Finite Heat Transfer Coefficient Research Articles

Extended detailed balance modeling toward solar cells with cement‐based radiative coolers

AbstractReducing the temperature of a solar cell increases its efficiency and lifetime. This can be achieved by radiative cooling, a passive and simple method relying on materials that dump heat into outer space by thermal emission within the atmosphere transparency window between 8 and . As most radiative coolers are expensive or possibly UV unstable, we have recently proposed cement‐based solutions as a robust and cost‐effective alternative. However, the assessment model used describes the cell in the radiative limit and with perfect thermal coupling to the cooler, in line with the literature. In this work, we lift these two approximations, by incorporating Auger and Shockley–Read–Hall nonradiative recombination and a finite heat transfer coefficient at the cell/cooler interface, to obtain a thermal description of the cell/cooler stack closer to reality, while preserving the universality and transparency of the detailed‐balance approach. We use this model to demonstrate that the cell performance gains provided by a radiative cooler are underestimated in the radiative limit and are hence more prominent in devices with stronger nonradiative recombination. Furthermore, we quantify the relation between cell temperature and heat transfer coefficient at the cell/cooler interface and show how this can be used to define design requirements. The extended model developed, and the resulting observations provide important guidelines toward the practical realization of novel radiative coolers for solar cells, including cement‐based ones.

Linear and Nonlinear Stability Analysis of Molten Salt Natural Circulation Loop

Abstract A molten salt natural circulation loop (MSNCL) has been setup to study the steady-state, transient, and stability characteristics of molten nitrate salt, mixture of sodium nitrate, and potassium nitrate in 60:40 ratios by weight. Natural circulation experiments in a temperature range of 290 °C–600 °C have been performed. A semi-analytical linear model was derived for stability analysis of rectangular natural circulation loops with conventional localized surface heating and cooling. The developed model includes the effect of wall thermal inertia, variable internal heat transfer coefficient, finite secondary side heat transfer coefficient at cooler, and heat losses for predicting the stability map. These effects are incorporated considering their significant role in modeling high-temperature molten salt-based natural circulation systems. The developed model has been first validated with the experimental data of water loop available in literature. The developed model is then validated with the experimental data generated in MSNCL. Validation of in-house developed nonlinear model has also been performed against the same experimental data. The comparison of both linear and nonlinear stability analysis with the experimental data shows good agreement and articulates the importance of various parameters which have been included in the developed model.

Steady-periodic thermal stresses in an infinite hollow compound cylinder

Closed-form expressions for temperatures and elastic thermal stresses in an infinite hollow two-material compound cylinder subject to steady-periodic sinusoidal ambient temperatures are presented, taking finite heat transfer coefficients into account. The fluctuating temperatures and stresses in the cylinder are expressed in terms of complex-valued modified Bessel functions under the assumption of temperature-independent material properties. Transient thermal loads composed of linear temperature ramps are expressed as Fourier series, and studied by the presented method. In order to verify the analytic results, examples involving sinusoidal and linear loads are examined by finite element calculations.

A semi-analytical model for linear stability analysis of rectangular natural circulation loops

A semi-analytical model for stability analysis of natural circulation loops (NCL) with conventional localized surface heating and cooling is derived based on linear stability analysis (LSA) methodology. Considerations for local pressure losses, wall thermal inertia and finite secondary side heat transfer coefficient at cooler are given in this model. Heat losses are also incorporated to extend the scope of the model to high temperature loops like those operating with pressurized water, molten salts and liquid metals. A new parameter space is introduced for representing the stability maps. This parameter space gives a direct representation of operating variables and focuses on stability behavior at only feasible (theoretically) operating conditions for a given loop. The model is validated against the experimental data of two rectangular natural circulation loops from literature. The stability maps generated by this LSA model are further verified by simulating the dynamic behavior of NCL at various operating conditions. This is accomplished by numerically solving the non-linear governing equations of NCLs. A study is performed to find the effect of some aspects like wall thermal inertia on stability behavior of natural circulation loops. Local pressure losses and wall thermal inertia are found to have considerable effect on the stability behavior of the loops studied.

Higher order modeling of a free-piston Stirling engine: analysis and experiment

This paper focuses on higher order modeling and design of the free-piston Stirling engine (FPSE) based on Ant Colony Optimization (ACO). First, the governing thermodynamics and dynamical equations of the engine have been derived. Then, the design parameters of the engine are selected taking into account the finite heat transfer coefficient (resulting in a fifth-order model) and pressure drop (resulting in a sixth-order model) in the dynamical system and the corresponding differential equations are derived in detail. In the following, the mentioned methods and their performance in modeling the FPSE dynamics are investigated. The simulated results show that the effect of the pressure drop on the places of the closed-loop poles of the system is not significant, while the heat transfer coefficient has a considerable effect on the engine dynamics. Accordingly, a fifth-order model along with ACO algorithm is proposed to justify the FPSE behavior. To validate the presented modeling scheme, the prototype engine SUTECH-SR-1 was experimented. It is found that the values of parameters obtained from the proposed design method are close to those of the experiment. Besides, the presented higher order model predicts the engine behavior with an acceptable accuracy through which the validity of the design technique is affirmed.

Rigorous theory of graded thermoelectric converters including finite heat transfer coefficients

Maximization of thermoelectric (TE) converter performance with an inhomogeneous material and electric current distribution has been investigated in previous literature neglecting thermal contact resistances to the heat reservoirs. The heat transfer coefficients (HTCs), defined as inverse thermal contact resistances per unit area, are thus infinite, whereas in reality, always parasitic thermal resistances, i.e., finite HTCs, are present. Maximization of the generated electric power and of cooling power in the refrigerator mode with respect to Seebeck coefficients and heat conductivity for a given profile of the material's TE figure of merit Z are mathematically ill-posed problems in the presence of infinite HTCs. As will be shown in this work, a fully self consistent solution is possible for finite HTCs, and in many respects, the results are fundamentally different. A previous theory for 3D devices will be extended to include finite HTCs and is applied to 1D devices. For the heat conductivity profile, an infinite number of solutions exist leading to the same device performance. Cooling power maximization for finite HTCs in 1D will lead to a strongly enhanced corresponding efficiency (coefficient of performance), whereas results with infinite HTCs lead to a non-monotonous temperature profile and coefficient of performance tending to zero for the prescribed heat conductivities. For maximized generated electric power, the corresponding generator efficiency is nearly a constant independent from the finite HTC values. The maximized efficiencies in the generator and cooling mode are equal to the efficiencies for the infinite HTC, provided that the corresponding powers approach zero. These and more findings are condensed in 4 theorems in the conclusions.

Multiplicities and thermal runaway of current leads for superconducting magnets

The multiple solutions of conduction and vapor cooled copper leads modeling current delivery to a superconducting magnet have been numerically calculated. Both ideal convection and convection with a finite heat transfer coefficient for an imposed coolant mass flow rate have been considered. Because of the nonlinearities introduced by the temperature dependent material properties, two solutions exist, one stable and one unstable regardless of the cooling method. The limit points separating the stable form the unstable steady states form the blow-up threshold beyond which, any further increase in the operating current results in a thermal runway. An interesting finding is that the multiplicity persists even when the cold end temperature is raised above the liquid nitrogen temperature. The effect of various parameters such as the residual resistivity ratio, the overcurrent and the variable conductor cross section on the bifurcation structure and their stabilization effect on the blow-up threshold is also evaluated.

Instability of a horizontal porous layer with local thermal non-equilibrium: Effects of free surface and convective boundary conditions

The onset of convective instability in a horizontal porous layer saturated by a fluid is studied. A regime of local thermal non-equilibrium (LTNE) is considered. The lower plane boundary is an impermeable isothermal wall, while the upper boundary is a free surface with finite heat transfer coefficients to the external environment. The temperature boundary conditions at the free surface are parametrised by two Biot numbers: one for the solid and one for the fluid. A modal linear stability analysis of the basic motionless state is carried out. Limiting cases allowing for an analytical dispersion relation are defined and analysed. The general regime of linear instability is investigated by a numerical solution of the governing differential equations for the normal modes. The neutral stability condition, as well as the critical value of the Darcy–Rayleigh number, is studied in some asymptotic cases and in the general case.

Power generation characteristics of a sandwich-type self-heating thermoelectric generator with spatially varying embedded heat source

Summary Power generation characteristics of a sandwich-type thermoelectric generator in which the heat source is embedded into thermoelectric elements are investigated. Our previous work on a similar concept only considered a uniform heat source distribution inside thermoelectric elements. In this work, the effect of the spatial distribution of a heat source is examined. In particular, the effect of the concentration of heat source near the one end, that is, the hot end, is intensively studied as a potential means of improving the efficiency of the device. Although the effects of heat source concentration in impractical cases without heat transfer limitations on the cold side remain ambiguous, it become clear that heat source concentration indeed has positive effects in more realistic cases with finite heat transfer coefficients imposed on the cold side. Because of the relatively low efficiency of typical thermoelectric generation, a significant amount of heat must be dissipated from the cold end of the thermoelectric element. Greater heat source concentration near the hot end leads to more effective utilization of available heat source, reduces the amount of heat rejected at the cold end, and lowers the hot end temperature of the thermoelectric element. Overall, it is suggested that heat source concentration can be used as a method to achieve more efficient operation and better structural integrity of the system. Copyright © 2015 John Wiley & Sons, Ltd.

Application of the Kirchhoff Transform to Thermal Spreading Problems With Convection Boundary Conditions

Thermal management and thermal analysis of microelectronic devices and packages are critical in ensuring the performance, reliability, and lifetime of today's electronic systems. When the thermal conductivity of a semiconductor or packaging material depends strongly on temperature, the use of a constant thermal conductivity value may significantly underestimate the temperature rise and thermal resistance. The Kirchhoff transform provides a convenient way of linearizing the heat conduction equation to use computationally efficient analytical solutions to calculate the device or package temperature. In the past, the application of the Kirchhoff transform has been restricted to temperature and heat flux boundary conditions in thermal spreading problems. In this paper, we developed an approximate solution for the application of the Kirchhoff transform to thermal spreading problems with convection in the sink plane and show the technique to be accurate to within 1% for relevant problems in device-level thermal analysis. The proposed technique is combined with a recently developed analytical solution for temperature rise in complex, multilayered structures in which a finite heat transfer coefficient in the sink plane needs to be considered. These analytical expressions and the Kirchhoff transform are valuable tools for accurately predicting the temperature in high-power, wide bandgap electronics, such as gallium nitride power amplifiers.

Effect of a finite external heat transfer coefficient on the Darcy-Bénard instability in a vertical porous cylinder

The onset of thermal convection in a vertical porous cylinder is studied by considering the heating from below and the cooling from above as caused by external forced convection processes. These processes are parametrised through a finite Biot number, and hence through third-kind, or Robin, temperature conditions imposed on the lower and upper boundaries of the cylinder. Both the horizontal plane boundaries and the cylindrical sidewall are assumed to be impermeable; the sidewall is modelled as a thermally insulated boundary. The linear stability analysis is carried out by studying separable normal modes, and the principle of exchange of stabilities is proved. It is shown that the Biot number does not affect the ordering of the instability modes that, when the radius-to-height aspect ratio increases, are displayed in sequence at the onset of convection. On the other hand, the Biot number plays a central role in determining the transition aspect ratios from one mode to its follower. In the limit of a vanishingly small Biot number, just the first (non-axisymmetric) mode is displayed at the onset of convection, for every value of the aspect ratio.

Numerical study of nitrogen desorption by rapid oxygen purge for a medical oxygen concentrator

Efficient desorption of selectively adsorbed N2 from air in a packed column of LiX zeolite by rapidly purging the adsorbent with an O2 enriched gas is an important element of a rapid cyclic pressure swing adsorption (RPSA) process used in the design of many medical oxygen concentrators (MOC). The amount of O2 purge gas used in the desorption process is a sensitive variable in determining the overall separation performance of a MOC unit. Various resistances like (a) adsorption kinetics, (b) column pressure drop, (c) non-isothermal column operation, (d) gas phase mass and thermal axial dispersions, and (e) gas-solid heat transfer kinetics determine the amount of purge gas required for efficient desorption of N2. The impacts of these variables on the purge efficiency were numerically simulated using a detailed mathematical model of non-isothermal, non-isobaric, and non-equilibrium desorption process in an adiabatic column. The purge gas quantity required for a specific desorption duty (fraction of total N2 removed from a column) is minimum when the process is carried out under ideal, hypothetical conditions (isothermal, isobaric, and governed by local thermodynamic equilibrium). All above-listed non-idealities (a–e) can increase the purge gas quantity, thereby, lowering the efficiency of the desorption process compared to the ideal case. Items (a–c) are primarily responsible for inefficient desorption by purge, while gas phase mass and thermal axial dispersions do not affect the purge efficiency under the conditions of operation used in this study. Smaller adsorbent particles can be used to reduce the negative effects of adsorption kinetics, especially for a fast desorption process, but increased column pressure drop adds to purge inefficiency. A particle size range of ∼300–500 μm is found to require a minimum purge gas amount for a given desorption duty. The purge gas requirement can be further reduced by employing a pancake column design (length to diameter ratio, L/D<0.2) which lowers the column pressure drop, but hydrodynamic inefficiencies (gas mal-distribution, particle agglomeration) may be introduced. Lower L/D also leads to a smaller fraction of the column volume that is free of N2 at the purge inlet end, which is required for maintaining product gas purity. The simulated gas and solid temperature profiles inside the column at the end of the rapid desorption process show that a finite gas-solid heat transfer coefficient affects these profiles only in the purge gas entrance region of the column. The profiles in the balance of the column are nearly invariant to the values of that coefficient. Consequently, the gas-solid heat transfer resistance has a minimum influence on the overall integrated N2 desorption efficiency by O2 purge for the present application.

A mathematical model of the Leidenfrost effect on an axisymmetric droplet

A simple mathematical model is developed for the Leidenfrost effect on an axisymmetric droplet. We first examine the practice of describing large droplets as cylindrical and small droplets as almost spherical, by solving the Young–Laplace equation. Best fit formulas are presented relating the droplet surface area to volume. The full model for Leidenfrost is then discussed. This shows that the calculation may be reduced to the solution of three first order ordinary differential equations involving the volume, evaporation rate, and vapor film thickness. Comparison with experimental results shows good agreement provided the model incorporates two components neglected in previous theoretical studies. First, a finite heat transfer coefficient between the vapor and substrate is required. Second evaporation from the upper surface of the droplet must be included, even for large droplets.

Heat Transfer through Metal Walls of Finite Thickness

Abstract A quenching technique is scrutinized, where the surface of a polymer melt is brought into contact with a metal wall of a well defined lower temperature at time zero. Usually, this wall temperature has approximately been kept constant with the aid of a streaming heat transfer fluid. It turns out, however, that an exactly invariable wall temperature or a finite Biot number (finite heat transfer coefficient to the cooling fluid) are inadequate assumptions. However, an exact interface temperature is to berealized, if the crystallization kinetics of the polymer is to be investigated painstakingly at this interface. The reason for this requirement lies in the fact that the said kinetics is extremely sensitive to small temperature changes. The present contribution shows that a water cooled metal wall of small thickness is inadequate for the purpose. A rather thick metal wall, which is preheated to the required temperature and thermally insulated at the outside, is clearly preferable. Copper is better than steel.

Development of a Novel Methodology To Validate Optimal Sterilization Conditions for Maximizing the Texture Quality of White Beans in Glass Jars

Optimal thermal processes were designed for white beans in glass jars heated in a still and end-over-end rotary pilot water cascading retort. For this purpose, isothermal kinetics of thermal softening of white beans were studied in detail using a tenderometer and a texturometer. The fractional conversion model was applied in both cases to model the texture degradation. The Arrhenius equation described well the temperature dependence of the reaction rate constant. With regard to the heat transfer, heat penetration parameters (fh and jh) were experimentally determined from 100 containers under static as well as rotational (end-over-end) conditions at 4, 7, 10, and 15 rpm. Theoretical optimal temperatures, maximizing volume average quality retention, were calculated using a computer program valid for conduction heating foods. Experimental verification of the calculated results was conducted. Considering the finite surface heat transfer coefficient, theoretical and experimental optimal temperatures were of the same order of magnitude, around 130 degrees C, while for an infinite surface heat transfer coefficient the calculated optimum temperature was much lower than the experimental value. The type of reaction kinetic model, fractional conversion or first-order models, does not significantly affect optimal sterilization temperatures. Although some differences were found, the developed theoretical approach was successfully applied to convective and mixed heating mode products. The use of the correct surface heat transfer coefficient is crucial to design optimal processing conditions.

Analysis of the QUELL experiment and comparisons with numerical simulations (QUENCHER)

This paper presents a detailed analysis of the Quench Long Length (QUELL) experiment. A number of different quench scenarios are compared with numerical simulations using the QUENCHER model. It is shown that in all cases the maximum helium pressure rise, the conductor temperature rise, the quench propagation velocity, and the quench voltage obtained from the numerical studies are in very good agreement with the experiment. Based on the experimental results during the heat pulse propagation, together with a more detailed analysis of the heat transfer mechanism between the helium in the central hole and the cable space a new heat diffusion term is proposed in QUENCHER. This diffusion mechanism is a direct consequence of the finite heat transfer coefficient between the cable and the central hole, and the fact that helium velocity in the hole is much larger than the cable space. Results are presented with and without the new diffusion term in the model.

Quality optimization of conduction heating foods sterilized in different packages

Heat transfer during the sterilization of conduction heating foods packaged in cylindrical, retort pouch and rectangular containers, was modelled using a finite difference numerical method. Finite surface heat transfer coefficients were considered. Optimal temperatures, defined as the processing conditions that maximize surface or volume average quality retention with the constraint of a target sterility value at the coldest point, were calculated for several types of container. Optimal conditions for several case studies were compared with temperatures estimated by generalized formulae available in literature for the prediction of optimal temperatures as a function of all relevant variables. For all case studies, optimal temperatures predicted in both ways were very similar, with deviations often below ± 1°C. For most packages, the simple‐to‐use generalized equations, developed for one‐dimensional geometries, can therefore be used instead of lengthy numerical calculations involving two‐ and three‐dimensional geometries.

Unidirectional solidification of pure metals with finite heat transfer coefficient

The problem of undirectional solidification of a pure metal under non-ideal conditions of heat transfer has been studied. An integro-differential equation has been derived, involving the position and velocity of the solid-liquid interface. Numerical and approximate solutions are obtained for the position of the solid-liquid interface and temperature distribution in terms of the cooling time. For solidification times less than k 2/ h 2 a, a simple approximated solution is found that fits closely to the results obtained Hills and Moore. For times greater than k 2/ h 2 a, numerical solutions are obtained by means of truncated iterative processes. Finall y, the procedure is applied to the case of continuous casting of steel, a non-pure metal, while freezing in the mold.

Analysis of Thermal Stress Resistance of Partially Absorbing Ceramic Plate Subjected to Asymmetric Radiation, II: Convective Cooling at Front Surface

Thermal stresses in a partially absorbing brittle ceramic plate asymmetrically heated by radiation and cooled by convection on the same surface with finite and infinite heat transfer coefficients are analyzed. Comparison of the results from this study with those obtained in Part I, where the plate is subjected to radiation heating in the front surface and cooled by convection at the rear surface, indicates that the magnitudes of the maximum steady‐state tensile thermal stresses are nearly identical. Significant differences are found in the transient thermal stresses and the temperature distribution. The relative temperature levels in the present case are found to be significantly lower than those obtained in Part I. Implications of these results to the design and operation of engineering structures such as concentrated solar receivers are discussed.

On optimum disposal of waste heat

The irreversibility associated with waste heat disposal across an exchanger represents an inherent trade-off point in the design of power plants. On the one hand, a large degree of irreversibility from a large temperature drop across the heat-transfer surface is detrimental to the thermodynamic efficiency of a cycle that produces waste heat. On the other hand, reduction of irreversibility can be achieved only by employing a larger heat transfer area. Therefore, one expects that there must be an optimum design that maximizes the work output per unit of heat transfer area for a given cycle. The efficiency at this optimum condition should be much closer to efficiencies in comparable cases of “good” design, and it must serve as a much more reasonable yardstick in assesing engineering merit. To exemplify this type of optimization, a Carnot engine cycle with a finite heat transfer coefficient during its heat rejecting process is analyzed in detail. An optimizing temperature drop accompanying the transfer of waste heat is displayed, and the maximum efficiency is calcuated. Influences of the heat transfer at the high-temperature side and the entropy produced during (real) adiabatic processes are also assessed to show the realistic potential of this simple design technique.