Introducing Rare Earth Dopants for Controlled Conductivity in Thermoelectric Cobaltites

The conversion of waste heat into electrical energy plays a key role in our current challenge to develop alternative energy technologies to reduce our dependence on fossil fuels. Thermoelectric (TE) materials are the first choice to handle this subject. In TE materials, cobaltites are the material of interest, due to their nontoxic properties. Cobaltites exhibits large TE power, low resistivity, and relatively small thermal conductivity at room temperature. TE material (BiCa_2?x R _x CoO _y ) where R is for rare earth like Nd, (x = 0.0, 0.2) was synthesized in nanoregime by simplified sol–gel method. Simplified sol–gel method was chosen because it gives maximum phase purity and tunable parameters for desired properties. The mechanism used to enhance thermoelectric properties is to reduce thermal conductivity of the material and increase electrical conductivity of the material using nanostructures. Material characterizations were done for structural studies using X-ray diffraction (XRD). XRD revealed monoclinic crystal structure. Temperature-dependent electrical conductivity showed an increase with increase in temperature. Thermal conductivity was also measured. Both electrical resistivity and thermal conductivity decrease as a result of neodymium doping which enhanced its importance as thermoelectric material. The different parameters were correlated to understand the conduction mechanism.     

Low Temperature Properties of a Superconducting Niobium Coaxial Cable

Semirigid coaxial cables with seamless metal shields are promising for readout from sensitive devices operating below liquid helium temperature. Low thermal conduction of such cables are also essential to reduce heat penetration into cryogenic temperature. We have developed thin semirigid coaxial cables employing niobium-titanium and niobium in both center and outer conductors, taking advantage of low thermal conductivity and extreme small electrical resistivity of superconductors. We assembled an adiabatic demagnetization refrigerator and measured thermal and electrical characteristics of those superconducting coaxial cables below T _c. Thin niobium coaxial cable with an outer diameter of 0.86 mm showed two-orders lower thermal conduction than expected, which is considered as the effect of impurity of niobium and forming process. Small attenuation was observed up to high frequency above 10 GHz at 3 K.     

High-temperature elastic moduli of thermoelectric SnTe1±x – y SiC nanoparticulate composites

In waste heat recovery applications, thermoelectric (TE) generators are subjected to thermal gradients and thermal transients, creating mechanical stresses in the TE legs. Such stresses are functions of the elastic moduli of the TE material. For SnTe_1±x matrices (where x = 0.0 or 0.016) composite specimens with 0–4 vol% SiC nanoparticle (SiC_NP) additions, the elastic moduli (Young’s modulus, shear modulus, and Poisson’s ratio) were measured by resonant ultrasound spectroscopy from room temperature (RT) to 663 K. The effects of matrix composition and the SiC_NP additions on the RT intercepts and the slopes of the elastic modulus as a function of temperature are also discussed.     

Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge

With a comprehensive and rigorous method, this paper has successfully examined the transient heat transfer in a steady and two-dimensional (2D) laminar boundary layer flow on a wedge with sudden change of thermal boundary conditions of uniform wall temperature (UWT) and heat flux (UHF). Additionally, a correlation of unsteady forced convection was also formulated through an exact solution of transient heat conduction (ξ=0) and the similarity solutions of a steady forced convection on a wedge (ξ=1) in this study. Particularly, for the wedge with −0.198838?ξ?1, the deviation of the wall temperatures estimated by correlation is less than 7.5% within full time of 0?ξ?1 comparing with numerical results in the case of UHF ranging from Pr=10⁻⁴ to 10⁴.     

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.     

Forced convection heat transfer from concentrated and distributed thermal sources

Abstract

This paper proposes a novel formulation for the analysis of forced convection heat transfer from both a concentrated thermal source and a uniformly distributed thermal source. The illustrative examples are the wedges of various configurations with dual thermal sources; namely, each of the wedges is imposed with uniform‐flux on the surface and embedded with a line source at the leading edge. By introducing a parameter of relative source strength ξ and a dimensionless temperature based on the two characteristic temperature of the sources, a nonsimilar boundary‐layer energy equation is obtained. The nonsimilar energy equation is readily reducible to the self‐similar equations of adiabatic wedge plumes for ξ=0, and to those of uniform‐flux wedges for ξ=1. Numerical solutions are obtained by employing an effective numerical scheme which has been developed for nonsimilar plumes subject to an integral equation of flux conservation condition. Results are presented for the cases of flat plate, right angle wedge, stagnation point and separating wedge flow for Pr=0.7, 1, 7, 10, and 100. Dimensionless wall temperature for all the cases are proportional linearly to ξ over the entire range of ξ from 0 to 1. Solutions for the limiting cases of ξ=0 and 1 are in excellent agreement with the reported data.     

Roles of heat transfer modes on transient cooling by quenching process

In order to predict the metallurgical structure of the quenched part by numerical simulation, one needs the boundary condition at the part-bath interface. This last, generally of the third kind, is deduced from measurement of temperature and heat flux density of the surface of work piece. The main goal of this work is the understanding of the heat transfers mechanisms that control the cooling speed according to the size of the work piece. We developed an original device of measurement which allowed temperature and local heat flux estimating at the part-bath interface during quenching process. Experimental results have updated the prevalence of one heat transfer mode according to the more or less thermal resistive character of the quenched part. This prevalence is linked to the mean Biot number Bi _m . When Bi _m ?<?<1, heat conduction inside the work piece does not have a significant role in the cooling: the part is practically isothermal. The cooling is primarily ensured by boiling and more particularly by film boiling. Consequently the profile of cooling velocity is quasi uniform in the part. This situation favours a uniform metallurgic transformation in all the part and the absence of in temperature gradients avoids the differentials of dilation which are at the origin of residual stress fields. Conversely, when Bi _m ?>?>?1, the part has a large thermal resistance such as the temperature of the bath is quickly imposed on its surface. Then, cooling is primarily ensured by convection. In this case, the part bulk is the seat of large thermal gradients which induce a strong distribution of cooling velocity. The latter is at the origin of some differences in metallurgical structure and of a residual stress field within the part. In the intermediate value range, 0.1?<?Bi _m ?<?10, boiling and convection ensure successively the cooling, but in the boiling there is a prevalence of nucleate boiling mode which determines the reached maximum value of cooling speed located always in the close vicinity of the part-bath interface.     

Two-phase lattice Boltzmann simulation of natural convection in a Cu-water nanofluid-filled porous cavity: Effects of thermal boundary conditions on heat transfer and entropy generation

The present work investigates the effect of four different thermal boundary conditions on natural convection in a fluid-saturated square porous cavity to make a judicious choice of optimal boundary condition on the basis of entropy generation, heat transfer and degree of temperature uniformity. Four different heating conditions- uniform, sinusoidal and two different linear temperature distributions are applied on the left vertical wall of the cavity respectively, while maintaining the right vertical wall uniformly cooled and the horizontal walls thermally insulated. The two-phase thermal lattice Boltzmann (TLBM) model for nanofluid is extended to simulate nanofluid flow through a porous medium by incorporating the Brinkman–Forchheimer-extended Darcy model. The close agreement between present LBM solutions with the existing published results lends validity to the present findings. The current results indicate that the uniform and bottom to top linear heating are found to be efficient heating strategies depending on Rayleigh number (10³?≤?Ra?≤?10⁵) and Darcy number (10^?1?≤?Da?≤?10^?6). It is observed that the nanofluid improves the energy efficiency by reducing the total entropy generation and enhancing the heat transfer rate although its augmentation depends on the optimal volume fraction of nanoparticles.     

A theory of convective gas motion in a cylindrical volume

The convective motion of gas in the gravitational field is described for an axisymmetric body with the cylinder ends maintained at different temperatures. A system including the equation of heat conduction, the Navier-Stokes equations, and the continuity equation is analyzed. The convective velocity components v _z ^′ (r, z), v _r ^′ (r, z) and the temperature T are determined as functions of the cylindrical coordinates. The time required for the establishment of thermal equilibrium by means of convection and heat conduction is estimated.     

Nonlinear thermal bending response of FGM plates due to heat conduction

Nonlinear thermal bending analysis is presented for a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations of an FGM plate are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. A two step perturbation technique is employed to determine the thermal load–deflection and thermal load–bending moment curves. The numerical illustrations concern nonlinear bending response of FGM plates without or with surface bonded piezoelectric actuators due to heat conduction and under different sets of electric loading conditions. The results reveal that for the case of heat conduction the nonlinear thermal bending responses are quite different to those of FGM plates subjected to transverse mechanical loads, and the temperature-dependency of FGMs could not be neglected in the thermal bending analysis.     

Effect of a non-constant magnetic field on natural convection in a horizontal porous layer heated from the bottom

An analytical and numerical investigation is conducted to study the effect of an electromagnetic field on natural convection in a horizontal shallow porous cavity filled with an electrically conducting fluid. The magnetic field is assumed to be induced by two long wires, carrying current, parallel to the horizontal boundaries of the system. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. The governing parameters of the problem under study are the thermal Rayleigh number, Ra, Hartmann number, Ha, position of the electrical wires, d, current intensity ratio, r, and aspect ratio of cavity, A. An analytical solution, valid for a shallow layer (A ? 1), is derived on the basis of the parallel flow approximation. The critical Rayleigh number, Ra _c , for the onset of motion is derived in closed form in terms of the parameters of the problem. For finite-amplitude convection the heat and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations.     

The onset of double diffusive convection in a sparsely packed porous layer using a thermal non-equilibrium model

We examine the effect of local thermal non-equilibrium on double diffusive convection in a fluid-saturated sparsely packed porous layer heated from below and cooled from above, using both linear and nonlinear stability analyses. The Brinkman model is employed as the momentum equation. A two-field model that represents the fluid and solid phase temperature fields separately is used for the energy equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. It is found that a small inter-phase heat transfer coefficient has significant effect on the stability of the system. There is a competition between the processes of thermal and solute diffusion that causes the convection to set in through either oscillatory or finite amplitude mode rather than stationary. The effect of solute Rayleigh number, porosity modified conductivity ratio, Lewis number, ratio of diffusivities, Vadasz number and Darcy number on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method predicts the occurrence of subcritical instability in the form of finite amplitude motions. The effect of thermal non-equilibrium on heat and mass transfer is also brought out.     

A criterion of applicability of the parabolic heat conduction equation

A criterion (K _MCV) of applicability of the parabolic heat conduction equation to isotropic materials is proposed that quantitatively determines the conditional boundary between linear and nonlinear regimes of nonequilibrium thermodynamics in the one-dimensional formulation of some heat transfer problems. The criterion is related to the heat flux relaxation time τ_r. Once this characteristic time is known, the condition K _MCV = 0 implies validity of the parabolic heat conduction equation. If τ_r is unknown, the adequacy of the parabolic heat conduction model can be judged from the absence of a temporal variation of the K _MCV/τ_r ratio under the main condition that the heat source power is independent of the time.     

Transient mixed convective heat transfer with melting effect from the vertical plate in a liquid saturated porous medium

This paper aims to numerically analyze the melting effect on transient mixed convective heat transfer from a vertical plate in a liquid saturated porous medium. The Darcy’s flow with the Boussinesq approximation and energy equations for this study is transformed into the non-dimensional equations by using pseudo-similarity coordinate (ζ) and dimensionless time (ξ). The resulting the boundary value problem is solved by the method of lines (MOLs) with central finite difference and Newton’s iteration to completely obtain the solutions for the whole transient mixed convective heat transfer from transient heat conduction to steady mixed convection in porous medium with melting effect in the presence of aiding and opposing external flows. As shown in the results, it is both found that the rate of dynamic heat transfer is reduced with increasing melting strength and the response time from transient heat conduction to steady mixed convection in porous medium for aiding external flow is shorter than that for opposing external flow in the presence of melting effect. Additionally, the melting effect may be reduced with increasing mixed convective strength Gr/Re^1/2 during transient mixed convective heat transfer in porous medium with aiding external flow.     

Fabrication of platinum nanoparticle counter electrode for highly efficient dye-sensitized solar cells by controlled thermal reduction time

We report the effect of the thermal reduction time during sintering on the electrocatalytic activity and the morphology of platinum nanoparticles (Pt-NPs) fabricated using thermal decomposition method. A uniform and dense distribution of Pt-NPs on fluorine-doped tin oxide glass substrate was achieved by controlling the thermal reduction time higher than 15 min and this morphology of Pt-NPs was responded for high electrocatalytic performance of counter electrode (CE). As expected, the excellent electrocatalytic activity with low charge-transfer resistance of 1.04 Ω cm² and highly conductivity of Pt-NPs CE prepared at the thermal reduction time of 15 min during sintering was obtained, which was desirable for dye-sensitized solar cells. The energy conversion efficiency of 9.43 % was obtained for the thermal reduction time of 15 min with fill factor of 63.05 %, J _sc of 18.82 mA cm^?2 and V _oc of 795 mV.     

Thermoelectric properties of GdBaCo2−x Fe x O5+δ ceramics

The influence of Fe doping on the lattice structure and thermoelectric properties of GdBaCo_2?x Fe _x O_5+δ (x = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0) ceramics was studied from room temperature to 525 K. The results show that presence of Fe will increase both electrical resistivity and Seebeck coefficients of the samples. Due to the lattice misfit and carrier concentration reduction caused by Fe, the thermal conductivity of the sample decreases. The activation energy of conductivity is larger than that of thermopower calculated in the semiconductive region, which means that the conduction mechanism may be determined as a small polaron hopping model. The optimum Fe doping amount is x = 0.6, which results in a ZT value 0.02 at 373 K.     

Fully coupled heat conduction and deformation analyses of visco-elastic solids

Visco-elastic materials are known for their capability of dissipating energy. This energy is converted into heat and thus changes the temperature of the materials. In addition to the dissipation effect, an external thermal stimulus can also alter the temperature in a visco-elastic body. The rate of stress relaxation (or the rate of creep) and the mechanical and physical properties of visco-elastic materials, such as polymers, vary with temperature. This study aims at understanding the effect of coupling between the thermal and mechanical response that is attributed to the dissipation of energy, heat conduction, and temperature-dependent material parameters on the overall response of visco-elastic solids. The non-linearly visco-elastic constitutive model proposed by Schapery (Further development of a thermodynamic constitutive theory: stress formulation, 1969, Mech. Time-Depend. Mater. 1:209?C240, 1997) is used and modified to incorporate temperature- and stress-dependent material properties. This study also formulates a non-linear energy equation along with a dissipation function based on the Gibbs potential of Schapery (Mech. Time-Depend. Mater. 1:209?C240, 1997). A numerical algorithm is formulated for analyzing a fully coupled thermo-visco-elastic response and implemented it in a general finite-element (FE) code. The non-linear stress- and temperature-dependent material parameters are found to have significant effects on the coupled thermo-visco-elastic response of polymers considered in this study. In order to obtain a realistic temperature field within the polymer visco-elastic bodies undergoing a non-uniform heat generation, the role of heat conduction cannot be ignored.     

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.     

The effect of longitudinal heat conduction on a regenerative heat exchanger

Abstract

This study is to discuss the effect of longitudinal heat conduction on a rotary regenerative heat exchanger. An example in Ref. [5] is computed to compare the effect of longitudinal heat conduction. The solutions presented in this study are obtained from the method of numerical analysis as shown in Ref. [3].     

Film boiling on a vertical plate in subcooled helium II

Film boiling heat transfer coefficients were measured on 10, 30 and 50 mm long vertical plates in subcooled He II for bulk liquid temperatures from 1.8 to 2.1 K. A film boiling model on a vertical plate in subcooled He II was presented based on convection heat transport in the vapor film, radiation heat transport, and heat transport in He II. The numerical solutions of the model were obtained and an equation which can express the numerical solutions within ±5% difference was derived. The equation predicted well the experimental data for lower ΔT range but significantly under-predicted the data for higher ΔT. A correlation of film boiling heat transfer including radiation contribution was presented by modifying the equation based the experimental data. This correlation can describe the experimental data within ±20% difference.