Effect of heat transfer law on the finite-time exergoeconomic performance of a Carnot refrigerator

The operation of a Carnot refrigerator is viewed as a production process with exergy as its output. The economic optimization of the endoreversible refrigerator is carried out in this paper. The Coefficient of Performance (COP) of the refrigerator is a secondary consideration of the practical engineering effort of maximizing cooling rate and exergy whose goodness is constrained by economical considerations. Therefore, the profit of the refrigerator is taken as the optimization objective. Using the method of finite-time exergoeconomic analysis, which emphasizes the compromise optimization between economics (profit) and the appropriate energy utilization factor (Coefficient of Performance, COP) for finite-time (endoreversible) thermodynamic cycles, this paper derives the relation between optimal profit and COP of an endoreversible Carnot refrigerator based on a relatively general heat transfer law q∝Δ(Tⁿ). The COP at the maximum profit is also obtained. The results obtained involve those for three common heat transfer laws: Newton's law (n=1), the linear phenomenological law in irreversible thermodynamics (n=−1), and the radiative heat transfer law (n=4).     

The Inverse Reconstruction of the Heat Transfer Coefficient for the Free Surface Water Jet

This article presents an application of inverse algorithm for reconstruction of heat transfer coefficient (HTC) for a water jet impinging a flat surface. Such an approach, allows for decoupling complex fluid flow from heat conduction in a solid impinged by jet. The approach starts with parameterization of a functional form of unknown boundary temperature and heat flux occurring at the fluid–solid interface. Later, Newton's law of cooling is used to force temporal invariability of HTC. Unknown coefficients of HTC distribution are determined from a least square fit between measured and computed temperatures. Temperatures entering the objective function are recorded by an infrared camera at the surface opposite to impinged one.     

Effect of nonlinear partial slip and thermal radiation on Oldroyd 8‐constant fluid in a channel with convective boundary condition

This investigation deals with the effects of nonlinear slip, nonlinear thermal radiation, and non‐Newtonian flow parameters on heat transfer of an incompressible magnetohydrodynamic steady flow of an Oldroyd 8‐constant fluid through two parallel infinite plates with convective cooling. The Rosseland approximation is adopted to simulate the radiation effects. Heat exchange with the surrounding at the surfaces is assumed to obey Newton's law of cooling. The system of coupled and highly nonlinear ordinary differential equations governing the model is solved numerically using the method of weighted residual. The combined effects of non‐Newtonian flow parameters, velocity slip parameter, magnetic field parameter, Biot numbers, thermal radiation on the fluid velocity, temperature distributions, skin friction, and the Nusselt number are presented graphically and discussed. It is found that the velocity slip has an increasing effect on the fluid velocity and temperature profiles. For larger values of the thermal radiation parameter, the temperature profile and the Nusselt number are noticed to be increased.     

Global sensitivity analysis of two-stage thermoelectric refrigeration system based on response variance

In this paper, a mathematical model of two-stage thermoelectric refrigeration system is established considering the influence of external heat transfer and its performance is analysed based on finite-time thermodynamics and Newton's heat transfer law. Taking the cooling capacity and coefficient of performance of the two-stage thermoelectric refrigeration system as separate objective functions, the general relationship between cooling capacity, coefficient of performance, and working design parameters of the system is determined. The influence of the fluctuation of the input design parameters on the output performance parameters is studied using a global sensitivity analysis based on the variance response. The main and total Global sensitivity indices of input parameters that affect the output performance are calculated, and the related sensitivity ranking are obtained. The results can be used to guide the performance analysis and parameter optimization of two-stage thermoelectric refrigeration system in application.     

Newton’s law of cooling and its interpretation

This paper will show that so-called “Newton’s law of cooling” that is often used for calculating of heat transfer by convection is actually not a law, but a model of heat exchange (heat transfer). Limits of validity of this law were discovered and will be shown. Moreover, an existing practice of modernizing this law for the purpose of calculating convective heat transfer will be questioned.     

Convective Heat Transfer in the Reusable Solid Rocket Motor of the Space Transportation System

This simulation involved a two-dimensional axisymmetric model of a full-motor initial grain of the reusable solid rocket motor of the Space Transportation System. It was conducted with the computational fluid dynamics (CFD) commercial code FLUENT^®. This analysis was performed to maintain continuity with most related previous analyses; serve as a non-vectored baseline for any three-dimensional vectored nozzles; provide a relatively simple application and test for various CFD solution schemes, grid sensitivity studies, turbulence modeling, and heat transfer; and calculate nozzle convective heat transfer coefficients. The theoretical prediction of turbulent convective heat transfer in supersonic nozzles is scarce and challenging. The accuracy of the present results and the selection of the numerical schemes and turbulence models were based on matching the rocket ballistic predictions of mass flow rate, head end pressure, measured chamber pressure drop and vacuum thrust, and specific impulse. The matching for these ballistic predictions was found to be good. This study was limited to convective heat transfer, and the results compared favorably with some of the methods cited. Good agreement with the backed-out data of the ratio of the convective heat transfer coefficient to the specific heat at a constant pressure was made at the nozzle throat. Qualitative agreement was achieved upstream and downstream of the nozzle throat due to effects that are absent in this study. These backed-out data were devised to match nozzle erosion that resulted from the combination of heat transfer (convective, radiative, and conductive), chemical (transpiration), and mechanical (shear and particle impingement forces) effects. To the author's knowledge, these effects have not been investigated/reported simultaneously.     

Convective Heat Transfer Coefficients in Concentric Annuli

Abstract

The geometric shape of a passage's cross-section has an effect on its convective heat transfer capabilities. For concentric annuli, the diameter ratio of the annular space plays an important role. The purpose of this study was to determine to what extent research has been done on convective heat transfer in smooth concentric annuli and, if possible, to improve on or contribute to existing theories. It was found that although various correlations exist, they are not in good agreement. For this study, experiments were conducted with a wide range of annular diameter ratios. The Wilson plot method was used to develop a convective heat transfer correlation for annular diameter ratios of 1.7 to 3.2. For Reynolds numbers (based on the hydraulic diameter), in the range of 4000 to 30000, the deduced correlation predicted Nusselt numbers accurately within 3% of experimental values.     

Energetic and Exergetic Performances of Plate Heat Exchanger Using Brine-Based Hybrid Nanofluid for Milk Chilling Application

Abstract

Theoretical study on the energetic and exergetic performances of a counter-flow corrugated plate heat exchanger using hybrid nanofluids for the milk chilling application has been done in the present investigation. Magnesia-silver and Alumina-silver nanoparticles have been dispersed in the ethylene glycol–water mixture and propylene glycol–water mixture (20:80 brine solutions) with different particle volume concentration separately. Effect of particle volume concentration and flow rate of the hybrid nanofluid on the heat transfer rate, convective, and overall heat transfer coefficients, mass flow rate of milk, pressure drop, pumping power, entropy generation rate, second law efficiency, irreversibility, irreversibility distribution ratio, non-dimensional exergy (NDE) destruction, and performance index have been studied. It has been observed that heat transfer rate, convective and overall heat transfer coefficients, pressure drop, pumping power, irreversibility, entropy generation rate, second law efficiency, and milk flow rate increase; while NDE destruction, performance index, and irreversibility distribution ratio decrease with the hybrid nanofluid flow rate and the volume concentration of the nanofluid. Within studied ranges, the hybrid nanofluid yields the maximum improvement of heat transfer rate and convective heat transfer coefficient of about 1.6% and 9.4%, respectively, compared to base fluid. It has also been found that silver?+?alumina shows slightly better performance improvement and hence hybrid nanofluid is recommended as a suitable alternative for the milk chilling units.     

Experimental and computational study of convective heat fluxes in swirling two-phase flows

The convective mode of heat transfer is mainly due to the bulk motion of the fluid. Its turbulent nature and enhanced heat transfer coefficients have always attracted the academic, scientific community, and industrialists for many decades. The current research is based on the experimental and theoretical investigations on the turbulent convective heat transfer in swirling (60–300 rpm) steam (1–3 bars) injection into cocurrently flowing water. An exponential increase in the convective heat transfers up till the most swollen part of the swirling steam-water volume of fluids has been observed. However, the convective heat transfer of the remaining part of the steam's plume shows an almost stagnant decreasing trend. The range of Rayleigh number that supports the transition in trends of the convective heat fluxes is 2.84 × 10¹¹–3.71 × 10¹¹. This transition affects the magnitude of the convective heat fluxes and the extent of the effective momentum fluxes, which is evident in the dominant role of the flow instabilities acting across the length of the steam's plume. Computational Fluid Dynamic analysis also has supported the exhibition of the heat fluxes magnitudes under the influence of the interacting Kelvin–Helmholtz instabilities and inertial instabilities across and along with the cocurrently acting shear layer.     

Steady Conjugate Heat Transfer from X-Ray or Laser-Heated Sphere in External Flow at Low Reynolds Number

ABSTRACT

A laser or an X-ray beam is used to heat a sphere that is immersed in uniform external flow. Temperature distributions as well as local and average convective heat transfer coefficients are calculated in order to evaluate the efficacy of cooling the solid sphere. The present work extends previous studies by: (1) applying a unique heat source imposed by irradiating the sphere with an intense X-ray energy beam; (2) performing the conjugate heat transfer analysis in fluid and solid domain; and (3) calculating the internal and surface temperature distribution. Absorption of the irradiation results in nonuniform heat generation, having an exponential spatial distribution of heat source. The limiting cases of heat source distribution are localized surface “laser” heating and near-uniform heat generation throughout the sphere. Key results are reported for two different source beam sizes (small and large) striking the sphere, with comparison to the solution for the isothermal wall boundary condition.     

Unsteady mass transfer in mixed convective heat flow from a vertical plate embedded in a liquid-saturated porous medium with melting effect

This paper numerically studies the transient mass transfer in mixed convective heat flow with melting effect from a vertical plate in a liquid saturated porous medium in the presence of aiding external flow. The governing equations are transformed into the non-dimensional form by using pseudo similarity coordinate (ζ) and dimensionless time (ξ). The resulting two dimensional boundary value problem (BVP) is then solved by the method of lines (MOLs) with the central finite difference and Newton's iteration to obtain the entire numerical solutions for all transient process from the initial stage (ξ = 0) to the final state (ξ = 1). The results show the rate of dynamic mass transfer at the solid–liquid interface is reduced with increasing the melting strength. In addition, the response time and the rate of the dynamic mass transfer for aiding buoyancy are respectively shorter and faster than those for opposing buoyancy from the transient molecular diffusion to the steady mixed convection in a porous medium with melting effect.     

Anisotropy Effects on Heat and Fluid Flow by Unsteady Natural Convection and Radiation in Saturated Porous Media

ABSTRACT

This article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with anisotropic, in both thermal conductivity and permeability, fluid-saturated porous medium. The bounding walls of the channel are gray and kept at a constant hot temperature.

In the present study we suppose the validity of the Darcy law for motion and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The numerical results allow us to represent the time–space variations of the different state variables. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely, the single scattering albedo ω, the temperature ratio R, the anisotropic thermal conductivity ratio R_c, and the anisotropic permeability ratio R_k, are addressed. Numerical results indicate that the controlling parameters of the problem, namely, ω, R, R_c, and R_k, have significant effects on the flow and thermal field behavior and also on the transient process of heating or cooling of the medium. Effects of such parameters on time variations of the volumetric flow rate q_v and the convected heat flux Q at the channel's outlet are also studied.     

Development of new correlations for forced convection heat transfer during cooling of products

This paper presents the new, simple but powerful effective Nusselt–Reynolds correlations for estimating the effective convective heat transfer coefficients of spherical and cylindrical products cooled in water and air flows. In this respect, both experimental and theoretical works were obtained. In the experimental case, several spherical and cylindrical products, namely, tomatoes, pears and cucumbers were cooled in water and air flow and their centre temperature variations were measured. In the theoretical case, the effective convective heat transfer coefficients for the individual spherical and cylindrical products were determined using the centre temperature data in the present approach including Dincer's models. Therefore, the new Nusselt–Reynolds correlations were developed using the effective convective heat transfer coefficient values and a general diagram of Nu/Pr^1/3 against Reynolds number was drawn. This study indicates that the present effective Nu–Re correlations are capable of estimating the effective convective heat transfer coefficients of any spherical and cylindrical shaped products exposed to water and air cooling in practical applications in a simple and accurate manner.     

Experimental Study of Heat Transfer and Pressure Loss in Channels with Miniature V Rib-Dimple Hybrid Structure

Abstract

In order to increase the thermal efficiency, the gas turbines are designed to operate at higher temperature, which requires highly efficient cooling structures for turbine blades. The dimples and ribs are effective surface structures to enhance the convective heat transfer in the gas turbine blade internal cooling. In the present study, a novel hybrid cooling structure with miniature V-shaped ribs and dimples is presented, and the heat transfer and pressure loss characteristics are obtained experimentally. The heat transfer performance of the rib–dimple structures, which include three different rib height-to-hydraulic diameter ratios of 0.017, 0.029 and 0.044 and one dimple configuration with the dimple depth-to-diameter ratio of 0.2, are studied by using the transient liquid crystal thermography technique for turbulent flow in rectangular channels within the Reynolds number range from 10,000 to 60,000. It is found that the miniature V-shaped ribs arranged upstream the dimples can significantly improve the heat transfer performance of the dimples, resulting in a more uniform heat transfer distribution on the surface. The V rib-dimple hybrid structure in the channel shows much higher heat transfer enhancement than the counterparts with only the dimples in the channels.     

Exergoeconomic performance of an endoreversible Carnot heat pump with complex heat transfer law

The finite-time exergoeconomic performance of an endoreversible Carnot heat pump with a complex heat transfer law, including generalized convective heat transfer law and generalized radiative heat transfer law q∝ (Δ T ⁿ ) ^m , is investigated in this paper. The focus of this paper is to obtain the compromised optimization between economics (profit) and the energy utilization factor (coefficient of performance, COP) for the endoreversible Carnot heat pump, by searching the optimum COP at maximum profit, which is termed as the finite-time exergoeconomic performance bound. The obtained results include those obtained in much of the literature and can provide some theoretical guidance for the design of practical heat pumps.     

Scaling Effects for Liquid Flows in Microchannels

Many experimental works on the forced convection through microchannels seem to show that when the hydraulic diameter is less than 1 mm, the conventional theory can no longer be considered suitable to predict the pressure drop and convective heat transfer coefficients. This conclusion seemed valid for both gas and liquid flows. Sometimes the authors justified this claim by invoking “new” micro-effects. In the last few years, this conclusion seems to be controverted by additional, more accurate experimental data. For this reason, the explanation of the experimental results obtained for microchannels in terms of friction factors and convective heat transfer in the laminar regime is sought for within the bonds of the conventional theory. In particular, this study focuses on the role of viscous heating in liquids flowing through microchannels, considering them as scaling effects. The role of the cross-sectional geometry on the viscous heating is highlighted for adiabatic and diabatic channels. Design correlations that are useful in defining the limit of significance of the most important scaling effects for microchannels, such as viscous heating and conjugate heat transfer, are also presented.     

Augmentation of Thermal Effectiveness in the Fixation of Fibrous Material Structures

Abstract

The technology of structure fixation of fibrous or porous media is a heat-consuming content process. In this study, an experimental investigation of the augmentation of thermal effectiveness for this technology was carried out. This can be performed with better utilization of heat from polycondensation's reaction of a binder solution and a convective–conductive heat transfer. The possible construction of technological equipment and new technology of fixation structure fibrous materials were proposed based on the results of our investigation.     

Convective gas cooling heat transfer and pressure drop characteristics of supercritical CO2/oil mixture in a minichannel tube

The effects of PAG oil concentration on the convective gas cooling heat transfer and the pressure drop characteristics of supercritical CO₂/oil mixture in minichannel tube were investigated. The test results showed that the average gas cooling heat transfer coefficient was decreased by 20.4% and the average pressure drop was increased by 4.8 times when the oil concentration was increased from 0 to 4 wt.%. The effects of the oil concentration on the convective gas cooling heat transfers and the pressure drops of the supercritical CO₂/oil mixture in minichannel tubes were experimentally confirmed to be significant.     

The influence of heat resistance and heat leak on the performance of a four-heat-reservoir absorption refrigerator with heat transfer law of Q∝Δ(T)

On the basis of an endoreversible absorption refrigeration cycle model with Newton's heat transfer law, an irreversible four-heat-reservoir cycle model with another linear heat transfer law of Q∝Δ(T⁻¹) is built by taking account the heat leak and heat resistance losses. The fundamental optimal relation between the coefficient of performance (COP) and the cooling load, the maximum COP and the corresponding cooling load, as well as the maximum cooling load and the corresponding COP of the cycle with another linear heat transfer law coupled to constant-temperature heat reservoirs are derived by using finite-time thermodynamics. The optimal distribution relation of the heat-transfer surface areas is also obtained. Moreover, the effects of the cycle parameters on the COP and the cooling load of the cycle are studied by detailed numerical examples. The results obtained herein are of importance to the optimal design and performance improvement of a four-heat-reservoir absorption refrigeration cycle.     

Unsteady conjugate laminar heat transfer of a rotating non-uniformly heated disk: Application to the transient experimental technique

Presented in the paper are the results of an investigation of 2D heat conduction effects on the transient heat transfer of a rotating disk heated up to a non-uniform initial temperature and suddenly subjected to unsteady cooling by still air. A self-similar solution of the transient laminar convective heat transfer confirmed that the heat transfer coefficient rapidly becomes time-independent and equal to its value at steady-state conditions. An analytical solution of the unsteady two-dimensional heat conduction inside a disk made of Plexiglas^® confirmed that the known infinite-slab approach can still be used as a transient technique for determining heat transfer coefficients. Use of the regular heat transfer regime theory for the same purpose can be recommended only for the cases with the moderate initial temperature non-uniformity.