Phase Change Process Inside a Small-radii Cylinder Subjected to Cyclic Convective Boundary Conditions: a Numerical Study

We numerically investigate the melting and solidi?cation behavior of phase change materials encapsulated in a small-radii cylinder subjected to a cyclic convective boundary condition (square wave). Initially, we explore the effect of the Stefan and Biot numbers on the non-dimensionalized time required (i.e. reference Fourier number Tref ) for a PCM initially held at Tcold to melt and reach the cross?ow temperature Thot. The increase in either Stefan or Biot number decreases Tref and can be predicted accurately using a correlation developed in this work. The variations of the PCM melt fraction, surface temperature, and heat transfer rate as a function of Fourier number are reported and analyzed for the above process. We further study the effect of the cyclic Fourier number on the periodic melting and freezing process. The melting or freezing front initiates at the outer periphery of the PCM and propagates towards the center. At higher frequencies, multiple two-phase interfaces are generated (propagating inward), and higher overall heat transfer is achieved as the surface temperature oscillates in the vicinity of the melting temperature, which increases the effective temperature difference driving the convective heat transfer.

Microstructural Characterization and Mathematical Modeling for Determination of Volume Fraction of Eutectoid Mixture of the Cu-8.5wt% Sn Alloy Obtained by Unidirectional Upward Solidification

The Cu-8.5wt % Sn alloy presents an extensive microsegregation during its solidification. That microsegregation results in the formation of a eutectoid mixture, which is detrimental to subsequent forming processes. This study deals with the influence of solidification time and cooling rate on the microstructure of that alloy. The unidirectional solidification technique allowed the acquisition of thermal data. The optical microscopy enabled the microstructural characterization of the material, the measurement of dendrite arm spacings and the quantification of the volume fraction of the eutectoid mixture. A semi-analytical mathematical model was proposed to estimate the volume fraction of the eutectoid mixture. The model expresses the volume fraction as an implicit function of the Fourier number. The results showed that the microstructure is dendritic and that the characteristic spacings increase with the solidification time between the liquidus and the peritectic temperatures. The data also showed that for higher cooling rates the dendrite arm spacings are smaller and that there is a tendency for the volume fraction of eutectoid mixture in the columnar zone to increase with the Fourier number and to decrease with the cooling rate. The proposed model allowed obtaining values of volume fraction with the same order of magnitude of the experimental data, but with behavior tendency opposite to that observed.

Coaxial Thermocouples for Heat Transfer Measurements in Long-Duration High Enthalpy Flows

Coaxial thermocouples have the advantages of fast response and good durability. They are widely used for heat transfer measurements in transient facilities, and researchers have also considered their use for long-duration heat transfer measurements. However, the model thickness, transverse heat transfer, and changes in the physical parameters of the materials with increasing temperature influence the accuracy of heat transfer measurements. A numerical analysis of coaxial thermocouples is conducted to determine the above influences on the measurement deviation. The minimum deviation is obtained if the thermal effusivity of chromel that changes with the surface temperature is used to derive the heat flux from the surface temperature. The deviation of the heat flux is less than 5.5% when the Fourier number is smaller than 0.255 and 10% when the Fourier number is smaller than 0.520. The results provide guidance for the design of test models and coaxial thermocouples in long-duration heat transfer measurements. The numerical calculation results are verified by a laser radiation heating experiment, and heat transfer measurements using coaxial thermocouples in an arc tunnel with a test time of several seconds are performed.

Determination of thermal diffusivity of the material by numerical-analytical model of a semi-bounded body

A mathematical description of the material thermal diffusivity aт in a semi-bounded body is proposed with a relatively simple algorithm for its numerical and analytical by solving the inverse problem of thermal conductivity. To solve the problem, it is necessary to obtain the temperature values of the unbounded plate as a result of a thermophysical experiment. A plate can be conditionally considered as a semi-bounded body as long as the Fourier number Fo ≤ Foк (Foк ≈ 0.04–0.06). It is assumed that the temperature distribution over cross-section of the heated layer of the plate R is sufficiently described by a power function whose exponent depends linearly on the Fourier number. A simple algebraic expression is obtained for calculating aт in the time interval ∆τ from the dynamics of temperature change T(Rп , τ) of a plate surface with thickness Rп heated under boundary conditions of the second kind. Temperature of the second surface of the plate T(0, τ) is used only to determine the time of the end of experiment τк. The moment of time τк, in which the temperature perturbation reaches the adiabatic surface x = 0, can be set by the condition T(Rп , τк) – T(0, τ = 0) = 0,1 K. The method of approximate calculation of dynamics of changes in depth of the heated layer R by the values of Rп , τк , and τ is proposed. Calculation of a т for the time interval ∆τ is reduced to an iterative solution of a system of three algebraic equations by matching the Fourier number, for example, using a standard Microsoft Excel procedure. Estimation of the accuracy of a т calculation was made by the test (initial) temperature field of the refractory plate with the thickness Rп = 0.05 m, calculated by the finite difference method under the initial condition T(x, τ = 0) = 300 (0 ≤ x ≤ Rп) at radiation-convective heating. The heating time was 260 s. Calculation of aт, i was performed for 10 time moments τi + 1 = τi + Δτ, τ = 26 s. Average mass temperature of the heated layer for the whole time was T = 302 K. The arithmetic-mean absolute deviation of aт(T = 302 K) from the initial value at the same temperature was 2.8 %. Application of the method will simplify the conduct and processing of experiments to determine the thermal diffusivity of materials.

Solar Still Efficiency Enhancement by Using Graphene Oxide/Paraffin Nano-PCM

Solar-driven water desalination technologies are rapidly developing with various links to other renewable sources. However, the efficiency of such systems severely depends on the design parameters. The present study focused on using graphene oxide (GO) with the Φ = 0.2, 0.4 and 0.6 wt.% dispersed in paraffin, as phase-change materials (PCMs), to improve the productivity of a solar still for desalination applications. The outcomes showed that by adding more graphene oxide to paraffin, the melting temperature got reduced. Solar still with GO/paraffin showed 25% productivity improvement in comparison with the solar still with only PCM. The obtained Nusselt number during the melting time also represented that free convection heat transfer into the melted region of the solar still has been enhanced by adding dispersed GO to the PCM, compared to the base paraffin. Also, increasing the hot wall temperature augments the Nusselt number. Finally, an empirical equation was derived to correlate the average Nusselt number as a function of Rayleigh number (Ra), the Stefan number (Ste), the subcooling factor (Sb), and the Fourier number (Fo). The obtained correlation depicted that Nusselt number enhancement has a reverse relation with Fourier number.

Semi-infinite solid heat transfer limitation

One-dimensional semi-infinite heat transfer solution is a common solution for transient heat transfer experiments. This solution is valid for a short certain amount of time before the semi-infinite solid became invalid. Crank Nicolson solution has been chosen to address this issue. This paper reports the time limitation for semi-infinite solid solution and justify the usability of Crank Nicolson solution given the same boundary conditions. The flat plate heat transfer experiment has been conducted. With the same boundary conditions, at Fourier number 0.1, the resultant heat transfer coefficient and adiabatic wall temperature have shown a good agreement between the semi-infinite solid solution and the Crank Nicolson solution. Beyond this Fourier number, both solutions have given inaccurate results. The inaccurate results are due to unsuitable boundary conditions. Future work will involve modification of the back face boundary conditions to address the time limitation of the one-dimensional semi-infinite solid heat transfer solution.

A Dimensionless Model for Transient Turbulent Natural Convection in Isochoric Vertical Thermal Energy Storage Tubes

In this study, turbulent natural convection heat transfer during the charge cycle of an isochoric vertically oriented thermal energy storage (TES) tube is studied computationally and analytically. The storage fluids considered in this study (supercritical CO2 and liquid toluene) cover a wide range of Rayleigh numbers. The volume of the storage tube is constant and the thermal storage happens in an isochoric process. A computational model was utilized to study turbulent natural convection during the charge cycle. The computational results were further utilized to develop a conceptual and dimensionless model that views the thermal storage process as a hot boundary layer that rises along the tube wall and falls in the center to replace the cold fluid in the core. The dimensionless model predicts that the dimensionless mean temperature of the storage fluid and average Nusselt number of natural convection are functions of L/D ratio, Rayleigh number, and Fourier number that are combined to form a buoyancy-Fourier number.