Choice of Efficient Linear Scale and Generalized Description of Internal Heat Transfer Coefficient in Porous Structures

The expedience of using the ratio of inertial β and viscous α hydraulic coefficients of a fluid flow in porous structures as the characteristic linear scale, when generalizing the experimental data on internal heat transfer in porous media, is shown. It is demonstrated that the correlation Nu = A · Pe, with both criteria based on β/α ratio, most efficiently describes the experimental data for a wide set of ordered and disordered porous structures, including sintered spheres, network materials, sintered felt and cellular foams of high porosity. The coefficient A depends on porosity and is equal to 0.004 for spheres, networks and felts, and 0.0004 for foams. For any specific case the values of α and β coefficients can be readily obtained from testing materials under consideration, control samples, or full-scale articles.     

Annular convective-radiative fins with a step change in thickness,and temperature-dependent thermal conductivity and heat transfer coefficient

This article investigates the thermal performance of convective-radiative annular fins with a step reduction in local cross section (SRC). The thermal conductivity of the fin’s material is assumed to be a linear function of temperature, and heat transfer coefficient is assumed to be a power-law function of surface temperature. Moreover, nonzero convection and radiation sink temperatures are included in the mathematical model of the energy equation. The well-known differential transformation method (DTM) is used to derive the analytical solution. An exact analytical solution for a special case is derived to prove the validity of the obtained results from the DTM. The model provided here is a more realistic representation of SRC annular fins in actual engineering practices. Effects of many parameters such as conduction-convection parameters, conduction-radiation parameter and sink temperature, and also some parameters which deal with step fins such as thickness parameter and dimensionless parameter describing the position of junction in the fin on the temperature distribution of both thin and thick sections of the fin are investigated. It is believed that the obtained results will facilitate the design and performance evaluation of SRC annular fins.     

New promising bulk thermoelectrics: intermetallics,pnictides and chalcogenides

The need of alternative “green” energy sources has recently renewed the interest in thermoelectric (TE) materials, which can directly convert heat to electricity or, conversely, electric current to cooling. The thermoelectric performance of a material can be estimated by the so-called figure of merit, zT = σ α ² T/λ (α the Seebeck coefficient, σ α ² the power factor, σ and λ the electrical and thermal conductivity, respectively), that depends only on the material. In the middle 1990s the “phonon glass and electron crystal” concept was developed, which, together with a better understanding of the parameters that affect zT and the use of new synthesis methods and characterization techniques, has led to the discovery of improved bulk thermoelectric materials that start being implemented in applications. During last decades, special focus has been made on skutterudites, clathrates, half-Heusler alloys, Si_1?x Ge _x-, Bi₂Te_3- and PbTe-based materials. However, many other materials, in particular based on intermetallics, pnictides, chalcogenides, oxides, etc. are now emerging as potential advanced bulk thermoelectrics. Herein we discuss the current understanding in this field, with special emphasis on the strategies to reduce the lattice part of the thermal conductivity and maximize the power factor, and review those new potential thermoelectric bulk materials, in particular based on intermetallics, pnictides and chalcogenides. A final chapter, discussing different shaping techniques leading to bulk materials (eventually from nanostructured TE materials), is also included.     

Effect of thermal inhomogeneity on the performance of a Brownian heat engine

We explore the effect of thermal inhomogeneity on the performance of a Brownian heat engine by considering exactly solvable models. We first consider a Brownian heat engine which is modeled as a Brownian particle in a ratchet potential moving through a highly viscous medium driven by the thermal kick it receives from a linearly decreasing background temperature. We show that even though the energy transfer due to kinetic energy is neglected, Carnot efficiency cannot be achieved at quasistatic limit. At quasistatic limit, the efficiency for such a Brownian heat engine approaches the efficiency of endoreversible engine η = 1 ? √T _c /T _h [F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)]. Moreover, the dependence of the current, the efficiency and the coefficient of performance of the refrigerator on the model parameters is also explored via Brownian dynamic simulations and analytically. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature [M. Asfaw, M. Bekele, Eur. Phys. J. B 38, 457 (2004), M. Asfaw, M. Bekele, Physica A 384, 346 (2007)]. Furthermore, for a Brownian heat engine driven by a piecewise constant temperature, we show that systematic removal of the inhomogeneous medium leads to a homogeneous medium with a uniform temperature where the effect of temperature inhomogeneity is replaced by an effective load.     

Kraus Operator-Sum Solution to the Master Equation Describing the Single-Mode Cavity Driven by an Oscillating External Field in the Heat Reservoir

Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator M _{l, m} is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ _|β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.     

Contact Properties and Adhesion of Incompressible Power-Law Gradient Media with High Gradients

We discuss contact stiffness and adhesion of flat-ended cylindrical indenters with a graded material the elastic coefficient of which is a power-function of the depth with an exponent 1 < k < 3. So far, only graded materials with k < 1 have been considered in the literature as the stiffness of the medium becomes zero when k is approaching 1. However, it is known that the case of incompressible media is an exception. We argue that in this case the final stiffness can be defined up to values of k < 3. The interval 1 < k < 3, which has not been considered earlier occurs to be of special interest, since for k > 1 the adhesive properties of contacts change qualitatively from "brittle" to very tough even in the case of a purely elastic material.     

Thermal performance enhancement in tubes using helically twisted tape with alternate axis inserts

This article presents an investigation on heat transfer enhancement in a round tube inserted with a helically twisted tape. The effects of a helically twisted tape with alternate axis (HTT-A) on heat transfer, friction factor, and thermal performance factor behaviours are reported for the turbulent regime. HTT-A geometries are tape pitch to tube diameter, P/D = 1.0, 1.5, and 2.0; alternate length to pitch length, l/P = 1.0, 1.5, and 2.0; twisted length to tape width, y/W = 3.0; and tape width to tube diameter, w/D = 0.2. The experiment has been performed by varying the volumetric air flow rate in order to adjust Reynolds number ranging from 6 000 to 20 000. The wall of the testing tube is uniformly heated as a constant heat flux while the tests are covered with thermal insulations to reduce heat loss to surroundings. Thermal performance is evaluated by comparing the present experimental results with the results of the modified HTT-A and also those obtained from previous study (conventional helically twisted tape, HTT). The thermal performance of tested tube with HTT-A is evaluated to obtain the degree of heat transfer enhancement and friction factor induced by HTT-A with respect to the plain tube under the same test conditions. Evenly, it is interesting to observe that the tube with HTT-A consistently possesses higher heat transfer and thermal performance factor than those with the HTT around 14.1% and 1.9%, respectively. The HTT-A with the smaller pitch ratio and adjacent twist length provides higher heat transfer rate and friction factor than the one with larger pitch ratio and alternate length as a result of a larger contact surface area, stronger swirl intensity and, thus, better fluid mixing near the tube wall. In the range determined, the tubes with the largest pitch ratio (P/D = 2.0) and smallest alternate length (l/P = 1.0) give the highest thermal performance factor at around 1.35. In addition, the empirical correlations of the Nusselt number, friction factor, and thermal performance factor are also described.     

Effect of Hall current and chemical reaction on MHD flow along a fluctuating porous flat plate with internal heat absorption/generation

Effect of Hall current on the unsteady free convection flow of a viscous incompressible and electrically conducting fluid past a fluctuating porous flat plate with internal heat absorption/generation in the presence of foreign gasses (such as H₂, CO₂, H₂O, NH₃) was investigated. The results are discussed with the effect of the parameters m, the Hall current, Mt, the hydromagnetic parameter, G _r the Grashoff number for heat transfer, G _c , the Grashoff number for mass transfer, S, the internal heat absorption/generation parameter, α, the transpiration parameter, S _c , the Schmidt parameter, and K _c the chemical reaction parameter for Prandtl number P _r = 0.71, which represents air. Further, the present study accounts for the 1st order chemical reaction affecting the flow characteristics. The governing equations are solved in closed form applying Hh _n (x) function. The effects of pertinent parameters characterizing the flow field are discussed with the help of graphs and tables. The important observation of the present study is that heat generation/absorption modifies the flow of current simultaneously to a magnetic force and thermal bouncy force. Heat generation combined with blowing leads to a sharp fall of temperature.     

Laminar free convection heat transfer and separated flow structure in a vertical channel with isothermal walls and two adiabatic opposing fins

Results of numerical study of laminar free convection and heat transfer in a vertical plane-parallel channel with two thin adiabatic fins on its walls are presented. The channel has the open inlet and outlet, and its surfaces are maintained at the same temperature. The channel height is unchanged with elongation parameter A = L/w = 10, and the fins are located in the middle of the channel toward each other. Fin height l/w = 0 ÷ 0.4 and Rayleigh number Ra = 10² ÷ 10⁵ are varied in calculations. The effect of these parameters on the flow structure, temperature field, local and integral heat transfer, and gas flow caused by gravitational forces are analyzed in detail. Numerical analysis is based on solving the full Navier–Stokes and energy equations in twodimensional statement and Boussinesq approximation. To determine the dynamic and thermal parameters at the inlet and outlet, the calculation is carried out with two large volumes attached to the inlet and outlet. The features of the flow and heat transfer at separated flow around the channel fins are studied in detail in this work.     

Experimental Study of the Influence of Structured Capillary-Porous Coatings on the Dynamics of Development of Transient Processes and the Crisis Phenomena at Stepwise Heat Release

The effect of structured plasma-sprayed capillary-porous coatings on transient processes and the development of crisis phenomena at boiling under pulsed heat release was studied. The working fluid was liquid nitrogen on the saturation line at atmospheric pressure. It is shown that under unsteady heat release, there is a degeneration of the development of the boiling crisis on heaters with structured capillary-porous coatings at q &lt; q_CHF (critical heat flux at steady heat release). Under unsteady pulsed heat release, no rapid transition to the film boiling regime (without passing through the nucleate boiling stage) is observed on heaters with such coatings until the thermal load is more than two times higher than the critical heat flux for steady heat release. This significantly increases the times of transition to post-critical heat transfer. Analysis of synchronized measurements of surface temperature of heaters and high-speed video recording of transient processes shows that the degeneration of the heat transfer crisis at q &lt; q_CHF on samples with coatings occurs due to significantly lower liquid boiling temperature differences and specific features of the dynamics of propagation of self-sustaining evaporation fronts in comparison with a smooth heater.     

Laminar free convection heat transfer between vertical isothermal plates

The paper represents results on numerical investigation of flow and heat transfer between two isothermal vertical plates under laminar natural convection. A system of complete Navier–Stokes equations is solved for a two-dimensional gas flow between the plates along with additional rectangular regions (connected to inlet and outlet sections), whose characteristic sizes are much greater than the spacing between the plates. The calculations were performed over very wide ranges of Rayleigh number Ra = 10 ÷ 10⁵ and a relative channel length AR = L/w = 1 ÷ 500. The influence of the input parameters on the gas-dynamic and thermal structure of thermogravitational convection, the local and mean heat transfer, and also the gas flow rate between the plates (convective draft. We determined sizes of the regions and regime parameters when the local heat flux on the walls tends to zero due to the gas temperature approach to the surface temperature. It is shown that the mean heat transfer decreases as the relative channel length AR grows, whereas the integral gas flow rate (convective draft) and Reynolds number in the channel Re = 2wUm/ν increase. The use of a modified Rayleigh number Ra* = Ra · (w/L) (Elenbaas number) leads to generalization of calculation data on mean heat transfer. These data are in good agreement with the correlations for heat transfer [1, 2] and gas flow rate [3]. The reasons of variation of the data in the range of low Rayleigh numbers are discussed in detail.     

Synthesis,growth and characterization of L-proline dimercuricchloride single crystals for frequency conversion applications

A semi-organic nonlinear optical L-proline dimercuricchloride (LPDMC) material has been synthesized. LPDMC single crystals were grown from aqueous solution by a slow cooling method. Good quality single crystals of size 19×6×3 mm³ have been grown over a period of 3 weeks. The grown crystals have been subjected to single crystal X-ray diffraction analysis to determine the cell parameters. The title compound crystallizes in the triclinic system with a noncentrosymmetric space group P1 and with unit-cell parameters a=7.2742(4) Å, b=9.4472(5) Å, c=10.4767(6) Å, α=108.621(3)^°, β=107.260(2)^°, γ=97.353(2)^° and volume=631.51(6) Å³. Optical and dielectric properties of the crystals have been studied. The thermal stability of the crystals was determined by thermogravimetric analysis/differential thermal analysis. The second harmonic generation efficiency of the crystals was obtained by the classical powder technique using a Nd:YAG laser and it is found to be 2.5 times that of potassium dihydrogen phosphate.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

Geometric optimization of T-shaped constructs coupled with a heat generating basement: A numerical approach motivated by Bejan’s constructal theory

This work relies on constructal design to perform the geometric optimization of morphing T-shaped fins that remove a constant heat generation rate from a rectangular basement. The fins are bathed by a steady stream with constant ambient temperature and convective heat transfer. The body that serves as a basement for the T-shaped construct generates heat uniformly and it is perfectly insulated on the outer perimeter. It is shown numerically that the global dimensionless thermal resistance of the T-shaped construct can be minimized by geometric optimization subjected to constraints, namely, the basement area constraint, the T-shaped fins area fraction constraint and the auxiliary area fraction constraint, i.e., the ratio between the area that circumscribes the T-shaped fin and the basement area. The optimal design proved to be dependent on the degrees of freedom (L₁/L₀, t₁/t₀, H/L): first achieved results indicate that when the geometry is free to morph then the thermal performance is improved according to the constructal principle named by Bejan “optimal distribution of imperfections.”     

Simulation of turbulent non-isothermal polydisperse bubbly flow behind a sudden tube expansion

The results of numerical simulation of the structure of non-isothermal polydisperse bubbly turbulent flow and heat transfer behind a sudden tube expansion are presented. The study was carried out at a change in the initial diameter of the air bubbles within d _m1 = 1–5 mm and their volumetric void fraction β = 0–10 %. Small bubbles are available in almost the entire cross section of the tube, while the large bubbles pass mainly through the flow core. An increase in the size of dispersed phase causes the growth of turbulence in the liquid phase due to flow turbulization, when there is a separated flow of liquid past the large bubbles. Adding the air bubbles causes a significant reduction in the length of the separation zone and heat transfer enhancement, and these effects increase with increasing bubble size and their gas volumetric flow rate ratio.     

A free convective boundary layer in a conducting fluid in the presence of a transverse magnetic field

The properties of free convection in a conducting fluid in laminar regime near a hot solid vertical w all in the presence of a transverse magnetic field are theoretically analyzed. The existence of two regimes of heat transfer from the wall to the fluid are established. In the first regime, at small heights x?x* where the magnetic field effect can be disregarded, heat transfer is described by the well-known results for a free convective boundary layer in a nonconducting fluid with the Nusselt number Nu_x∝x^3/4. In the second regime, at x? x* where the magnetic field plays a crucial role, the dependence of heat transfer on the height and field strength is \(Nu_x \propto {{\sqrt x } \mathord{\left/ {\vphantom {{\sqrt x } B}} \right. \kern-\nulldelimiterspace} B}\). The location of the boundary between these regimes strongly depends on the magnetic field, x*∝ B^?4.     

Experimental investigation of heat transfer from different pin fin in a rectangular channel

In this study, the effect of both hexagonal pin fins (HPFs) and cylindrical pin fins (CPFs) into the rectangular channel on heat transfer augmentation, Nusselt number and friction factor were experimentally investigated. In planning of the experiments, different Reynolds number, pin fin array, pin fin geometry and the ratio of the distance between pin fin spacing (s) to the pin fin hydraulic diameter (s/D_h) were chosen as the design parameters. Air was used as the fluid. The Reynolds number, based on the channel hydraulic diameter of the rectangular channel, was varied from 3188 to 19531. In the experiments, the heating plate was made of stainless steel foil. The foil was electrically heated by means of a high current DC power supply to provide a constantly heated flux surface. The heat transfer results were obtained using the infrared thermal imaging technique. The heat transfer results of the hexagonal pin fins (HPFs) and cylindrical pin fins (CPFs) are compared with those of a smooth plate. Best heat transfer performance was obtained with the hexagonal pin fins. The maximum thermal performance factor ((?), was obtained as Re = 3188, staggered array, s/D_h = 0, ? = 2.28.     

Das integrale Reflexionsvermögen von gebogenen Quarzkristallen für Röntgenstrahlen im Transmissionsfall

A calculation procedure is described which permits evaluation of the material functions (electrical conductivityσ and radiation densityu as a function of the heat flux potentialS)from the measured arc characteristicsE(I) andU(I) (field strength and radiated power per unit arc length as a function of current strength). Hereto must be employed the additional relationship of energy balance and the current transport equation. The procedure is applied to N₂ and Ar. If furthermore the radial temperature distribution is known the temperature dependence ofσ, u.S andκ (thermal conductivity) may also be determined. In this way the material functions of the N₂-plasma are evaluated from available measurements.     

Engines with ideal efficiency and nonzero power for sublinear transport laws

It is known that an engine with ideal efficiency (η = 1 for a chemical engineand e =e_Carnot for a thermal one) has zero powerbecause a reversible cycle takes an infinite time. However, at least from a theoreticalpoint of view, it is possible to conceive (irreversible) engines with nonzero power thatcan reach ideal efficiency. Here this is achieved by replacing the usual linear transportlaw by a sublinear one and taking the step-function limit for the particle current(chemical engine) or heat current (thermal engine) versus the applied force. It is shownthat in taking this limit exact thermodynamic inequalities relating the currents to theentropy production are not violated.     

NATURAL CONVECTION FROM A VERTICAL RECTANGULAR FIN

An experimental investigation of steady-state natural convection from vertical rectangular mild steel and aluminum fins was conducted using laser holographic interferometry. Infinite-fringe interferograms demonstrate the effect of fin base heating. Depending on the fin material and base temperature, the local heat transfer coefficients vary along the fin with maximum values at positions about 22-48% of the fin height measured from the base. Temperature measurements along the fin show good agreement with the classical one-dimensional corwective and adiabalic tip solutions. Hence, in the thermal design of vertical aluminum fins of low Biot numbers, the classical one-dimensional fin solutions may be used together with an average heat transfer coefficient obtained from established correlations for natural convection from an isothermal flat plate.