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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]

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]

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]

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

Heat transfer equations describe in most general terms the relationship of temperature, time and space coordinates. In order to achieve a solution matching a given phenomenon, unicity conditions of the solution have to be determined. One of them is the heat transfer coefficient. In complex heat transfer processes, to which belong quenching operation, that coefficient is being determined experimentally or numerically.This paper presents a technique for identifying the local heat transfer coefficient when cooling hot bodies in water during quenching. A dynamic method was applied, using inverse solution of the heat transfer equation. In that solution, a temperature experimentally determined during sensor cooling is set in the equation. The paper presents the results of measurements and calculations as well as a discussion of results for various cooling conditions and positions of the active surface of the sensor. [Copyright &y& Elsevier]

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]

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, the characterization of laminar convective heat transfer in rhombic shaped microchannel with H1 (axially constant heat flux and circumferentially constant temperature) and H2 (constant axial and circumferential wall heat flux) boundary conditions is presented. A three-dimensional numerical model is developed for hydrodynamically and thermally developing flow in different rhombic geometries with side-angles varying from 10° to 90°. The numerical model is first validated with the other model developed in the literature for rectangular geometry and subsequently the results are compared with rhombic channel with different side-angles. This model is then extended to determine the temperature and heat flux distributions in rhombic microchannel, which is used to find the local and hydrodynamically and thermally fully developed Nusselt numbers. It is found that the fully developed Nusselt number varies only with the side-angles of rhombic channel and generalized correlations are developed as a function of side-angles for H1 and H2 boundary conditions. Correlations for developing length, local and fully-developed Nusselt numbers for rhombic channels are currently not available. These results will be useful in design and optimization of rhombic microchannel for electronic cooling applications. [ABSTRACT FROM AUTHOR]

This paper presents forced convective heat transfer in a channel with a built-in square obstacle. The governing equations with the boundary conditions are solved using a finite volume method. The computations were done for a fixed blockage ratio ( S =1/8) at Pr =0.71, and Reynolds ( Re ) and Stuart ( N ) numbers ranging from 1 to 250 and 0 to 10, respectively. The results are presented to show the effect of the channel walls and streamwise magnetic field at different Reynolds numbers on forced convection heat transfer from a square cylinder. A correlation is obtained for Nusselt number, in which the effect of a magnetic field is taken into account. The obtained results revealed that the existence of channel walls decreases the effects of magnetic field on Nusselt number. It also showed that by increasing Stuart number the thickness of thermal boundary layer increases and the convective heat transfer decreases. [ABSTRACT FROM AUTHOR]

Recent works have examined the thermal and dynamical aspects of natural convection occurring in tilted hemispherical cavities whose disk constitutes the hot active wall. The influence of some important aspects on the natural flows have been considered such as the Rayleigh Number, the disk inclination angle with respect to the horizontal plane and the thermal boundary condition on the disk (Dirichlet, Neumann). Combinations of these parameters have been treated in steady state as well as is transient regime. Correlations of Nusselt–Rayleigh type (steady state) and Nusselt–Rayleigh–Fourier type (transient regime) that allow quantifying the heat transfer are proposed in these surveys. The objective of this paper is to synthesize and summarize these works in order to facilitate their implementation in engineering applications. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re =1–40 and Richardson number, Ri =0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re =1–2, between Re =2–3 and between Re =3–4 for Ri =0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work. [Copyright &y& Elsevier]

Abstract: This paper aims to study the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method. To include these effects, hydrodynamic boundary condition equations are modified. In this problem, cold fluid enters the microchannel and leaves it after cooling the hot walls. For a wide range of inlet Knudsen number (Kn), computations are performed, and for validation, appropriate comparisons between present and previous available results are made. As the results, stream lines, longitudinal variations of friction coefficient, Nusselt number, slip velocity and temperature jump, and velocity and temperature profiles in different cross sections are presented. The results show that lattice Boltzmann method can be used to simulate mixed convection in a microchannel, and the effects of buoyancy forces are important for Kn < 0.05, specially for hydrodynamic properties, and thus should be included. For Kn > 0.05, these effects can be ignored. In addition, it is observed that buoyancy forces generate a rotational cell in the microchannel flow, leading to the negative slip velocity at Kn = 0.005. [Copyright &y& Elsevier]

Abstract: In this paper, fluid flow and heat transfer across a long equilateral triangular cylinder placed in a horizontal channel is studied for Reynolds number range 1–80 (in the steps of 5) and Prandtl number of 0.71 for a fixed blockage ratio of 0.25. The governing Navier-Stokes and energy equations along with appropriate boundary conditions are solved by using a commercial CFD solver FLUENT (6.3). The computational grid is created in a commercial grid generator GAMBIT. The flow and temperature fields are presented by stream-line and isotherm profiles, respectively. The wake/recirculation length, mean drag coefficient and average Nusselt number, etc. are calculated for the above range of conditions studied here. The critical value of the Reynolds number (i.e., transition to transient) is found to lie between Re=58 and Re=59. The average Nusselt number and the wake length increase with increasing value of the Reynolds number; however, the mean drag coefficient decreases with increasing value of the Reynolds number. Finally, simple correlations for wake length, mean drag coefficient and average Nusselt number are obtained for the range of conditions studied here. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present heat transfer measurements of gas in a tube under rarefied condition. The measurements are made in a circular tube of inner diameter 25mm for approximately constant wall temperature boundary conditions, with nitrogen, oxygen, argon, and helium as the working fluids. The range of Knudsen and Reynolds numbers covered in this study are 0.0022–0.032 and 0.13–14.7, respectively. Whereas the continuum values are correctly reproduced in our setup, the measured values for Nusselt numbers are very small in the slip regime. The measured values are two-five orders of magnitude smaller than the corresponding values in the continuum regime, and suggest that the Nusselt number is a strong function of Reynolds, Knudsen and Brinkmann numbers in the slip flow regime. These are among the first heat transfer measurements in the slip flow regime and the current theoretical and simulation models are inadequate to explain such low values of Nusselt number. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider an inverse problem of heat equation with Robin boundary condition for identifying heat transfer coefficient. Combining the method of fundamental solutions with discrepancy principle for the choice of the locations for source points, we give a method for solving the reconstruction problem. Since the resultant matrix is severe ill-conditioning, Tikhonov regularization with L-curve method is employed. Some numerical examples are given for verifying the efficiency and accuracy of the presented method. [Copyright &y& Elsevier]

Abstract: This paper reports the results of a numerical study of the Nusselt number for the H1 and T boundary conditions in laminar, fully-developed flows of pseudoplastic and dilatant fluids in rectangular ducts. Equations for the apparent viscosity that span the entire shear rate range were utilized and the Nusselt numbers were calculated as a function of a shear rate parameter that determines the flow regime where the duct is operating. Numerical results for the Nusselt number in all flow regimes are included along with correlation equations. Finally, errors associated with applying power law solutions are discussed. [Copyright &y& Elsevier]

Abstract: This paper deals with analytical solution of steady-state heat transfer for laminar, two-dimensional and rarefied gas flow in an infinite microtube subjected to mixed boundary conditions. To account for the slip-flow characteristics of microscale heat transfer, temperature jump condition at the wall has been incorporated in the model while the fluid velocity is assumed to be constant (slug flow). The energy equation in the thermal entrance region has been solved by the method of separation of variables. The solution yields closed form expressions for bulk-mean temperature and Nusselt number in terms of Knudsen number and Peclet number. [Copyright &y& Elsevier]

Abstract: In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters. [Copyright &y& Elsevier]

Abstract: Due to the complexity of the flow and the difficulty of measuring heat transfer directly in gas turbines or even in turbine cascade, heat transfer coefficients have been extracted from data obtained in mass transfer measurements using the heat/mass transfer analogy. The present paper shows the validity of the heat/mass transfer analogy from separate heat transfer and mass transfer measurements on simulated turbine blades with equivalent experimental and geometric conditions. The Nusselt numbers from heat transfer experiments employing a constant temperature boundary condition are compared to the Sherwood number from mass transfer experiments employing a constant concentration boundary condition. [Copyright &y& Elsevier]

Abstract: The problem of laminar natural convection heat transfer in a square cavity with an adiabatic arc shaped baffle is analyzed in this paper. As boundary conditions of the cavity, two vertical opposite walls are kept at constant but different temperatures and the remaining two walls are kept thermally insulated. Results are presented for a range of Rayleigh numbers, arc lengths of the baffle, and shape parameters of the baffle. Finally, parametric results are presented in terms of isothermal lines and streamlines. It is identified that flow and thermal fields are modified by the blockage effect of the baffle. The degree of flow modification due to blockage is enhanced by increasing the shape parameter of the baffle. [Copyright &y& Elsevier]

The forced convective heat transfer characteristics for incompressible power-law fluids past a bundle of circular cylinders have been investigated numerically. The cylinder-to-cylinder hydrodynamic interactions have been approximated via a simple cell model. The momentum and energy equations have been solved using a finite difference based numerical method for a range of physical and kinematic conditions. The role of the two commonly used thermal boundary conditions, namely, constant temperature or constant heat flux, on heat transfer characteristics has also been studied. Extensive numerical results elucidating the effect of shear-thinning viscosity on the values of Nusselt number have been obtained for Peclet numbers ranging from 1 to 5000, Reynolds number in the range 1–500, flow behaviour index 1⩾n⩾0.5 and three values of voidages, namely, 0.4, 0.5 and 0.6, typical of tubular heat exchangers and tube banks. Under all conditions, varying levels of enhancement in Nusselt number are observed due to shear-thinning behaviour. The surface averaged Nusselt number shows strong dependence on the values of voidage, power-law index, Reynolds and Peclet numbers. The paper is concluded by presenting comparisons with the scant experimental results available in the literature. [Copyright &y& Elsevier]