A numerical study on the forced convection heat transfer from an isothermal and isoflux sphere in the steady symmetric flow regime

The effects of Reynolds and Prandtl numbers on the heat transfer characteristics of an unconfined sphere for different thermal boundary conditions (isothermal and isoflux) on the sphere surface have been investigated numerically by using a finite volume method for the range of conditions as 5 ⩽ Re ⩽ 200 and 0.7 ⩽ Pr ⩽ 400 (the maximum value of Peclet number being 2000). Based on the numerical results obtained herein, heat transfer correlations are developed for the constant temperature and the constant heat flux boundary conditions on the solid sphere surface in the steady symmetric flow regime. The variation of local Nusselt number on the sphere surface shows the effect of Prandtl number on heat transfer from a sphere in this flow regime. In addition, this work also demonstrates an approach to solve such flow problems using the Cartesian form of the field equations.     

Analysis of combined mode heat transfer in a porous medium using the lattice Boltzmann method

ABSTRACT

Application of the lattice Boltzmann method (LBM) in solving a combined mode conduction, convection, and radiation heat transfer problem in a porous medium is extended. Consideration is given to a 1-D planar porous medium with a localized volumetric heat generation zone. Three particle distribution functions, one each for the solid temperature, the gas temperature, and the intensity of radiation, are simultaneously used to solve the gas- and the solid-phase energy equations. The volumetric radiation source term appears in the solid-phase energy equation, and it is also computed using the LBM. To check the accuracy of the LBM results, the same problem is also solved using the finite volume method (FVM). Effects of convective coupling, flow enthalpy, solid-phase conductivity, scattering albedo porosity, and emissivity on axial temperature distribution are studied and compared with the FVM results. Effects of flow enthalpy, solid-phase conductivity, and emissivity are also studied on radiative output. LBM results are in excellent agreement with those of the FVM.     

Effect of surface radiation on conjugate natural convection in a horizontal annulus driven by inner heat generating solid cylinder

This paper reports a numerical study of the laminar conjugate natural convection heat transfer with and without the interaction of the surface radiation in a horizontal cylindrical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal circular boundary. Numerical solutions are obtained by solving the governing equations with a pressure correction method on a collocated (non-staggered) mesh. Steady-state results are presented for the flow and temperature distributions and Nusselt numbers for the heat generation based Grashof number ranging from , solid-to-fluid thermal conductivity ratios of 1, 5, 10, 50 and 100, radius ratios of 0.226 and 0.452 and surface emissivities of 0–0.8 with air as the working medium. It is observed that surface radiation reduces the convective heat transfer in the annulus compared to the pure natural convection case and enhances the overall Nusselt number.     

Time and spatial heat transfer performance around an isothermally heated sphere placed in a uniform, downwardly directed flow (in relation to the enhancement of latent heat storage rate in a spherical capsule)

The aim of this study is to reveal the temporal and spatial heat transfer performance of an isothermally heated sphere placed in a uniform, downwardly directed flow using a micro-foil heat flow sensor (HFS). A HFS, whose response time is about 0.02 s, was pasted on the surface of a heated copper sphere. Experiments were carried out using air with a Grashof number of 3.3 × 10⁵ and with several Reynolds numbers (Re) up to 1800. Three flow patterns appeared: a chaotic flow at Re<240; a two-dimensional steady separated flow at 240 Re<500, and a three-dimensional unsteady separated flow at Re 500. In addition, the instantaneous and time-averaged heat transfer performance around the sphere in each of the three regions was clarified. Next, enhancement of the latent heat storage rate of a solid phase change material (PCM) in a spherical capsule was performed. The flow around the spherical capsule, in which the solid PCM was filled and placed in a heated, upwardly directed flow, is the approximate adverse flow phenomenon around the heated sphere which was placed in a downwardly directed flow. In other words, the buoyant flow and the forced flow are in the opposite directions in these two cases. Tests of latent heat storage were run for two Reynolds numbers which represented different flow characteristics in the heat transfer experiments, Re=150 and 1800. Furthermore, copper plates were inserted into the solid PCM, of which thermal conductivity was considerably low, to enhance the latent heat storage rate for the two Reynolds number flows.     

Simulation Studies on Multimode Heat Transfer from a Square-Shaped Electronic Device with Multiple Discrete Heat Sources

ABSTRACT

The results of a numerical study of the problem of multimode heat transfer from a square-shaped electronic device provided with three identical flush-mounted discrete heat sources are presented here. Air, a radiatively nonparticipating fluid, is taken to be the cooling medium. The heat generated in the discrete heat sources is first conducted through the device, before ultimately being dissipated by convection and surface radiation. The governing partial differential equations for temperature distribution are converted into algebraic form using a finite-volume based finite difference method, and the resulting algebraic equations are subsequently solved using Gauss-Seidel iterative procedure. A grid size of 151 × 91 is used for discretizing the computational domain. The effects of all relevant parameters, including volumetric heat generation, thermal conductivity, convection heat transfer coefficient, and surface emissivity, on various important results, such as the local temperature distribution, the peak temperature of the device, and the relative contributions of convection and surface radiation to heat dissipation from the device, are studied in sufficient detail. The exclusive effect of surface radiation on pertinent results of the present problem is also brought out.     

Thermal behavior of functionally graded solid sphere with nonuniform heat generation

This article deals with the thermoelastic analysis of the functionally graded solid sphere due to nonuniform heat source inside the body under the constant surface temperature. The sphere material is considered to be graded along the radial direction where an exponentially varying distribution is assumed. Also, the material assumed with constant Poisson’s ratio. The implicit finite difference scheme is used to determine the transient temperature, radial displacement, and stress field within the sphere. The results are illustrated numerically and graphically for functionally graded solid sphere consists of metal and ceramic.     

Development of a finite element based heat transfer model for conduction mode laser spot welding process using an adaptive volumetric heat source

Numerically computed results of weld pool dimensions in conduction mode laser welding are sensitive to the estimated value of the actual beam energy absorbed by the substrate. In a conduction based heat transfer analysis, the incorporation of the laser beam induced energy as a surface only heat flux fails to realize enhanced heat transfer in weld pool as molten material attains higher temperature and convective transport of heat becomes predominant. An alternate is to include fluid flow analysis considering phenomenological laws of conservation of mass and momentum that greatly increases the complexity in modeling. Uncertainty of material properties such as effective thermal conductivity and viscosity in the weld pool also impedes such extensive fluid flow analysis. A simpler and tractable approach can be to consider a volumetric heat source within weld pool in a conduction based heat transfer analysis. Earlier efforts to accommodate volumetric heat source such as double-ellipsoidal form remained unpopular since the size of the final weld pool shapes is required to be known to begin with the calculation. The present work describes an improved approach where a volumetric heat source is defined adaptively as the size of the weld pool grows in size within the framework of a conduction based heat transfer analysis. The numerically computed results of weld pool dimensions following this approach have shown fair agreement with the corresponding measured values for laser spot weld samples.     

Lattice Boltzmann simulation of tree-shaped fins enhanced melting heat transfer

Abstract

A thermal lattice Boltzmann model is developed to simulate the melting process with natural convection in a cavity filled with tree-shaped solid fins, in which the velocity field and temperature field distribution functions are considered. The present model incorporates the total enthalpy and a free parameter in the equilibrium distribution function to handle conjugate heat transfer. The results indicate that natural convection of liquid phase change material (PCM) plays a significant role in the melting heat transfer of PCM. Increasing the number of branching levels leads to a more rapid melting process, and selecting appropriate bifurcation angle has more efficient heat transfer performance.     

Inverse shape design for heat conduction problems via the ball spine algorithm

ABSTRACT

In this article, a novel iterative physical-based method is introduced for solving inverse heat conduction problems. The method extends the ball spine algorithm concept, originally developed for inverse fluid flow problems, to inverse heat conduction problems by employing a subtle physical-sense rule. The inverse problem is described as a heat source embedded within a solid medium with known temperature distribution. The object is to find a body configuration satisfying a prescribed heat flux originated from a heat source along the outer surface. Performance of the proposed method is evaluated by solving many 2-D inverse heat conduction problems in which known heat flux distribution along the unknown surface is directly related to the Biot number and surface temperature distribution arbitrarily determined by the user. Results show that the proposed method has a truly low computational cost accompanied with a high convergence rate.     

Entropy generation in transpiration cooling of concentric spherical shells

The present paper deals with transpiration cooling of two concentric spherical shells. The analysis includes the calculation for the radial distribution of temperature and volumetric entropy generation, and the total rate of entropy generation in the thermal system. Standard air is considered as the cooling fluid. Results showed that the entropy generation increases with increasing temperature difference between the sphere surfaces. Variation of either mass flow rate or radius ratio affects volumetric entropy distribution and the total rate of entropy generation of the processes. The increase of mass flow rate or radius ratio increases the total rate of entropy generation. The performance of the system is analyzed by calculating irreversibility to heat transfer ratio at both inner and outer sphere surfaces. It was found that irreversibility to heat transfer ratio at the inner sphere surface increases with increasing mass flow rate, or decreasing radius ratio. The opposite is true for the outer sphere surface.     

Bio-heat transfer analysis during short pulse laser irradiation of tissues

The objective of this paper is to analyze the temperature distributions and heat affected zone in skin tissue medium when irradiated with either a collimated or a focused laser beam from a short pulse laser source. Experiments are performed on multi-layer tissue phantoms simulating skin tissue with embedded inhomogeneities simulating subsurface tumors and as well as on freshly excised mouse skin tissue samples. Two types of lasers have been used in this study – namely a Q-switched pulsed 1064 nm Nd:YAG short pulse laser having a pulse width of 200 ns and a 1552 nm diode short pulsed laser having a pulse width of 1.3 ps. Experimental measurements of axial and radial temperature distribution in the tissue medium are compared with the numerical modeling results. For numerical modeling, the transient radiative transport equation is first solved using a discrete ordinates method for obtaining the intensity distribution and radiative heat flux inside the tissue medium. Then the temperature distribution is obtained by coupling the bio-heat transfer equation with either hyperbolic non-Fourier or parabolic Fourier heat conduction model. The hyperbolic heat conduction equation is solved using MacCormack’s scheme with error terms correction. It is observed that experimentally measured temperature distribution is in good agreement with that predicted by hyperbolic heat conduction model. The experimental measurements demonstrate that converging laser beam focused directly at the subsurface location can produce desired high temperature at that location compared to that produced by collimated laser beam for the same laser parameters. Finally the ablated tissue removal is characterized using histological studies as a function of laser parameters.     

Analysis for the dual-phase-lag bio-heat transfer during magnetic hyperthermia treatment

Magnetic fluid hyperthermia is one of hyperthermia modalities for tumor treatment. The control of temperatures is necessary and important for treatment quality. Living tissue is highly non-homogenous, and the velocity of heat transfer in it should be limited. Thus, this work analyzes the temperature rise behaviors in biological tissues during hyperthermia treatment within the dual-phase-lag model, which accounts the effect of local non-equilibrium on the thermal behavior. A small tumor surrounded by the health tissue is considered as a solid sphere. The influences of lag times, metabolic heat generation rate, blood perfusion rate, and other physiological parameters on the thermal response in tissues are investigated. While the metabolic heat generation takes little percentage of heating source, its effect on the temperature rise can be ignored. The control of the blood perfusion rate is helpful to have an ideal hyperthermia treatment. The lag times, τ_q and τ_T, affect the bio-heat transfer at the early times of heating. The total effect of τ_q and τ_T on the bio-heat transfer may be different for the same τ_T/τ_q value.     

UNSTEADY HEAT TRANSFER FROM A ROTATING DISK WITH SOLIDIFICATION

Abstract

Unsteady heat transfer from an infinite rotating disk when phase change from liquid to solid occurs is investigated numerically. The moving boundary is fixed for all times by a coordinate transformation, and a finite difference method is used to obtain the instantaneous location of the solid-Uquid interface and the heat transfer from the surfaces of solid and liquid. It is observed that the instantaneous heat flux at the surface of the solid can be obtained with sufficient accuracy by measuring the thickness of the solid, or vice versa, When the Prandtl number is varied, the minimum response time of heat transfer in both solid and liquid phases occurs around Pr = 1.     

Heat Transfer and Entropy Generation in Concentric/Eccentric Double-Pipe Helical Heat Exchangers

Abstract

Double-pipe helical heat exchangers are integral to contemporary mechanical refrigeration equipment. Modification of flow geometry has been widely adopted to enhance heat transfer performance of a heat exchanger. The objective of this study is to numerically investigate heat transfer and entropy generation in a double pipe helical heat exchanger with various cross-sections. A computational model for laminar convective heat transfer was developed and validated against the results from previously published literature. To capture entropy generation, the entropy balance equation for open system is adopted. Effect of inner pipe Dean number, inner pipe and annulus inlet mass flow rate ratio, eccentricity, and flow configuration (co-flow and counter-flow) were examined and discussed in light of computational results. To ensure fair comparison, the considered geometries have same inner pipe cross-section area, same annulus cross-section area, and same outer surface area of inner pipe. The results suggest that square cross-section offers best performance in term of heat transfer, pressure drop and entropy generation. In addition, concentric configuration is more appropriate for low flow rate application while eccentric outer configuration is more suitable for high flow rate application.     

Low Rayleigh number flow in a heat generating porous media

A numerical analysis has been performed for the steady-state temperature and stream function distributions in a short cylinder, having an isothermal side and top, an insulated bottom, for a uniform heat generating porous medium. The analysis uses the stream function formulation of Darcy's equation in cylindrical coordinates and the Boussinesq approximation. A single energy equation was used for the fluid and solid, since conduction was the expected mode of heat transfer at low heat generation rates for a lead sphere air porous media system. The solution of the non-dimensionalized momentum and energy equations resulted in small Rayleigh numbers (2×10⁻⁶ to 0.2) indicating the heat transfer is by conduction. Solutions for the stream lines and isotherms were obtained using a transient explicit finite-difference approximation using a mean bed thermal conductivity.     

A memory response in the vibration of a microscale beam induced by laser pulse

Abstract

In the application of pulsed laser heating, such as the laser hardening of metallic surfaces, the conduction limited process is the dominant mechanism during the laser-workpiece interaction. As a consequence, time unsteady analysis of this problem becomes necessary. The present study examines the effect of ultra-short-pulsed laser heating in the problem of coupled thermoelastic vibration of a microscale beam resonator. Due to the shortcomings of power law distributions in fractional derivatives, the usage of some other forms of derivatives with some other kernel functions is proposed. With this motivation, the heat transport equation is defined in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer. Finite sinusoidal Fourier and Laplace transform techniques are then employed to determine the lateral vibration of the beam and the temperature increment within the medium. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are drawn. An excellent predictive capability is demonstrated due to the presence of the energy absorption depth, memory dependent derivative, and delay time.     

Numerical simulation of the growth characteristics of laser chemical vapor deposition of silicon carbide

A thermal model, which involves heat transfer in substrate and gases, mass transfer in gases, and chemical reaction on the top surface of the substrate, is set up to simulate the Laser Chemical Vapor Deposition (LCVD) process of Silicon Carbide (SiC) by a finite volume method. Methyltrichlorosilane (MTS; SiCl₃CH₃) and hydrogen (H₂) are chosen as precursor and carrier gas, respectively. A designed set of model cases is executed for both stationary and moving laser beams. For the cases of stationary laser beam, the shape of the SiC deposits is higher and wider with increasing laser power. For the cases of moving laser beam, a narrow strip of SiC deposits is formed along the laser scanning path. Due to the low sticking coefficient of SiC deposits at high temperature, the volcano-like defects occur on the top center of the SiC deposits for both stationary and moving laser beams.     

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

The transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21012     

Fabrication–microstructure–performance relationships of reversible solid oxide fuel cell electrodes–review

Abstract

A reversible solid oxide fuel cell system can act as an energy storage device by storing energy in the form of hydrogen and heat, buffering intermittent supplies of renewable electricity such as tidal and wave generation. The most widely used electrodes for the cell are lanthanum strontium manganate–yttria stabilised zirconia and Ni–yttria stabilised zirconia. Their microstructure depends on the fabrication techniques, and determines their performance. The concept and efficiency of reversible solid oxide fuel cells are explained, along with cell geometry and microstructure. Electrode fabrication techniques such as screen printing, dip coating and extrusion are compared according to their advantages and disadvantages, and fuel cell system commercialisation is discussed. Modern techniques used to evaluate microstructure such as three-dimensional computer reconstruction from dual beam focused ion beam–scanning electron microscopy or X-ray computed tomography, and computer modelling are compared. Reversible cell electrode performance is measured using alternating current impedance on symmetrical and three electrode cells, and current/voltage curves on whole cells. Fuel cells and electrolysis cells have been studied extensively, but more work needs to be done to achieve a high performance, durable reversible cell and commercialise a system.