Experimental and numerical study of melting in a cylinder

Well-controlled and well-characterized experimental measurements are obtained during the melting of a moderate-Prandtl-number material (n-eicosane) in a cylindrical enclosure heated from the side. The study aims to provide benchmark experimental measurements for validation of numerical codes. Experimental results in terms of measured temperatures and melt front locations are reported in both graphical and tabular forms. The melt front was captured photographically and its location ascertained using digital image processing techniques. To facilitate numerical validation exercises, a complete set of experimental results have been made available on a website for public access. An illustrative numerical comparison exercise was also undertaken using a multiblock finite volume method and the enthalpy method for a range of Stefan numbers. The experimental boundary conditions can be adequately represented with a constant and uniform side wall temperature, a constant and uniform lower surface temperature, and an adiabatic top wall. Very good agreement was obtained between the predictions and the experiment for Stefan numbers of up to 0.1807. The experimental results for a Stefan number of 0.0836 are recommended as being the most suitable for numerical benchmarking, since the boundary conditions are best controlled in this set of experiments.     

Thermoelastic study of a functionally graded annular fin with variable thermal parameters using semiexact solution

Abstract

In this paper, the thermoelastic behavior of a functionally graded material (FGM) annular fin is investigated. The material properties of the annular fin are assumed to vary radially. The heat transfer coefficient and internal heat generation are considered to be functions of temperature. A closed form solution of nonlinear heat transfer equation for the FGM fin is obtained using the homotopy perturbation method (HPM) which leads to nonuniform temperature distributions within the fin. The temperature field is then coupled with the classical theory of elasticity and the associated thermal stresses are derived analytically. For the correctness of the present closed form solution for the stress field, the results are compared with the ANSYS-based finite element method (FEM) solution. The present HPM-based closed form solution of the stress field exhibits a good agreement with the FEM results. The effect of various thermal parameters such as the thermogeometric parameter, conduction-radiation parameter, internal heat generation parameter, coefficient of variation of thermal conductivity, and the coefficient of thermal expansion on the thermal stresses are discussed. The results are presented in both nondimensional and dimensional form. The dimensional stress analysis discloses the suitability of FGM as the fin material in practical applications.     

Heat capacity and thermal conductivity considerations for coal particles during the early stages of rapid heating

Heating and cooling transients for a number of individual coal particles in the 100-μm size range were measured under rapid heating conditions (10⁴–10⁵ K/s heating rate). In addition to temperature measurements, each particle was fully characterized with respect to external surface area, volume, mass, and density prior to heating. Measured temperatures were compared with model predictions and a sensitivity analysis was performed to critically evaluate model assumptions regarding particle thermal properties. Simulations using temperature-dependent heat capacity and thermal conductivity correlations routinely applied to coal severely under predicted the particle temperature rise during the early stages of heating. Simulations using constant room temperature values for heat capacity and thermal conductivity showed excellent agreement with measurements during the early stages of heating. Increases in coal heat capacity and thermal conductivity reported in the literature are observed under slow heating conditions and result from bond breaking and structural changes which lead to an increase in vibrational modes of freedom in the coal structure. Results of the present study suggest that under rapid heating conditions the coal structure is frozen and that these vibrational modes only become accessible at higher temperatures or longer soak times. These considerations are important if one desires to accurately model the combustion behavior of coals.     

Fouling of Some Canadian Crude Oils

A thermal fouling study was undertaken using three sour Canadian crude oils. Experiments were carried out in a re-circulation fouling loop equipped with an annular (HTRI) electrically heated probe. Fluids at pressures of about 1000–1340 kPa under a nitrogen atmosphere were re-circulated at a velocity of 0.75 m/s for periods of 48 hours, and the decline in heat transfer coefficient followed under conditions of constant heat flux. Bulk temperatures were varied over a range of 200–285^?C, and initial surface temperatures ranged from 300–380^?C. Heat fluxes were in a range of 265–485 kW/m².

Surface temperature effects on fouling of the three oils were compared, and fouling activation energies were estimated. For the lightest oil, a more detailed study of velocity and bulk and surface temperature effects was carried out. The fouling rate decreased slightly with increasing velocity but increased with both surface and bulk temperatures; a rough correlation was developed using a modified film temperature weighted more heavily on the surface temperature. Deposits showed high concentrations of sulfur and minerals, indicating the importance of iron sulfide deposition.     

Heat transfer characteristics during melting of a metal spherical particle in its own liquid

There are manufacturing applications like surface modification and repair technologies where metal particles go into the superheated melt pool heated by an intense heat source and as the workpiece moves away from the energy source this pool solidifies to form a continuous built-up layer. In the present study two-dimensional axisymmetric Navier–Stokes and energy equations are solved using finite volume method to predict the time required for a metal sphere to melt in a melt pool of the same material. The effect of forced convection, characterised by Reynolds number, and superheat of the melt pool, characterised by Stefan number, has been studied in detail for material of different Prandtl numbers. Effect of buoyancy is neglected for the present investigation. It is found that the effect of convection on melting time is more pronounced if RePr/Ste^2/3 is high. The rate of melting of the metal sphere with time under different conditions is also presented. Finally, the heat transfer characteristic is represented by the correlation of Nusselt number with Reynolds number, Stefan number and Prandtl number.     

Optimal characteristics and heat transfer efficiency of SiO2/water nanofluid for application of energy devices: A comprehensive study

In a comprehensive study, the thermal conductivity, dynamic viscosity, and the rheological behavior of a SiO₂/water nanofluid are investigated experimentally at the temperatures, solid concentrations, and the shear rates of 25°C to 50°C, 0% to 1.5%, and 400 to 1400(s^?1), respectively. The Response Surface Methodology (RSM) is utilized to obtain regression models for the thermal conductivity and the dynamic viscosity. Subsequently, the sensitivity of the aforementioned models to 10% changes in the temperature, and the nanofluid concentration is analyzed. Afterward, Nondominated Sorting Genetic Algorithm II (NSGA‐II) is utilized to find the maximum thermal conductivity and the minimum viscosity. The nondominated optimal points are presented through a fitted correlation on a Pareto front to make the results more practical. The measurements of the investigated nanofluid could be summarized as a paper of a handbook. The workability of the investigated nanofluid is also examined in both laminar and turbulent flow regimes through analysis of the heat transfer merit graphs. To this end, the ratio of the dynamic viscosity enhancement to the thermal conductivity enhancement and the Mouromtseff number are chosen as two criteria of the laminar and turbulent flow regimes, respectively. Finally, the results are compared with those for SiO₂/glycerin and SiO₂/ethylene glycol nanofluids to check the workability in different base fluids. From a thermal‐efficiency point of view, the SiO₂/water nanofluid is not suggested for use in both laminar and turbulent pipe flows, except in temperatures higher than 30°C and volume concentrations lower than 1% for the case of laminar flow. This is because the favorable heat transfer enhancement of the nanofluid is more than the unfavorable increase of the pumping power. From the rheological point of view, though, a SiO₂/water nanofluid would be a good choice in lubricating moving surfaces for both laminar and turbulent flow regimes. It is found that in higher nanofluid concentrations, the thermal conductivity of a SiO₂/water nanofluid is highly influenced by temperature. Moreover, adding nanoparticles at temperatures of 35°C to 40°C would have the highest increasing effect on the thermal conductivity. It is also revealed that increasing the temperature does not significantly affect the viscosity when 1% SiO₂ nanoparticles are suspended within the water.     

Highly conductive composites made of phase change materials and graphite for thermal storage

Conventional phase change materials (PCMs) are already well known for their high thermal capacity and constant working temperature for thermal storage applications. Nevertheless, their low thermal conductivity (around 1 W m⁻¹ K⁻¹) leads to low and decreasing heat storage and discharge powers. Up to now, this major drawback has drastically inhibited their possible applications in industrial or domestic fields. The use of graphite to enhance the thermal conductivity of those materials has been already proposed in the case of paraffin but the corresponding applications are restricted to low-melting temperatures (below 150 °C). For many applications, especially for solar concentrated technologies, this temperature range is too low. In the present paper, new composites made of salts or eutectics and graphite flakes, in a melting temperature range of 200-300 °C are presented in terms of stability, storage capacity and thermal conductivity. The application of those materials to thermal storage is illustrated through simulated results according to different possible designs. The synergy between the storage composite properties and the interfacial area available for heat transfer with the working fluid is presented and discussed.     

Effect of static magnetic field on thermal conductivity measurement of a molten Si droplet by an EML technique: Comparison between numerical and experimental results

In order to investigate quantitatively the effect of melt convection in an electromagnetically levitated molten droplet on the thermal conductivity of liquid silicon measured by the electromagnetic levitation (EML) technique superimposed with a static magnetic field, the numerical simulations for melt convection in the droplet and additionally, for the measurement of thermal conductivity were carried out. In addition, the thermal conductivity of molten silicon was measured by the EML technique, and then compared with those obtained numerically. In the numerical simulations of melt convection, the buoyancy force, thermocapillary force due to the temperature dependence of the surface tension on the melt surface, and electromagnetic force in the droplet were considered as the driving forces of convection. As a result, the numerical simulations could sufficiently explain the measurement of thermal conductivity by the EML technique under a static magnetic field. Also, it was suggested that a magnetic field of more than 4 T should be applied to measure the real thermal conductivity of molten silicon by the EML technique.     

An asymptotic,large time solution of the convection Stefan problem with surface radiation

An asymptotic, large time solution has been obtained for the convection Stefan problem with surface radiation. The moving boundary problem has been reformulated as a fixed boundary problem where Lagrange-Burmann expansions are used to complete the variable transformation. An asymptotic solution of the problem is obtained by requiring that the asymptotic expansions assumed for the interface position X(t) and wall temperature u_w(t) for large times are consistent with the resulting interfacial Lagrange-Bürmann expansions. It is found that the asymptotic expansions admit Neumann's solution as the leading terms and that logarithmic terms start intervening at the third-order terms of the expansions for nonzero Stefan number.     

Thin Film Non-Noble Transition Metal Thermophysical Properties

The transient thermoreflectance (TTR) technique coupled with a pump-probe experimental setup enables the observation of thermal transport phenomena on a sub-picosecond time scale. The reflectance from non-noble transition metals (at least one unoccupied d-orbital in the conduction band) can be shown to have a linear dependence when compared to small changes in the electron and lattice temperatures. This thermal dependence can be combined with the parabolic two step (PTS) model to enable measurement of the electron-phonon coupling factor and thermal conductivity of thin film materials. Experimental results are presented for thin film samples of the non-noble transition metals platinum and nickel. Results are presented using laser wavelengths ranging from 740 nm to 805 nm and using a range of laser fluences (ranging from ～0.35 to 2 J/m²). Over this range of wavelengths and fluences the material properties are shown to be independent of the measurement conditions.     

Transverse temperature distribution and heat generation rate in composite superconductors subjected to constant thermal disturbance

Analytical solution of one-dimensional, transient heat conduction with a distributed heat source is obtained to predict the transverse temperature distribution and heat generation rate per unit volume of the composite superconductor. The solution indicates that temperature distribution and heat generation rate depend on three dimensionless parameters: the dimensionless external disturbance w₀, the dimensionless interface temperature θ¹, and the dimensionless parameter φ that is dependent on the thickness and the thermal conductivity of the superconductor. Results of transient and steady-state solutions are presented. It is shown that the heat generation rate per unit volume of the composite, Q/Qc, is directly proportional to the current in the stabilizer.     

Dual Phase Lag Model on Magneto-Thermoelasticity Infinite Non-Homogeneous Solid Having a Spherical Cavity

In this article, the induced displacement, temperature and stress fields in an infinite non-homogeneous elastic medium with a spherical cavity are obtained in the context dual-phase-lag model. The surface of the cavity is stress free and is subjected to a thermal shock. The material is assumed to be elastic and has an inhomogeneity in the radial direction. The type of non-homogeneity is such that the elastic constants, thermal conductivity and density are proportional to the n ^th power of the radial distance. The solutions are obtained analytically employing the Laplace transforms technique. The numerical inversion of the transforms is carried out using Fourier series expansions. The stresses components, temperature and displacement are computed numerically and presented graphically. A comparison of the results is made for different theories. If the magnetic field is neglected, the results obtained are deduced as a special case from this study.     

Homotopy Perturbation Method for Thermal Stresses in an Annular Fin with Variable Thermal Conductivity

An approximate analytical solution method for thermal stresses in an annular fin with variable thermal conductivity is presented. Homotopy perturbation method (HPM) is employed to estimate the non-dimensional temperature field by solving nonlinear heat conduction equation. The closed-form solutions for the thermal stresses are formulated using the classical thermoelasticity theory coupled with HPM solution for temperature field. The plane state of stress conditions are considered in this study. The effects of thermal parameters such as variable thermal conductivity parameter (β), thermogeometric parameter (K), and the non-dimensional coefficient of thermal expansion (χ) on the temperature field and stress field are studied. The results for temperature field and stress field obtained from HPM-based solution are found to be in very close agreement with the results available in literature. Furthermore, the HPM solution is found to be very efficient and handles nonlinear heat transfer equation with greater convenience.     

Numerical Solution of a Three-Phase Stefan Problem with High Power Input

The numerical solution of a one-dimensional, three-phase Stefan problem with a low Stefan number is presented. Joule heating and thermal radiation are demonstrated to be negligible compared to the high power input. The front tracking method is used along with a second-order Lagrangian interpolation of the temperature profile near the moving surface defined by the location of the phase change. Results are compared with analytical, numerical, and experimental solutions available in literature.     

Laminar free-convection over a vertical isothermal plate with uniform blowing or suction in water with variable physical properties

The majority of studies for laminar free-convection over a vertical isothermal plate with uniform blowing or suction concern gases and air. The existing results for water have been produced assuming a linear relationship between fluid density and temperature and constant viscosity and thermal conductivity. However, it is known that the density-temperature relationship for water is non-linear at low temperatures and viscosity and thermal conductivity are functions of temperature. In this study the problem of laminar free-convection over a vertical isothermal plate with uniform blowing or suction in water has been investigated in the temperature range between 20 and 0 °C taking into account the temperature-dependence of μ, k and ρ. The results are obtained with the numerical solution of the boundary layer equations. The variation of μ, k and ρ with temperature has a strong influence on the results.     

GENERALIZED THERMOELASTICITY OF AN INFINITE BODY WITH A CYLINDRICAL CAVITY AND VARIABLE MATERIAL PROPERTIES

ABSTRACT

The equations of generalized thermoelasticity with one relaxation time in an isotropic elastic medium with temperature-dependent mechanical and thermal properties are established. The modulus of elasticity and the thermal conductivity are taken as linear function of temperature. A problem of an infinite body with a cylindrical cavity has been solved by using Laplace transform techniques. The interior surface of the cavity is subjected to thermal and mechanical shocks. The inverse of the Laplace transform is done numerically using a method based on Fourier expansion techniques. The temperature, the displacement, and the stress distributions are represented graphically. A comparison was made with the results obtained in the case of temperature-independent mechanical and thermal properties.     

A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity

Approximate but highly accurate solutions for the temperature distribution, fin efficiency, and optimum fin parameter for a constant area longitudinal fin with temperature dependent internal heat generation and thermal conductivity are derived analytically. The method of least squares recently used by the authors is applied to treat the two nonlinearities, one associated with the temperature dependent internal heat generation and the other due to temperature dependent thermal conductivity. The solution is built from the classical solution for a fin with uniform internal heat generation and constant thermal conductivity. The results are presented graphically and compared with the direct numerical solutions. The analytical solutions retain their accuracy (within 1% of the numerical solution) even when there is a 60% increase in thermal conductivity and internal heat generation at the base temperature from their corresponding values at the sink temperature. The present solution is simple (involves hyperbolic functions only) compared with the fairly complex approximate solutions based on the homotopy perturbation method, variational iteration method, and the double series regular perturbation method and offers high accuracy. The simple analytical expressions for the temperature distribution, the fin efficiency and the optimum fin parameter are convenient for use by engineers dealing with the design and analysis of heat generating fins operating with a large temperature difference between the base and the environment.     

An Integral Approximate Solution to Ablation of a Two-Layer Composite with a Temporal Gaussian Heat Flux

Ablation is the most common approach for thermal management for reentry of the spacecraft to the atmosphere. An analytical solution of the ablation of a two-layer composite, which includes an ablative layer and a nonablative substrate, subject to a Gaussian heat flux is presented in this paper. The problem is divided into five stages and the temperature distributions in both layers in the five stages are obtained using an integral approximate method. The locations of ablation interface, thermal penetration depth, and ablation rate are obtained and the effects of Stefan number, subcooling parameter, thickness of the ablative material, and ratio of thermal diffusivities between two materials are investigated.     

Experimental Study of Thermo-Physical Properties of Nanofluids Based on γ-Fe2O3 Nanoparticles for Heat Transfer Applications

The main goal of the present study was to prepare and also to investigate the effects of both temperature and weight concentration on the thermo-physical properties of γ-Fe₂O₃/water nanofluids. The γ-Fe₂O₃ nanoparticles were synthesized by laser pyrolysis technique and characterized using TEM, XRD, and EDX techniques. Thermal conductivity, viscosity and surface tension of γ-Fe₂O₃/water nanofluids were investigated within the range of the temperature of 20°C to 70°C for various weight concentrations of nanoparticles (0.5, 1.0, 2.0, and 4.0 wt%). The experimental results show that the thermal conductivity ratio is much higher than of thermal conductivity of base fluid. Thus, the relative thermal conductivity was 59% for a concentration of 4.0 wt% and a temperature of 50°C. Also, it has been observed that the influence of weight concentration of nanoparticles on viscosity was lower at temperatures over 55°C. At standard temperature of 25°C and 2.0 wt.% concentration of nanoparticles, the relative dynamic viscosity was 5.61%. Experimental results show that the surface tension increases with increase of weight concentrations and decreases with increase of temperatures. For a temperature of 70°C and 2.0 wt.% concentration of nanoparticles, the relative surface tension was 46%. The experimental results were compared with data available in literature.     

Temperature Distribution in Different Materials Due to Short Pulse Laser Irradiation

The purpose of this study is to analyze the heat-affected zone in materials such as meat samples, araldite resin-simulating tissue phantoms, and fiber composites irradiated using a mode-locked short pulse laser with a pulse width of 200 ps. The radial surface temperature profiles are compared with that of a continuous wave (CW) laser of the same average power. The short pulse laser results in a more localized heating than a continuous laser with a corresponding high peak temperature. A parametric study addressing the effect of pulse train frequency, material thickness, and amount of scatterers and absorbing agent in the medium and different initial sample temperatures is performed, and the measured temperature profiles are compared with the theoretical non-Fourier hyperbolic formulations and Fourier parabolic heat conduction formulations for both CW and pulsed laser cases.