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The frictional and thermal entropy generation rates (S ˙ f r and S ˙ t h) of two heatsinks with serpentine (Conf. A) and double serpentine (Conf. B) channels with water/silver Nano fluid (NF) were numerically investigated. The results demonstrated that the augmentation of nanoparticle concentration (φ) from 0% to 1% leads to decrease S ˙ t h by 6.36% and 3.51% in Conf. A and Conf. B, respectively, for Re=500. The escalation of Re from 500 to 2000 increases this percentages to 9.93% and 7.51%, respectively. Also, the increase of Re from 500 to 2000 at a constant φ reduces S ˙ t h by 63% and 68% in Conf. A and Conf. B, respectively, due to enhance the heat dissipation. Moreover, the increasing of φ from 0% to 1% decreases S ˙ f r by 12.41% in both configurations and at four studied Res due to decreasing the NF velocity. Besides, the escalation of Re from 500-2000 intensifies S ˙ f r nearly by 62% and 67% in Conf. A and Conf. B, respectively. The entropy contour plots reveal that S ˙ f r intensifies near the turn regions of the serpentine channels. Also, S ˙ t h is intensifies at the entrance of heatsink channels due to the high temperature gradient at these points. Conversely, S ˙ f r escalates at the exit of the channels due to intensification of the vortexes formed at the turn parts and along the serpentine channel. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann schemes are known for their efficiency and low dissipation properties. However, the standard lattice Boltzmann method (LBM) is limited to Cartesian grids, and this approach can be troublesome when approximating thermal flows over curved walls. The present work proposes to solve the two-dimensional lattice Boltzmann equation under curvilinear coordinate transformation to simulate thermal flows with body-fitted grids. Several test cases are discussed, and the results are extensively compared with a very favourable outcome to the available numerical and experimental data, confirming the importance of the implemented methodology. Natural convection in a square cavity and a wavy cavity, as well as flow in a concentric cylindrical annulus are used for validation. Forced convection over a heated two-dimensional cylinder is also included. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to analyze the accuracy of the single and two-phase numerical methods for calculation of ferrofluid convective heat transfer in the presence of a magnetic field. The findings of current study are compared with previous single-phase numerical results and experimental data. Accordingly, the effect of various parameters including nanoparticles concentration, Reynolds number and magnetic field strength on the performance of the single and two-phase models are evaluated. Design/methodology/approach: A two-phase mixture numerical study is carried out to investigate the influence of four U-shaped electromagnets on the hydrodynamic and thermal characteristics of Fe3O4/Water ferrofluid flowing inside a heated channel. Findings: It is observed that the applied external magnetic field signifies the convective heat transfer from the channel surface, despite local reduction at a few locations. The maximum heat transfer enhancement is predicted as 23% and 25% using single and two-phase models, respectively. The difference between the results of the two models is mainly attributed to the slip velocity effect which is accounted for in the two-phase model. The magnetic field gradient leads to a significant increase in the slip velocity which in turn causes a slight difference in velocity and temperature profiles obtained by the single and two-phase models in the magnetic field region. According to percentage error calculation, the two-phase method is generally more accurate than the single-phase method. However, the percentage error of both models improves by decreasing either magnetic field intensity or Reynolds number. Originality/value: For the first time in the literature, to the best of the authors' knowledge, the current work analyzes the accuracy of the single and two phase numerical methods for calculation of ferrofluid convective heat transfer in the presence of a magnetic field. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to numerically investigate the thermal performance evaluation of a microchannel with different porous media insert configurations. Design/methodology/approach: Heat transfer and pressure drop of fluid flow through a three-dimensional (3D) microchannel with different partially and filled porous media insert configurations are investigated numerically. The number of divisions and positions of porous material inside the microchannel for 12 different arrangements are considered. A control volume method is used for single-phase laminar flow with the Darcy–Forchheimer model used for the porous media. The geometry of the problem consists of a microchannel with a rectangular cross-section of 0.4 mm × 0.2 mm and length 20 mm, with a stainless steel porous material insert with a porosity coefficient of ε = 0.32 and a Darcy number of Da = 2.7 × 10−4. Findings: Numerical results show that when the transverse arrangement is used, as the number of partitions increases, the thermal performance is improved and the heat transfer increases up to 300% compared to that of the plain microchannel. Comparing the obtained results from the microchannels with transverse and longitudinal configurations, at low Reynolds numbers, the transverse arrangement of porous blocks and at high Reynold numbers, the longitudinal arrangement present the best thermal performance which is virtually four times higher compared to the obtained Nu numbers from the plain microchannel. The results show that as the volume of porous material is constant in the cases with various transverse porous blocks, the pressure drop is not changed in these cases. Also, the highest thermal performance ratio is when the porous material is placed along the walls in a longitudinal direction. Originality/value: To the best knowledge of the authors, in the previous research, the effect of the arrangement and location of the porous medium in the transverse and longitudinal direction in the microchannel and their effect in different states on the behavior of flow and heat transfer has not been numerically investigated. In this study, the porous media configuration and its placement in a 3D microchannel were numerically studied. The effect of porous material layout and configurations in different longitudinal and transverse directions on the pressure drop, heat transfer and thermal performance in the 3D microchannel is investigated numerically. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to investigate the unsteady stagnation-point flow and heat transfer of fractional Maxwell fluid towards a time power-law-dependent stretching plate. Based on the characteristics of pressure in the boundary layer, the momentum equation with the fractional Maxwell model is firstly formulated to analyze unsteady stagnation-point flow. Furthermore, generalized Fourier's law is considered in the energy equation and boundary condition of convective heat transfer. Design/methodology/approach: The nonlinear fractional differential equations are solved by the newly developed finite difference scheme combined with L1-algorithm, whose convergence is verified by constructing a numerical example. Findings: Some interesting results can be revealed. The larger fractional derivative parameter of velocity promotes the flow, while the smaller fractional derivative parameter of temperature accelerates the heat transfer. The temperature boundary layer is thicker than the velocity boundary layer, and the velocity enlarges as the stagnation parameter raises. This is because when Prandtl number < 1, the capacity of heat diffusion is greater than that of momentum diffusion. It is to be observed that all the temperature profiles first enhance a little and then reduce rapidly, which indicates the thermal retardation of Maxwell fluid. Originality/value: The unsteady stagnation-point flow model of Maxwell fluid is extended from integral derivative to fractional derivative, which has more flexibility to describe viscoelastic fluid's complex dynamic process and provide a theoretical basis for industrial processing. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate the mixed convection of a two-phase water–aluminum oxide nanofluid in a cavity under a uniform magnetic field. Design/methodology/approach: The upper wall of the cavity is cold and the lower wall is warm. The effects of different values of Richardson number, Hartmann number, cavitation length and solid nanoparticles concentration on the flow and temperature field and heat transfer rate were evaluated. In this paper, the heat flux was assumed to be constant of 10 (W/m2) and the Reynolds number was assumed to be constant of 300 and the Hartmann number and the volume fraction of solid nanoparticles varied from 0 to 60 and 0 to 0.06, respectively. The Richardson number was considered to be 0.1, 1 and 5. Aspect ratios were 1, 1.5 and 2. Findings: Comparison of the results of this paper with the results of the numerical and experimental studies of other researchers showed a good correlation. The results were presented in the form of velocity and temperature profiles, stream and isotherm lines and Nusselt numbers. The results showed that by increasing the Hartmann number, the heat transfer rate decreases. An increase from 0 to 20 in Hartmann number results in a 20 per cent decrease in Nusselt numbers, and by increasing the Hartmann number from 20 to 40, a 16 per cent decrease is observed in Nusselt number. Accordingly, it is inferred that by increasing the Hartmann number, the reduction in the Nusselt number is decreased. As the Richardson number increased, the heat transfer rate and, consequently, the Nusselt number increased. Therefore, an increase in the Richardson number results in an increase of the Nusselt number, that is, an increase in Richardson number from 0.1 to 1 and from 1 to 5 results in 37 and 47 per cent increase in Nusselt number, respectively. Originality/value: Even though there have been numerous investigations conducted on convection in cavities under various configurations and boundary conditions, relatively few studies are conducted for the case of nanofluid mixed convection in square lid-driven cavity under the effect of magnetic field using two-phase model. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to validate whether the local thermal equilibrium for unsteady state is an appropriate assumption for the porous media with closed pores. It also compares the transient temperatures between the pore scale and volume averaged approaches to prove that the volume averaged method is an appropriate technique for the heat transfer in closed-cell porous media. The interfacial heat transfer coefficient for the closed-cell porous media is also discussed in details. Design/methodology/approach: The governing equations for the pore scale and continuum domains are given. They are solved numerically for the pore scale and volume-averaged domains. The results are compared and discussion was done. The performed discussions and explanations are supported with figure and graphics. Findings: A local thermal non-equilibrium exits for the closed-cell porous media in which voids are filled with water during the unsteady heat transfer process. Local thermal non-equilibrium condition exists in the cells under high temperature gradient and it disappears when the heat transfer process becomes steady-state. Although a local thermal equilibrium exists in the porous media in which the voids are filled with air, a finite value for heat transfer coefficient is found. The thermal diffusivity of air and solid phase are close to each other and hence a local thermal equilibrium exists. Research limitations/implications: The study is done only for the closed-cell porous media and for Rayleigh number till 105. Two common working fluids as water and air are considered. Practical implications: There are many applications of porous media with closed pores particularly in the industry, such as the closed-cell metal foam or the closed cells in porous materials such as foods and plastic-based insulation material. The obtained results are important for transient heat transfer in closed-cell porous materials. Social implications: The obtained results are important from the transient application of heat transfer in the closed-cell material existing in nature and industry. Originality/value: The authors' literature survey shows that it is the first time the closed-cell porous media is discussed from local thermal non-equilibrium point of view and it is proved that the local thermal non-equilibrium can exist in the closed-cell porous media. Hence, two equations as solid and fluid equations should be used for unsteady heat transfer in a closed-cell porous medium. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to present a high-order algorithm implemented with the modal spectral element method and simulations of three-dimensional thermal convective flows by using the full viscous dissipation function in the energy equation. Three benchmark problems were solved to validate the algorithm with exact or theoretical solutions. The heated rotating sphere at different temperatures inside a cold planar Poiseuille flow was simulated parametrically at varied angular velocities with positive and negative rotations.Design/methodology/approach The fourth-order stiffly stable schemes were implemented and tested for time integration. To provide the hp-refinement and spatial resolution enhancement, a modal spectral element method using hierarchical basis functions was used to solve governing equations in a three-dimensional space.Findings It was found that the direction of rotation of the heated sphere has totally different effects on drag, lateral force and torque evaluated on surfaces of the sphere and walls. It was further concluded that the angular velocity of the heated sphere has more influence on the wall normal velocity gradient than on the wall normal temperature gradients and therefore, more influence on the viscous dissipation than on the thermal dissipation.Research limitations/implications This paper concerns incompressible fluid flow at constant properties with up to medium temperature variations in the absence of thermal radiation and ignoring the pressure work.Practical implications This paper contributes a viable high-order algorithm in time and space for modeling convective heat transfer involving an internal heated rotating sphere with the effect of viscous heating.Social implications Results of this paper could provide reference for related topics such as enhanced heat transfer forced convection involving rotating spheres and viscous thermal effect.Originality/value The merits include resolving viscous dissipation and thermal diffusion in stationary and rotating boundary layers with both h- and p-type refinements, visualizing the viscous heating effect with the full viscous dissipation function in the energy equation and modeling the forced advection around a rotating sphere with varied positive and negative angular velocities subject to a shear flow. [ABSTRACT FROM AUTHOR]

A method to simulate ice accretion on swept wings using a two-dimensional Navier-Stokes airflow solver, an Eulerian droplets field formulation and a PDE based thermodynamic model is presented. The current approach, called 2.5D in this paper, is developed by applying a rotation of the system of coordinates to allow simulations on a cut normal to the leading edge. The crossflow velocity component in the simulation plane is computed with the third momentum equation simplified by assuming null derivatives in the spanwise direction. The consistency of the ice accretion software, NSCODE-ICE, is first verified by a grid convergence study on 2D icing cases and an icing layers convergence study on 2D and 2.5D icing simulations. The validation of the approach is performed on an unswept two-dimensional glaze ice case and on a rime ice case. The current 2.5D approach is then validated on an infinite MS-317 swept wing and compared to results from usual semi-empirical infinite swept wing corrections. The new approach succeeds to model the stagnation line where other correction methods fail, leading to a better representation of the convective heat transfer in this area. [ABSTRACT FROM AUTHOR]

• Heat transfer and flow over rectangular cylinders are conducted. • The relationship between Nusselt numbers with flow regimes is determined. • Cylinder with smaller aspect ratio destroy less exergy with a higher Nusselt number. • A criterion for the onset of emersion of the two-layer vortices is found. • Three kinds of secondary vortices are identified. This numerical study investigates the forced convection heat transfer from and flow topology around isothermal rectangular cylinders. The effects of various cross-sectional aspect ratios (AR = 0.25–4), Reynolds numbers (Re = 30–200), and Prandtl numbers (Pr = 0.7, 5) are examined on the results. Two or three-dimensional simulations are conducted depending on the Re and AR employed. The results show that the near primary vortices (Kármán wake) undergo a downstream transition to the two-layered vortices, followed by a transition from the two-layered vortices to the secondary vortices for AR ≤ 1. For smaller aspect ratios, the prevailing of the secondary vortices is further accelerated, i.e., they emerge at a lower Re and a shorter downstream distance from the cylinder. Three types of secondary vortices distinguished based on their shape, strength, and generation mechanism were observed. A geometric criterion (spacing ratio) for the onset of evolution of the two-layer structure is proposed for each AR. It is observed that the sensitiveness of the Nusselt number to AR and Re can be ascribed to the change in the scenarios of the flow separation and reattachment (flow regimes), vortex strength, and wake-recirculation size (L r). The Nusselt number grows with increasing Re and Pr but diminishes with AR. The relationship between the average Nusselt number and L r is direct in the steady flow, while they are inversely linked in the two- and three-dimensional unsteady flow. Reducing AR from 4 to 0.25, depending on Re and Pr , leads to a 90%–170% enhancement in the Nusselt number, whereas increasing AR amplifies the total heat transfer due to an enlargement in the heat transfer surfaces. The second law of thermodynamics analysis reveals that cylinders with smaller AR generate lower entropy (destroy lower exergy); therefore, they are more efficient. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to report a novel formulation of convective heat transfer source term for the case of flow through porous medium. Design/methodology/approach – The novel formulation is obtained by analytical solution of an idealized dual problem. Computations are performed by dedicated tool for fixed bed combustion named GRATECAL and developed by the authors. However, the proposed method can also be applied to other porous media flow problems. Findings – The new source term formulation is unconditionally stable and it respects exponential decay of temperature difference between the fluid and porous solid medium. Practical/implications – The results of this work are applicable in the simulation of convective heat transfer between the fluid and porous medium. Applications include e.g. fixed bed combustion, catalytic reactors and lime kilns. Originality/value – The reported solution is believed to be original. It will be useful to all involved in numerical simulations of fluid flow in porous media with convective heat transfer. [ABSTRACT FROM AUTHOR]

The problem of radiative–conductive–convective heat transfer in a three-dimensional domain is studied in the framework of the diffusion ( P 1 ) steady-state approximation. The unconditional unique solvability of this nonlinear model is proved in the case of Robin-type boundary conditions for the temperature and the mean intensity function. An iterative algorithm for the numerical solution of the model is proposed. Numerical examples demonstrating the importance of the radiative heat transfer at high temperatures are presented. [ABSTRACT FROM AUTHOR]

Purpose – Mathematical and numerical models are developed to study the melting of a Phase Change Material (PCM) inside a 2D cavity. The bottom of the cell is heated at constant and uniform temperature or heat flux, assuming that the rest of the cavity is completely adiabatic. The paper used suitable numerical methods to follow the interface temporal evolution with a good accuracy. The purpose of this paper is to show how the evolution of the latent energy absorbed to melt the PCM depends on the temperature imposed on the lower wall of the cavity. Design/methodology/approach – The problem is written with non-homogeneous boundary conditions. Momentum and energy equations are numerically solved in space by a spectral collocation method especially oriented to this situation. A Crank-Nicolson scheme permits the resolution in time. Findings – The results clearly show the evolution of multicellular regime during the process of fusion and the kinetics of phase change depends on the boundary condition imposed on the bottom cell wall. Thus the charge and discharge processes in energy storage cells can be controlled by varying the temperature in the cell PCM. Substantial modifications of the thermal convective heat and mass transfer are highlighted during the transient regime. This model is particularly suitable to follow with a good accuracy the evolution of the solid/liquid interface in the process of storage/release energy. Research limitations/implications – The time-dependent physical properties that induce non-linear coupled unsteady terms in Navier-Stokes and energy equations are not taken into account in the present model. The present model is actually extended to these coupled situations. This problem requires smoother geometries. One can try to palliate this disadvantage by constructing smoother approximations of non-smooth geometries. The augmentation of polynomials developments orders increases strongly the computing time. When the external heat flux or temperature imposed at the PCM is much greater than the temperature of the PCM fusion, one must choose carefully some data to assume the algorithms convergence. Practical implications – Among the areas where this work can be used, are: buildings where the PCM are used in insulation and passive cooling; thermal energy storage, the PCM stores energy by changing phase, solid to liquid (fusion); cooling and transport of foodstuffs or pharmaceutical or medical sensitive products, the PCM is used in the food industry, pharmaceutical and medical, to minimize temperature variations of food, drug or sensitive materials; and the textile industry, PCM materials in the textile industry are used in microcapsules placed inside textile fibres. The PCM intervene to regulate heat transfer between the body and the outside. Originality/value – The paper's originality is reflected in the precision of its results, due to the use of a high-accuracy numerical approximation based on collocation spectral methods, and the choice of Chebyshev polynomials basis in both axial and radial directions. [ABSTRACT FROM AUTHOR]

Highlights: [•] Effect of magnetic field on heat transfer for 3D MHD flow is examined. [•] Magnetic field increase declined temperature for heating and increased for cooling. [•] Magnetic field increase enhanced the heat transfer and Nu number for two cases. [Copyright &y& Elsevier]

Abstract: This article presents a numerical investigation on the convective heat transfer performance of nanofluids over a permeable stretching surface in the presence of partial slip, thermal buoyancy and temperature dependent internal heat generation or absorption. Two different types of nanoparticles, namely Cu and Al2O3 are considered by using water-based fluid with Prandtl number P r =6.785 for simulating the heat transfer and flow behavior of nanofluids. The proposed model is validated with the available experimental data and correlations. The similarity solutions which depend on nanoparticle volume fraction ϕ (0⩽ ϕ ⩽0.2), slip parameter, suction/injection parameter, etc. are presented through graphs and tables and discussed in detail. [Copyright &y& Elsevier]

Abstract: Unsteady heat transfer of a cylinder in pulsating cross flow is investigated. The heat transfer process is considered as a nonlinear single-input, single-output system, with large amplitude velocity perturbations as “input” and total heat transfer rate from the cylinder surface to the fluid as “output”. Quantitatively accurate, low-order models of the heat source dynamics are obtained with a variety of nonlinear system identification methods from time series data generated with unsteady CFD computations. A polynomial type, equation error identification scheme is found to yield very accurate results. In order to obtain the heat source response function in the frequency domain, the equation error model is converted into the frequency domain using harmonic balance as well as harmonic probing approaches. In the harmonic balance approach, a set of nonlinear algebraic equations is solved for the coefficients of the harmonic ansatz. In the harmonic probing method, a recursive relation is obtained to deliver the higher order transfer functions of the nonlinear heat source. Alternatively, a nonlinear black box identification technique is used to identify the heat source dynamics. It is found to capture the amplitudes of higher harmonics with increased accuracy. [Copyright &y& Elsevier]

Abstract: A steady and laminar convective flow has been numerically simulated in the fully-developed annular region of a finned double-pipe subjected to the constant heat flux boundary condition imposed at the inner-pipe wall. Finite element method has been employed in this study. Friction factor and Nusselt number have been studied as flow characteristics against variations in the ratio of radii of the inner and the outer pipes, the fin height, the fin half angle and the number of fins. The results show significant enhancement in the heat transfer rate in both the cases when sufficient pumping power is available and when it is not. The minimum and maximum increase in the product of friction factor and Reynolds number relative to the finless geometry is more than one time and more than 40 times respectively while gain in the relative value of Nusselt number lies in the range 1–177. This provides an evidence of more than four times enhancement in the heat transfer coefficient relative to that in the pressure loss as a result of extended fin surfaces. [Copyright &y& Elsevier]