Effect of melt superheat on heat transfer coefficient for aluminium solidifying against copper chill

Solidification of metal castings inside moulds is mainly dependent on the heat flow from the metal to the mould which is in turn proportional to an overall heat transfer coefficient h which includes all resistances to heat flow such as the presence of an air gap. In the present work the heat transfer coefficient is determined using a directional solidification set-up with end chill for solidifying commercial-purity aluminium with different superheats (40 K and 115 K) against copper chill. A computer program solving the heat conduction and convection in the solidifying metal is used together with the experimental temperature history in order to determine the heat transfer coefficient at the interface. The variation of h as a function of time, surface temperature and gap temperature for each melt superheat is found. The results indicate that h reaches a maximum value for surface temperature close to the liquidus. The analysis of heat flux from the metal to the mould indicates that it is mainly by conduction. The air gap size is evaluated with time, surface temperature and with melt superheat. It is found that higher h values and smaller gap sizes are obtained with higher superheats.     

Transverse heat transfer coefficient in the dual channel ITER TF CICCs Part II. Analysis of transient temperature responses observed during a heat slug propagation experiment

A heat slug propagation experiment in the final design dual channel ITER TF CICC was performed in the SULTAN test facility at EPFL-CRPP in Villigen PSI. We analyzed the data resulting from this experiment to determine the equivalent transverse heat transfer coefficient h_BC between the bundle and the central channel of this cable. In the data analysis we used methods based on the analytical solutions of a problem of transient heat transfer in a dual-channel cable, similar to Renard et al. (2006) and Bottura et al. (2006). The observed experimental and other limits related to these methods are identified and possible modifications proposed. One result from our analysis is that the h_BC values obtained with different methods differ by up to a factor of 2. We have also observed that the uncertainties of h_BC in both methods considered are much larger than those reported earlier.     

Quasi-static Thermal Deflection of a Thin Clamped Hollow Circular Disk Due to Heat Generation

This paper deals with the determination of the thermal deflection in a thin clamped hollow circular disk defined as a ≤ r ≤ b; 0 ≤ z ≤ h under an unsteady temperature field due to internal heat generation within it. A thin hollow circular disk is considered having an arbitrary initial temperature and subjected to heat flux at the outer circular boundary (r = b) where an inner circular boundary (r = a) is at zero heat flux. Also, the upper surface (z = h) and the lower surface (z = 0) of the disk are at zero temperature. The governing heat conduction equation has been solved by using an integral transform technique. The inner and outer edges of the disk are clamped ${\frac{\partial \omega }{\partial r}=0}$ at r = a, r = b. The results are obtained in a series form in terms of Bessel’s functions and are illustrated graphically.     

Unsteady free convective boundary-layer flow near a stagnation point in a heat-generating porous medium

The free convection boundary-layer flow near a stagnation point in a porous medium is considered when there is local heat generation at a rate proportional to (T ? T _∞) ^p , (p ≥ 1), where T is the fluid temperature and T _∞ the ambient temperature. Two cases are treated, when the surface is thermally insulated and when heat is supplied at a constant (dimensionless) rate h _s from the boundary. If h _s = 0 the solution approaches a nontrivial steady state for time t large in which the local heating has a significant effect when p ≤ 2. For p > 2 the effects of the local heating become increasingly less important and the solution dies away, with the surface temperature being of O(t ^?1) for t large. When h _s > 0 and there is heat input from the surface, the solution for p ≤ 2 again approaches a nontrivial steady state for t large and all h _s . For p > 2 there is a critical value h _s,crit (dependent on the exponent p) of h _s such that the solution still approaches a nontrivial steady state if h _s < h _s,crit. For h _s > h _s,crit a singularity develops in the solution at a finite time, the nature of which is analysed.     

The effect of quenching media on the heat transfer coefficient of polycrystalline alumina

Surface heat transfer coefficient values were measured for polycrystalline alumina quenched into water, into oil, and into liquid nitrogen. Since the measurements of the surface heat transfer coefficient h for alumina (and ceramics in general) are very limited, we compare our measurements with calculations of h for the water quench and with measurements of h on non-ceramic materials for the oil and liquid nitrogen quenches.     

Non-Contact Methods for Measuring Front Cavity Depths of Laboratory Standard Microphones Using a Depth-Measuring Microscope

To achieve an acceptable degree of accuracy at high frequencies in some standardized methods for primary calibration of laboratory standard (LS) microphones, the front cavity depth l_fc of each microphone must be known. This dimension must be measured using non-contact methods to prevent damage to the microphone diaphragm. The basic capabilities of an optical depth-measuring microscope were demonstrated by the agreement of its measurements within 0.7 μm of the known values of reference gage blocks. Using this microscope, two basic methods were applied to measure l_fc. One (D) uses direct measurements at the microphone front surface annulus and conventional data reduction techniques. The other (GB) uses measurements at the surface of a gage block placed on the annulus, and plane-fitting data reduction techniques intended to reduce the effects of the slightly imperfect geometries of the microphones. The GB method was developed to provide a smoother surface of measurement than the relatively rough surface of the annulus, and to simulate the contact that occurs between the annulus and the smooth, plane surface of an acoustic coupler during microphone calibration. Using these methods, full data sets were obtained at 33 measurement positions (D), or 25 positions (GB). In addition, D and GB subsampling methods were applied by using subsamples of either the D or the GB full data sets. All these methods were applied to six LS microphones, three each of two different types. The GB subsampling methods are preferred for several reasons. The measurement results for l_fc obtained by these methods agree well with those obtained by the GB method using the full data set. The expanded uncertainties of results from the GB subsampling methods are not very different from the expanded uncertainty of results from the GB method using the full data set, and are smaller than the expanded uncertainties of results from the D subsampling methods. Measurements of l_fc using the GB subsampling method with only nine measurement positions exhibit expanded uncertainties (with coverage factor k = 2) within 4 μm, and can improve the uncertainty of microphone calibrations by an order of magnitude over the result from use of generic standardized microphone type nominal l_fc values and tolerance limits.     

Coupled thermoelastic vibrations of a Timoshenko beam

In the present paper we deal with tne dynamic behaviour of a Timoshenko beam subjected to a step heat flux to the surface z = + h/2 at time t = 0⁺. The mathematical analysis is based on integral transforms, the Muller's method of solving algebraic equations and the Heaviside expansion theorem. From the numericad results presented, one can see the effect of inertia and that of tne coupling between temperature and strain fields on the dynamic behaviour of the beam as well as the distribution of the temperature fields with time.     

Modeling of an isolated liquid hydrogen droplet evaporation and combustion

In this model, diffusive governing equations of Liquid Hydrogen (LH) evaporation and combustion were solved. The simulation reveals that, there exists a critical radius (a_cri) where radiation heat is equal to conduction heat (Q_rad = Q_cond) and a_cri is a function of ambient temperature during LH droplet evaporation process. Under pure evaporation condition, for large liquid hydrogen droplets (a > a_cri) radiation heat is dominant at a given environment temperature, but as liquid droplet size decreases, radiation heat becomes insignificant and thermal conduction will be dominant for liquid evaporation. When LH droplet is burned in a cold environment (T_∞ = 300 K), there are two films above the LH surface, Film I is from LH surface to flame front within which a dense hydrogen gas cloud is formed; Film II is from flame front to the free stream where oxygen is diffused inward to react with hydrogen. The flame front is located about 95 times of the droplet radius (r_f = 95a) and the flame temperature could rise up to 2077 K. When an LH droplet is immersed in a hot environment (T_∞ = 2050 K), the flame front is located at a similar distance to the LH droplet (r_f/a = 114) and flame temperature could go up to 3769 K.     

Impact of classical assumptions in modelling a microchannel gas cooler

Most of the current air-to-refrigerant heat exchanger models use the classic ?-NTU approach, or some of its assumptions. These models do not account for longitudinal heat conduction in the tube and the fin, and the heat conduction between different tubes. This paper presents a more fundamental numerical approach to heat exchanger modelling which takes into account the 2D longitudinal heat conduction in any element, does not apply the fin theory, and captures a more detailed representation of air properties. Using the fundamental numerical approach, the paper assesses the impact of the traditional heat exchanger model assumptions when modelling a microchannel gas cooler working with CO₂. The study revealed significant differences in capacity predictions depending on the ?-NTU relationship adopted. Large errors in capacity prediction of individual tubes occurred due to the adiabatic-fin-tip assumption when the neighbouring tubes were of different temperature.     

Portable forced-air tunnel evaluation for cooling products inside cold storage rooms

Freezing process efficiency is affected by the required conditions to keep the air flow and temperature at the product surface. The objective of this work was to obtain results on comparative studies with air exhaustion and blowing using an experimental portable forced-air freezing tunnel. The device was designed to improve cooling rates inside storage room without the need for a cooling/freezing tunnel. A heterogeneity factor was proposed for air circulation evaluation and compared with convective heat transfer coefficient (h_ef) values. Lower modules of heterogeneity factor values represent smaller temperature differences among samples. Comparing two different air flow processes, heterogeneity factor values were similar for regions where the cooling air could flow without obstructions. However, larger differences were observed for regions with hampered air circulation. Results indicated that the air distribution, as well as the heat transfer, occurs more uniformly around the products in the exhausting process than in the blowing system.     

Total Hemispherical Emittance of Polyimide Films for Space Use in the Temperature Range from 173 to 700 K

This paper describes the temperature dependence of the total hemispherical emittance _h in the temperature range from 173 to 700 K for three types of thermal control materials, which are based on a thin polymide film coated with aluminum on the back surface. The results obtained from the measurements are compared with calculated values from optical constants. The principle of the present measurement is based on the steady-state calorimetric method, and _h is obtained by measuring the equilibrium temperature of a sample corresponding to different heat inputs to a heater attached to the sample. On the other hand, the present calculation method is performed by using data for the optical constants of polyimide films and vapor-deposited metal in the wavelength region from 0.25 to 100 m. These results agree with each other on the whole. It has been observed that the temperature dependence of _h is remarkable, and the values have a maximum around 410 K.     

Specific Heat of the 1D Spin-1/2 Ising Model with Added Dzyaloshinskii–Moriya Interaction

The 1D spin-1/2 Ising model in a uniform magnetic field with added the Dzyaloshinskii–Moriya (DM) interaction is considered. The energy spectrum is obtained using the fermionization approach and defining some mean field order parameters. Then the specific heat is determined in an infinite chain system. Results show that there is only one peak in the specific heat as a function of the temperature. In the Neel phase, the position of the peak is found almost field-independent, but the maximum value of the specific heat decreases by increasing the magnetic field. Also, in the region of the saturated ferromagnetic phase, by increasing h, the peak becomes wider and goes to higher temperatures, which is a signal for the saturated ferromagnetic phase. In addition, the specific heat at low temperature shows two peaks structure on both sides of the quantum critical point.     

Thermodynamic optimization of combined power and refrigeration cycle using binary organic working fluid

A combined cycle has been proposed for the production of power and refrigeration simultaneously. The cycle can be driven by low grade heat sources such as solar, geothermal and waste heat sources. In the first part of this paper, a model has been developed to perform a parametric analysis to evaluate the effects of important parameters on the performance of the cycle, which is a combination of Rankine and absorption refrigeration cycle. Propane–decane has been used as an organic dual working fluid. In the second part, multi objective genetic algorithm is applied for Pareto approach optimization of the cycle. There are three important conflicting objectives namely, turbine work (W_t), cooling capacity (Q_c) and thermal efficiency (η_th) which have been selected to find the best possible combination of these performance parameters. Optimization has been carried out by varying turbine inlet pressure, superheated temperature and condenser temperature as design variables. Among optimum design parameters, a trade-off point is selected. Turbine inlet pressure, superheated temperature and condenser temperature are assumed to be 29.5 bar, 410 K and 386.6 K respectively as the values assigned to this point. Furthermore, it has been shown that some interesting and important relationships can be discovered among optimal objective functions and decision variables involved, consequently.     

Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

In this article, heat transfer in a moving fin with variable thermal conductivity, which is losing heat by simultaneous convection and radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) which is an analytical solution technique that can be applied to various types of differential equations. The effects of parameters such as the Peclet number, Pe, thermal conductivity parameter, a, convection–conduction parameter, N _c, radiation–conduction parameter, N _r, dimensionless convection sink temperature, θ _a, and dimensionless radiation sink temperature, θ _s, on the temperature distribution are illustrated and explained. The analytical solution is found to be in good agreement with the direct numerical solution. Moreover, the results demonstrate that the DTM is very effective in generating analytical solutions for even highly nonlinear problems.     

Transverse heat transfer coefficient in the dual channel ITER TF CICCs. Part III: Direct method of assessment

The data resulting from the thermal-hydraulic test of the ITER TF CICC are used to determine the flow partition and the overall effective heat transfer coefficient (h_BC) between bundle and central channel in a direct way, i.e. by analysis of the heat transfer between both flow channels, based on the mass and energy balance equations and the readings of thermometers located inside the cable. In cases without a local heat source in the considered cable segment the obtained h_BC values were consistent with those obtained in earlier studies by analysis of experimental data using indirect methods. It was also observed that the transverse heat transfer was strongly enhanced in a cable segment heated from outside. This phenomenon results from the mass transfer from the bundle region to the central channel. The experimental h_BC data obtained for the case without a heat source in the considered segment were also compared with those calculated using various heat transfer correlations.     

Stochastic inverse heat conduction using a spectral approach

An adjoint‐based functional optimization technique in conjunction with the spectral stochastic finite element method is proposed for the solution of an inverse heat conduction problem in the presence of uncertainties in material data, process conditions and measurement noise. The ill‐posed stochastic inverse problem is restated as a conditionally well‐posed L₂ optimization problem. The gradient of the objective function is obtained in a distributional sense by defining an appropriate stochastic adjoint field. The L₂ optimization problem is solved using a conjugate‐gradient approach. Accuracy and effectiveness of the proposed approach is appraised with the solution of several stochastic inverse heat conduction problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Measurement of Thermal Conductivity of Anisotropic SiC Crystal

Silicon carbide (SiC) crystals with excellent heat conduction and thermal stability can be widely used in microelectronic devices and integrated circuits. It is important for the study of a functional type SiC material to have accurate thermal-conductivity and thermal-diffusivity values of SiC crystal. A 3ω technique is employed to determine the anisotropic thermal conductivity of SiC crystal. Three micrometal probes with different widths are deposited by chemical-vapor deposition on the surface of SiC crystal. Each micrometal probe is used as a heater, and also as a thermometer. The temperature fluctuation signals of a micrometal probe represent heat conduction in different directions in the specimen. Thermal conductivities both in the cross-plane and in-plane directions of SiC crystal are achieved through fitted values. The results indicate that thermal conductivities in three different directions of SiC crystal can be characterized using the metal heater construction.     

Numerical method for the solution of non‐linear two‐dimensional inverse heat conduction problem using unstructured meshes

A new method of solving multidimensional heat conduction problems is formulated. The developed space marching method allows to determine quickly and exactly unsteady temperature distributions in the construction elements of irregular geometry. The method which is based on temperature measurements at the outer surface, is especially appropriate for determining transient temperature distribution in thick‐wall pressure components. Two examples are included to demonstrate the capabilities of the new approach. Copyright © 2000 John Wiley & Sons, Ltd.     

New measurements of the surface resistance anisotropy of superconducting tin as part of a rf cavity

The temperature dependence of the anisotropic surface resistance of superconducting tin at a frequency of 9.4 GHz has been determined from measurements of quality factors of split polarization H₁₁₁ modes of a superconducting cylindrical cavity with the end plate of the sample single crystal. Near the critical temperature there is a point at which the difference of the principal values of the tensor of R_ik for crystallographic planes (110) and (100) reverses its sign.