstly carried out to get an approximate range near the optimal pitch ratio which can provide the initial value for the inverse optimization problem; afterwards, the inverse optimization problem is solved by a modified simplified conjugate gradient method, and the accurate optimal pitch ratio is obtained; finally the optimization results are discussed in detail. The results indicate that, (1) the inverse optimization analysis presented in this paper can provide an accurate optimal value of the pitch ratio; (2) taking the entransy dissipation as the objective function could lead to a faster converge process and give a more stable result than taking the temperature data as the objective function; (3) the optimal value under the fixed heat flux boundary condition is slightly larger than that under the fixed temperature boundary condition. [ABSTRACT FROM AUTHOR]

Abstract This paper is an extension of the previous work by Degiovanni & Remy (2014) [1], where it was analytically demonstrated that the appropriate representation of interfacial heat transfer consists in defining a generalized impedance Z. The latter is intrinsic to the flow and does not depend on the thermal boundary conditions. In this work, we demonstrate the pertinence of this representation for complex flow problems where a direct analytical formula of the impedance cannot be calculated or can only be presented in terms of complex equations that are not easily applicable. The general idea is to perform numerical experiments to estimate this impedance using an inverse method, thus obtaining Green's function. Numerical simulations are carried out using the software Fluent for each flow problem. We will show that by using the inverse method on the numerical results for a constant temperature boundary condition, we are able to calculate the intrinsic Green's function for each flow problem, from which we can accurately calculate the thermal characteristics for any other thermal boundary condition, particularly for a constant heat flux. [ABSTRACT FROM AUTHOR]

Highlights • The heat transfer flow of a Walters’ liquid B in a porous medium with Navier slip is investigated. • The physical problem is modelled into nonlinear PDE’s to ODE’s via similarity transformation. • The analytical solutions derived for velocity and temperature fields by Kummer’s function. • Temperature profiles are analyzed for two type of boundary heating processes namely PST and PHF. • The temperature distribution inside the stretching sheet is found to be controlled by Pr, N R and N I. Abstract This paper investigates the steady-state momentum and radiation heat transfer flow of a viscoelastic fluid in a porous media in the presence of a linear Navier slip boundary condition. The velocity of the fluid over the linear stretching sheet is varied linearly with the axial distance while a Walters’ liquid-B model is assumed for the viscosity. A similarity transformation reduces the Navier–Stokes equations to a set of partial differential equations that are converted into ordinary differential equations and solved analytically for the velocity. Moreover, heat is balanced between a temperature dependent heat source and radiation and leads to a differential equation with variable coefficients. The temperature equation is transformed to a confluent hypergeometric differential equation using the Rosseland approximation for the radiation and solved analytically. Results are discussed for two boundary conditions of the sheet, the prescribed surface temperature and the wall heat flux. Parameters like the Reynolds number, the viscoelastic parameter and the boundary slip parameter are found to determine the flow field. In addition, the Prandtl number, the radiation number, the wall temperature and the heat source/sink parameters are found to control the temperature distribution inside the stretching sheet. [ABSTRACT FROM AUTHOR]

In this paper, the heat transfer and flow behavior of a circular tube fitted with rectangular winglet vortex generators (RWVGs) are investigated numerically and experimentally with uniform heat flux boundary conditions for Reynolds number ranging from 5000 to 17,000. Water is employed as working fluid. The RWVGs are inserted into the tube, with the slant angle β of 10°, 20°, 30°, 35°, respectively. The asymmetric winglet height is set on the one side at H 1 / D  = 0.5, and on the other side at H 2 / D  = 0.2, 0.3, 0.4, and 0.5, respectively. The effects of β and H 2 / D on the heat transfer and flow behavior are studied numerically by employing FLUENT software. The results show that the RWVGs can agitate the cold fluid from the core flow region to the tube wall, and therefore, enhancing the mixing of hot and cold fluids. The Nusselt number and friction factor increase with the increase of β , or H 2 / D . Specifically, the Nusselt number and friction factor are increased at 1.16–2.49 times and 2.09–12.32 times, respectively, compared with the plain tube. The Performance Evaluation Criterion ( PEC ) increases first, and then decreases with the increase of β and H 2 / D . The maximum PEC is found to be 1.18 for β  = 30°, H 2 / D  = 0.5 and Re  = 5000. Based on numerical data, new correlations of Nu and f by using four nondimensional parameters are also developed. The experimental platform is set up and the numerical results agree well with those of the experiment. In addition, the mechanism of heat transfer enhancement of RWVGs can be well explained by the principle of field synergy. [ABSTRACT FROM AUTHOR]

This paper shows that the connection of MOR-based boundary condition independent (BCI) dynamic compact thermal models (DCTMs) and detailed models of heat transfer problems is not straightforward and is subject to numerical issues. In order to overcome this drawback, a novel definition of MOR-based BCI DCTMs is provided, which makes this connection feasible. As a result, the proposed BCI DCTMs can be connected without limitations to any detailed model of heat transfer problems and/or to any other MOR-based BCI DCTM. [ABSTRACT FROM AUTHOR]

This paper derives analytical solutions for the critical Kelvin–Helmholtz (KH) instability conditions at the interface between a cylindrical gas column and a pool of viscous immiscible fluid confined in a chamber of finite size. The analysis focuses on conditions of negligible heat and mass transfer. The derivations are based on the established approaches reported in the literature with different boundary conditions. The most unstable instability conditions have also been calculated numerically. Experiments designed to measure the actual air column break-up conditions in water have been carried out to validate the analytical models. Comparisons show that the most unstable conditions predicted by the Viscous Corrections of the Viscous Potential Flow KH model are the best match to the experimentally measured break-up conditions. Parametric investigation of the instability theories shows that the vapour column size has a noticeable effect on the critical conditions, but has a negligible effect on the most unstable conditions when the column radius is greater than 1.2 mm. Furthermore, the critical instability conditions are sensitive to the chamber size and the perturbation symmetry, while the most unstable conditions are insensitive to these parameters. [ABSTRACT FROM AUTHOR]

Current aims regarding environmental protection, like reduction of fossil fuel consumption and greenhouse gas emissions, require the development of new technologies. These new technologies enable the production of renewable energy, which is both cleaner and more abundant in comparison to using fossil fuels for energy production. This necessity encourages researchers to develop new ways to capture solar energy, and if possible, store it for later use. In this paper, the Pavement Solar Collector (PSC), and its use to extract low temperature thermal energy, is studied. Such a system, which harvests energy by flowing water through a heat exchanger embedded in the pavement structure, could have a significant energy output since pavement materials tend to absorb large amounts of solar radiation. The main objective of this paper is to develop a modeling framework for the PSC system and validate it with a self-instructed experiment. Such a model will allow for a detailed parametric study of the system to optimize the design, as well as an investigation on the effect of aging (e.g. decreasing solar absorptivity) on the performance of the system. A long-term energy output of the system that is currently lacking is calculated based on results of the study on weather parameters. This newly acquired data could be the start of a comprehensive data set on the performance of a PSC, which leads to a comprehensive feasibility study of the system. [ABSTRACT FROM AUTHOR]

This paper reports a multiscale asymptotic analysis and computation for predicting heat transfer performance of periodic porous materials with radiation boundary condition. In these porous materials thermal radiation effect at micro-scale have an important impact on the macroscopic temperature field, which is our particular interest in this study. The multiscale asymptotic expansions for computing temperature field of the problem are constructed, and associated explicit convergence rates are obtained on some regularity hypothesis. Finally, the corresponding finite element algorithms based on the multiscale method are brought forward and some numerical results are given in details. The numerical tests indicate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate magnetohydrodynamic free convective flow of micropolar fluid over a moving flat plate using the Lie group transformations and numerical methods. Instead of using conventional no-slip boundary conditions, we used both the velocity and thermal slip boundary conditions to achieve physically realistic and practically useful results. The governing boundary layer equations are non-dimensionalized and transformed into a set of coupled ordinary differential equations (ODEs) using similarity transformations generated by the Lie group, before being solved numerically using Matlab stiff ODE solver ode15s and Matlab trust-region-reflective algorithm lsqnonlin . The effects of governing parameters on the dimensionless velocity, angular velocity, temperature, skin friction and heat transfer rate are investigated. Our analysis revealed that the dimensionless velocity and angular velocity decrease whilst the dimensionless temperature increases with the velocity slip parameter. Thermal slip reduces the dimensionless velocity and temperature but raises the dimensionless angular velocity. Magnetic field suppresses the velocity but elevates the temperature and angular velocity. Results reported in this paper are in good agreement with the ones reported by the previous authors. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of nonlinearities on electronic device thermal transient responses. The discussions in the paper are based on practical examples where thermal responses of a power device are recorded in various boundary conditions for different values of dissipated power. Then, the measurement results are analysed using the Network Identification by a Deconvolution method and the differences between particular cases are discussed in detail. The presented experimental results demonstrate that the nonlinearities due to the temperature dependence of thermal model parameters might have important influence on the results, especially when still air cooling is applied. In addition, in selected cases the simulations results obtained with compact thermal models were compared with measurements. [ABSTRACT FROM AUTHOR]

In this paper, a three-dimensional simulation of fully coupled multiphase fluid flow and heat transfer through deforming porous media is presented in the context of EFG mesh-less method. Spatial discretization of the system of governing equations is performed using EFG and a fully implicit finite difference scheme is employed for temporal discretization. Penalty method is used for imposition of essential boundary conditions. The developed numerical tool is employed to simulate two problems of nuclear waste disposal and CO 2 sequestration in deep underground strata. The obtained results demonstrate the capability and robustness of the developed EFG code. [ABSTRACT FROM AUTHOR]

In this paper, we apply a novel immersed boundary method to simulate pore-scale level fluid flow and convective heat transfer in realistic numerically generated open-cell solid foams in a Cartesian computational domain. Five different periodic foam samples of varying porosities ( ε = [ 0.877 , 0.948 ] ) are generated by numerically mimicking the actual foam formation process (minimizing surface area). The step-by-step procedure for generating the periodic foam geometries is presented. The specific surface areas of the generated foams of different porosities are compared with real foam geometries showing a reasonable agreement. The Reynolds number ( Re ) is varied from Re ≈ 0 (creeping flow) to Re ≈ 500 , and finally drag and Nusselt correlations have been proposed. A detailed analysis is presented on the local velocity and temperature field for the fluid-solid interaction in a complex cellular porous medium. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of heat transfer in a slightly rarefied gas flowing in a circular tube with constant wall temperature boundary condition. Local temperature measurements are carried out for the first time in rarefied gas flows to investigate into the anomalous values of Nusselt number ( Nu ) obtained by a previous experimental study (Demsis et al., 2009). The present measurements agree well with the low Nu reported by Demsis et al. (2009) when the Nu is obtained using their procedure; additionally, the measurements reveal the importance of end effects in determining the Nusselt number in rarefied gases. The Nusselt number obtained in the present experiments tends to zero with increasing axial conduction. Nu shows a weak dependence on Knudsen number for the range investigated here (0.001 <  Kn  < 0.012). [ABSTRACT FROM AUTHOR]

Nanofluids are advanced two-phase coolants that exhibit heat transfer augmentation phenomena. Extensive research has been performed since the year 2000 onwards to understand the physical mechanisms of heat transfer in nanofluids when employed inside traditional heat exchanging geometries. The focus of this paper is to understand if and how the geometry of heat exchangers might be potentially affecting the nanofluid coolant flow boundary conditions established and how this might be hence further affecting their thermal characteristics. HyperVapotrons are highly robust and efficient heat exchangers able to transfer high heat fluxes of the order of 10–20 MW/m 2 . They employ a complex two-phase heat transfer mechanism which is strongly linked to the hydrodynamic structures present in the coolant flow inside the devices. A cold isothermal nanofluid flow is established inside two HyperVapotron model replicas. A high spatial resolution (30 μm) visualisation of the nanofluid flow fields inside each replica is measured and compared to those present during the use of a traditional coolant (water). Significant geometry specific changes are evident with the use of dilute nanofluids which is something unexpected and novel. Evidence of a shear thinning mechanism is found inside the momentum boundary layer of the nanofluid flows that might prove beneficial to the coolant pumping power losses when using nanofluids instead of water and is expected to affect their thermal performance from a hydrodynamic point of view. [ABSTRACT FROM AUTHOR]

In this paper, the analytical solution of Fourier and non-Fourier model of heat transfer in longitudinal fin in presence of internal heat generation has been studied under periodic boundary condition. The whole analysis is given in dimensionless form. These two mathematical models have been solved analytically, using Laplace transform technique. Temperature distribution in longitudinal fin is measured using residual theorem in complex plane for the inverse Laplace transform technique. Thermal wave nature is appeared for small value of F o . The longitudinal fin temperature is evaluated for different value of parameters with respect to space coordinate. The effect of variability of different parameters on temperature distribution in fin is studied in detailed. It has been observed that the cooling process is faster in non-Fourier model in comparison to Fourier model. [ABSTRACT FROM AUTHOR]

Air source heat pump (ASHP) units have found worldwide applications due to their advantages of high energy efficient and environmental friendly. Frost deposition and accumulation on the surface of the outdoor coil in an ASHP unit is inevitable and always play significant negative effects. To accurately predict and control a frosting-defrosting cycle, the interrelated heat, mass, and momentum transport phenomena within frost, melted frost and at the air-frost interface, a moving boundary condition, should be clearly understood. This review paper focuses on the developments in frost retarding and defrosting investigations for ASHP units from 2000 to 2017. 12 frost retarding measures and 5 defrosting methods are firstly introduced, followed by 6 typical system optimization methods during reverse cycle defrosting. Alternative control strategies to start and end a defrosting operation are thereby presented. Basing on previous analysis, the existing gaps in the research works on frost retarding and defrosting are identified, and recommendations are finally offered as per the viewpoint of the present authors. This comprehensive and systematic review around an entire frosting-defrosting cycle might provide an overview of the analytical tools for scholars, researchers, product developers, and policy makers, and shed new light on the designing and performance optimization of ASHP units. [ABSTRACT FROM AUTHOR]

This paper investigate the numerical study of MHD boundary layer flow, heat and mass transfer analysis of water based nanofluids containing single and multi-walled CNTs over a vertical cone embedded in porous medium with convective boundary condition under the influence of chemical reaction and suction/injection. The similarity transformation technique is used for converting the governing non-linear partial differential equations, which represents the momentum, temperature and concentration of nanofluid, into the system of coupled ordinary differential equations. The transformed conservation equations together with boundary conditions are solved by using Finite element method. The sway of various pertinent parameters on hydrodynamic, thermal and solutal boundary layers is investigated and the results are displayed graphically. Furthermore, the values of local skin-friction coefficient, rate of temperature and concentration is also inspected for various values of non-dimensional parameters and the results are shown in tabular form. The numerical data results are compared with available data for special cases and found in good agreement. It is found that the skin-friction coefficient, Nusselt number and Sherwood number enhances with rising values of Biot number ( B1 ) in both SWCNTs-water and MWCNTs-water based nanofluids. [ABSTRACT FROM AUTHOR]

The heat and moisture states of building floors without impermeable boundary construction, which affect the indoor thermal and moist environment, are determined by the heat and moisture distribution features and coupled transfer process of the under-soil and groundwater level. Previous studies based mainly on mathematical models only considered heat transfer or simplified the boundary conditions as adiabatic and impermeable, which resulted in limitations in application, specifically greater errors in shallow groundwater areas. In this paper, a scale model experiment that combined the floor, soil and groundwater was conducted to study the affected degree of the thermal and wet conditions of the floor in terms of the combined effect of soil heat and moisture transfer and indoor thermal and moist environment. The results showed that under the influence of the latent heat of vaporization, groundwater increases the floor temperature in the short term, and under the influence of water vapor pressure, groundwater decreases the relative humidity of the floor in the short term. The influence range of underground moisture source, analysis of building energy consumption effected by underground moisture source, process of ground surface hot and humid states reaching equilibrium, were discussed by numerical calculations. [ABSTRACT FROM AUTHOR]

The present paper reports the results obtained from Large Eddy Simulation (LES) analyses concerning the effect of conjugate heat transfer with walls when dealing with heat transfer to supercritical pressure fluids. A specific operating condition was investigated with and without walls showing a clearly understandable effect on turbulence of the actual characteristics of the wall, something further complicating turbulence modelling, already quite difficult in this field. Unlike the experience of past studies, which considered conjugate heat transfer by LES or DNS when dealing with constant property fluids, and resulted in a limited influence on the observed phenomena, in the present work relevant effects are instead identified. In fact, in the case of supercritical pressure fluids, the strong changes in fluid properties close to the pseudo-critical threshold may provide a strong feedback on the velocity field and then on turbulence; in particular, the presence of a wall with realistic properties strongly damps the large temperature and fluid properties fluctuations obtained when imposing a constant heat flux. Consequently, unlike fluids in standard conditions, heat transfer to supercritical fluids seems to be depending on the actual fluid-and-wall coupling, thus adding a further challenging aspect in this already complicated topic. Though further analyses are underway for confirming the observed behaviour, the presented findings related to a simple example open new scenarios in the development of heat transfer correlations and CFD models to be used for supercritical fluids. In fact, the available data, both experimental and by DNS, can no more be considered independent from the imposed boundary conditions at the wall and the effect of the wall properties should be seriously taken into account. [ABSTRACT FROM AUTHOR]

In this paper, dispersion effects on forced convection heat transfer in a gaseous slip flow through a microtube filled with anisotropic porous medium are investigated semi-numerically. Microtube is subjected to constant heat flux and a local thermal non-equilibrium condition is assumed. Rarefaction effects are taken into account by applying first-order velocity slip and temperature jump boundary conditions. Dispersion is proven to have a significant impact on heat transfer in rarefied gases. Temperature distributions for both solid and fluid phases are obtained. Nusselt number variation with respect to porous shape factor and Biot number is illustrated, indicating enhancement up to 10% in predicted heat transfer due to dispersion. The influence of Reynolds number on thermal dispersion is proven to be insignificant. Dispersion plays a significant role as gas becomes more rarefied. It is seen that an increase in shape factor of a porous media can improve Nu for a non-rarefied gas, but as rarefaction effects grow, this can affect heat transfer negatively. Also, effects of dispersion on heat transfer diminishes for higher values of Biot Number due to the overcoming of interstitial heat transfer to thermal dispersion effect. [ABSTRACT FROM AUTHOR]

Protective structures are designed explicitly to fulfil a function that in many cases is an extreme event; therefore, an explicit design has to properly and precisely account for the nature of the solicitation imposed by the extreme event. Extreme events such as explosions or earthquakes are reduced to design criteria on the basis of either empirical or historical data. To determine the design criteria, the physical data has to be translated into physical variables (amplitudes, pressures, frequencies, etc.) that are then imposed to the protective structure. While there is debate on the precision and comprehensive nature of this translation, years of research have provided strong physical arguments in supporting these methods. Performance is then quantified on the basis of the structure’s capability to perform its required function. Classified solicitations may then be used to translate performance into prescribed requirements that provide an implicitly high confidence that the structure performs its function. When addressing fire, performance has been traditionally determined by imposing standardized requirements that necessarily attempt to bear a strong relationship with the reality of potential events – the fire performance of a protective structure is thus defined as a fire resistance period. This paper addresses the concept of fire resistance and its relevance to the design of protective structures. The mathematical description of the thermal boundary conditions for a fire is of extreme complexity, therefore simplified approaches, that include the Fire Resistance concept, are currently used. By using classical heat transfer and structural engineering arguments, the work described herein demonstrates that an adequate level of complexity and precision for the thermal boundary conditions and input parameter is fundamental to correctly describe the response of a structure during a fire event. Simple criteria are presented to qualify the relevance of current approaches and to highlight important issues to be considered. [ABSTRACT FROM AUTHOR]

A variety of physical problems in science may be expressed using the advection-diffusion-reaction (ADR) equation that covers heat transfer and transport of mass and chemicals into a porous or a nonporous media. In this paper, the meshless generalised reproducing kernel particle method (RKPM) is utilised to numerically solve the time-dependent ADR problem in a general n -dimensional space with variable coefficients and boundary conditions. A time-dependent Robin boundary condition is formulated and precisely enforced in a novel approach. The accuracy and robustness of the meshless solution is verified against finite element simulations and a general one-dimensional analytical solution obtained in this study. [ABSTRACT FROM AUTHOR]

In this paper, we consider boundary stabilization for a cascade of ODE–heat system with a time-varying state delay under actuator saturation. To stabilize the system, we design a state feedback controller via the backstepping method and find a bound on the domain of attraction. The latter bound is based on Lyapunov method, whereas the exponential stability conditions for the delayed cascaded system are derived by using Halanay’s inequality. Numerical examples illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Forced convection heat transfer in fully developed gaseous laminar slip flow in transversally corrugated micropipes is investigated for first-order slip boundary conditions on the wall. The governing equations subject to first-order slip boundary conditions are solved analytically by means of the epitrochoid conformal mapping. Closed-form exact expressions are obtained for the velocity and temperature fields for the first time. The effects of the corrugation on the pressure drop and heat transfer rate are discussed in detail. Exact results obtained in this paper are compared with the recent approximate analytical solution in the literature, Sadeghi et al. (2011) [1]. [ABSTRACT FROM AUTHOR]

• Added missing literature references and improved literature review. • Fixed formulas going beyond the column. • Added experimental setup diagram. • Added a graph for comparing numerical results with experimental data. • Compacted part of the article with a proof of convergence, reduced the amount of information for readability. This paper presents a detailed and developed method for finding soil nonlinear thermophysical characteristics. Two-layer container complexes are constructed. The side faces of which are thermally insulated, so that one can use the one dimensional heat equation. In order not to solve the boundary value problem with a contact discontinuity and not to lose the accuracy of the solution method, a temperature sensor was placed at the junction of the two media, and a mixed boundary value problem is solved in each region of the container. In order to provide the initial data for the inverse coefficient problem, two temperature sensors are used: one sensor was placed on the open border of the container and recorded the temperature of the soil at this border, and the second sensor was placed at a short distance from the border, which recorded the air temperature. The measurements were carried out in the time interval (0 , 4 t max). At first, the initial-boundary value problem of nonlinear thermal conductivity equation with temperature dependent coefficients of thermal conductivity, heat capacity, heat transfer and material density is investigated numerically. The nonlinear initial-boundary value problem is solved by the finite difference method. Two types of difference schemes are constructed: linearized and nonlinear. The linearized difference scheme is implemented numerically by the scalar Thomas' method, and the nonlinear difference problem is solved by the Newton's method. Assuming the constancy of all thermophysical parameters, except for the thermal conductivity of the material, on the segment (0 , t max) , the quadratic convergence of Newton's method is proved and the thermal conductivity is calculated, while the solution of the linearized difference problem was taken as the initial approximation for the Newton's method. By freezing all other thermophysical parameters, and using the measured temperatures in the segment (t max , 2 t max) , the coefficient of specific heat of the material is found. Proceeding in a similar way, using the initial data on the segment (2 t max , 3 t max) , the density of the soil is determined. Also, based on the measured initial data on the segment (3 t max , 4 t max) , the heat transfer coefficient is determined. Based on the experimentally measured data, at each time interval, the corresponding functional is minimized using the gradient descent method. The differentiation of a nonlinear difference problem with respect to the desired parameter method is used to find the gradient of the functional. This method allows you to find the functional gradient and the damping coefficient of the gradient descent in an explicit form. In this case, the compilation and solution of the conjugate problem, which is a frequently used method for solving the inverse problems, is not needed. The performed numerical calculations show that for small time intervals the solutions of the linearized difference problem differ little from the solution of the nonlinear difference problem (1 - 3%). And for long periods of time, tens of days or months, the solutions of the two methods differ significantly, sometimes exceeding 20%. In addition, all thermophysical characteristics (8 coefficients) were found for a two-layer container with sand and black soil. Also the dependence of the temperature difference at the boundary between the environment and the soil for the heat transfer coefficient was shown. [ABSTRACT FROM AUTHOR]

Abstract: Discrepancies in friction stir welding model predictions for temperature, strain, and strain rate may be due to material, process parameters, boundary conditions, heat transfer properties, or constitutive laws. The focus of this work is to investigate the effect of the constitutive law on friction stir welding model predictions. This paper provides a description of constitutive laws with their uses and limitations to facilitate the selection of an appropriate constitutive law for a given modeling objective. None of the path-independent constitutive laws evaluated in this paper has been validated over the full range of strain, strain rate, and temperature in friction stir welding. Holding all parameters other than constitutive law constant in a friction stir weld model for AA 5083 resulted in temperature differences of up to 21%. Varying locations for maximum temperature difference indicate that the constitutive laws resulted in different temperature profiles. Peak strains and strain rates predicted vary by up to 130% and 166%, respectively. Predicted flow stress profiles are also affected by the choice of constitutive law. [Copyright &y& Elsevier]

In this paper, thermal-flow boundary layer of single-phase Nanofluid over a horizontal cylinder tube under magnetic force is investigated using Optimal Collocation Method (OCM) and numerical method. After presenting the governing equations and solving them by OCM, the accuracy of results is examined by fourth order Runge–Kutta numerical method. The boundary conditions contain infinite condition due to stretching cylinder, thus it needs to a powerful analytical method to solve it. OCM which is firstly introduced by authors is the simple/powerful method for this analysis. Effects of different nanoparticles (TiO 2 , Cu and Ag) are investigated on the temperature/velocity profiles as well as Nusselt number and boundary layer thickness. Additionally, the influence of relevant parameters such as the magnetic parameter, the solid volume fraction of nanoparticles on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed. [ABSTRACT FROM AUTHOR]

In this paper, an analysis is made for the steady 3D flow of Sisko fluid over a bidirectional stretching sheet. Heat transfer analysis is illustrated while utilizing the effect of Cattaneo-Christov heat flux model. Besides these the impact of homogeneous-heterogeneous chemical reactions on the fluid flow is investigated. Results of the numerical computations are described in terms of the temperature and concentration plots. Different behaviors of temperature and concentration distributions for shear-thinning and shear-thickening cases are reported. The mathematical formulation consisting of nonlinear governing equations and boundary conditions is first casted into dimensionless form by suitable transformations. Interpretation of various emerging parameter is given through groups. The results indicate that a rise in the thermal relaxation parameter demonstrate a decline in the fluid temperature and thermal boundary layer thickness. [ABSTRACT FROM AUTHOR]

This paper presents an analytical investigation of thermal transport due to a steady, laminar, axisymmetric liquid jet impinging normally on a superhydrophobic (SHPo) surface maintained at constant surface temperature. At the liquid-surface boundary of the spreading thin film, an isotropic hydrodynamic slip and temperature jump are imposed to approximate the SHPo surface boundary condition. Applying an integral analysis within the thin film results in a system of differential equations which are solved numerically to obtain local hydrodynamic and thermal boundary layer thicknesses, thin film height, and local and radially averaged heat flux. The classical smooth hydrophobic scenario with no-slip and no-temperature jump showed excellent agreement with previous differential analysis of the same problem. The influence of varying temperature jump length on the local Nusselt number was obtained over a range of Reynolds and Prandtl numbers. Increasing temperature jump length results in a dramatic decrease in the local thermal transport near the impingement point. The greatest decrease occurs at small temperature jump lengths. Further, local and average Nusselt numbers are less influenced by the Reynolds and Prandtl numbers as temperature jump length increases. Overall, variations in the temperature jump length exert much more influence than variations in the hydrodynamic slip length. [ABSTRACT FROM AUTHOR]

Transverse flow induced by helical spacer wires has important effects on the flow and heat transfer behavior of reactor core. In this paper, transverse flow in a wire-wrapped hexagonal seven-pin bundle was simulated by the open source code, OpenFOAM, based on computational fluid dynamic (CFD) method. The Shear Stress Transport (SST) k-ω model and Spalding wall function were used to resolve the momentum field. Hexahedral dominated meshes were generated to achieve high grid quality. Periodic boundary condition and parallel processing were adopted to save the computational cost. Transverse velocity distributions in four different kinds of subchannel gaps were analyzed. The results show that the influence of wire number and position on the transverse velocity distribution is obvious. For an interior gap, transverse flow seems to be dominated by wires near the gap, and its direction changes periodically in one helical pitch. However, for a peripheral gap, transverse velocity is affected by more wires and its direction is decided by the direction of wire rotation. Parameter studies reveal that the Reynolds number ( Re , at the range of 6000–100,000) has little effect on the normalized transverse flow, while the pitch to pin diameter ratio ( P/D , at the range of 1.11–1.22) and the helical pitch to pin diameter ratio ( H/D , at the range of 12–24) have a great influence on it, especially the P/D . Large discrepancies between our simulation results and some existing correlations were observed. This indicates that new correlations comprehensively considering both P/D and H/D effects need to be developed in future. [ABSTRACT FROM AUTHOR]

For the inverse heat conduction problem to estimate the time and space-dependent thermal boundary condition, a double decentralized fuzzy inference (DDFI) method with a temporal-spatial decoupling characteristic is proposed. A set of decentralized fuzzy inference modules (DFIMs) corresponding to the temperature measurement points are established. Each DFIM contains a set of decentralized fuzzy inference units (DFIUs), and each DFIM performs the fuzzy inference process from the vector of time series of temperature measurements at the corresponding temperature measurement points. The inference results of DFIUs in the time domain are weighed and synthesized by dynamic response coefficients to obtain the time adjustment vector of the thermal boundary condition. In the space domain, the inference results of DFIMs are weighed and synthesized by the normal distribution function to obtain the space adjustment vector. Numerical experiments are performed to study the effects of the number of measurement points, measurement errors and the buried depth of thermocouples on the inversion results. Comparison with the existing dynamic matrix control inverse method is also conducted, and it shows the validity of the inverse method established in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the inverse problems of simultaneous reconstruction of time-dependent thermal conductivity, convection or absorption coefficients in the parabolic heat equation governing transient heat and bio-heat thermal processes. Using initial and boundary conditions, as well as heat moments as over-determination conditions ensure that these inverse problems have a unique solution. However, the problems are still ill-posed since small errors in the input data cause large errors in the output solution. To overcome this instability we employ the Tikhonov regularization. A discussion of the choice of multiple regularization parameters is provided. The finite-difference method with the Crank–Nicolson scheme is employed as a direct solver. The resulting inverse problems are recast as nonlinear minimization problems and are solved using the lsqnonlin routine from the MATLAB toolbox. Numerical results are presented and discussed. [ABSTRACT FROM AUTHOR]

Heat source layout optimization is an effective way to enhance heat transfer for electronic cooling. In this paper, the heat source layout optimization in two-dimensional heat conduction is investigated using simulated annealing (SA) method. Mathematical analysis is conducted to transform the heat source layout problem into a combinatorial optimization problem, which can be solved by SA. Three typical cases with various boundary conditions are introduced to validate the effectiveness of SA for heat source layout optimization. The solutions of SA are compared to the ones of random distribution (RD) and the ones of bionic optimization (BO). The results indicate that the maximum temperature of the domain can be remarkably reduced after optimizing the heat source layout using SA compared to RD. Compared to BO, it needs more computational time for SA to obtain the solution. Furthermore, the maximum temperature after optimizing by BO is lower than the ones by SA for the cases with symmetric boundary conditions. While for the case with asymmetric boundary conditions, SA performs better and the maximum temperature lower than BO is obtained. It can be concluded that simulated annealing method is effective to optimize the heat source layout problem in heat conduction. [ABSTRACT FROM AUTHOR]

The wrapping pattern of thin insulation is an important issue in cryogenic installations because it can significantly affect heat transport. The major objective of this study is to develop the numerical boundary conditions (BC) needed to model the wrapping pattern of thin insulation. An example of the practical application of the proposed BC includes the heat transfer of Rutherford NbTi cables immersed in superfluid helium (He II) across thin layers of electrical insulation. The proposed BC and a mathematical model of heat transfer in He II are implemented in the open source CFD toolbox OpenFOAM. The implemented mathematical model and the BC are compared with experiments. The study confirms that the thermal resistance of electrical insulation can be lowered by implementing the proper wrapping pattern. The proposed BC can be useful in the study of new patterns for wrapping schemes. Further possible improvements of the tool are indicated in the paper. [ABSTRACT FROM AUTHOR]

Partitioned approaches for the simulation of coupled conjugate heat transfer are gaining popularity in fields that require accurate thermal predictions. Considerable efforts have been put into determining stable coupling schemes, but performance enhancements have been neglected. This paper presents, for the first time, a detailed and comprehensive study of the numerical properties of Dirichlet-Robin coupling procedures, used in conjugate heat transfer simulation, with emphasis put on the optimal local coupling formulation that was recently derived from a stability analysis. This all-new optimal coupling approach provides local adaptability and has never been tested on a complex setup. This investigation looks to determine the relevance and the limitations of the theory when applied to complex conjugate heat transfer setups. The stability theory of the optimal Dirichlet-Robin coupling scheme is first recalled, then, a realistic 3D application, with complex geometry and flow structures, is used to evaluate the performance and sensitivity of Dirichlet-Robin couplings, with respect to various numerical parameters. This detailed study allows, for the first time, to evaluate the advantages and limitations of the recently proposed optimal procedure, when used on realistic 3D CHT problems. It turns out that the local optimal Dirichlet-Robin formulation outperforms all what is found in literature, and insures unconditional stability with monotone convergence for all considered setups of the 3D model. [ABSTRACT FROM AUTHOR]