Dimensionless Temperature Difference Research Articles

Thermodynamic analysis of flow and heat transfer inside channel with two parallel plates

We investigate analytically the first and second law characteristics of fluid flow and heat transfer inside a channel having two parallel plates with finite gap between them. Fully developed forced convection is considered. Fluid is assumed non-Newtonian and followed the power law model. Analytical expressions for dimensionless entropy generation number (NS), irreversibility distribution ratio (Φ) and Bejan number (Be) are determined as a function of dimensionless distance (Y), Peclet number (Pe), Eckert number (E), Prandtl number (Pr), dimensionless temperature difference (Ω) and fluid index (m and n). Spatial distribution of entropy generation number, irreversibility ratio and Bejan number are presented graphically.

Thermoeconomic design and analysis of a sensible-heat thermal energy storage system with Joulean heating of the storage element

A second-law-based thermoeconomic model of a sensible heat-storage system with Joulean heating is derived and discussed in which the storage element is cooled by flowing stream of gases. In this analysis, unit cost values are attached to the irreversible losses caused by the finite-temperature difference heat transfer and pressure drop during the heat removal process. Important dimensionless parameters are identified and the results are presented in terms of the optimum number of heat transfer units (NTUopt) as a function of the dimensionless unit cost per unit heat conductance (γUA) and dimensionless temperature difference (τ) of the storage systems. The storage systems studied are optimized by introducing a new performance criterion described as the cost rate number(Γ∗). Performance results of low- and high-temperature storage systems are also examined and the results are compared with that obtained from Krane's analysis to illustrate the usefulness of the present approach. The influence of important unit cost parameters on NTUopt and Γopt∗ are also studied in somewhat more detail.

Determining Soil Water Flux and Pore Water Velocity by a Heat Pulse Technique

A method is presented for measuring soil water flux density (J) with a thermo‐TDR (time domain reflectometry) probe. Constant heat input during a small time interval (15 s) is used to emit a heat pulse from a line heat source. Asymmetry in the thermal field near the heat source is quantified by computing the maximum dimensionless temperature difference (MDTD) between upstream and downstream locations. Heat transfer theory was used to relate MDTD to J A thermo‐TDR probe was used to obtain measurements of MDTD in water‐saturated soil materials of different textures (sand, sandy loam, and clay loam) with imposed water flux densities ranging from 1.16 × 10−5 to 6.31 × 10−5 m3 m−2 s−1 A nearly linear relationship between measured MDTDs and fluxes was observed for all soil materials. Measured and predicted MDTDs agreed well for flow experiments in sand. Greater discrepancies were observed for flow experiments in sandy loam and clay loam. Despite the lack of universal agreement between measured and predicted MDTDs, the experimental results indicate that the proposed method may provide a useful means of measuring J The method presented herein improves upon earlier methods by reducing distortion of the water flow field and minimizing heat‐induced soil water redistribution. Because the thermo‐TDR probe can be used to make TDR‐based measurements of volumetric water content (θ), the proposed method also may permit measurement of pore water velocity (J/θ).

Thermoeconomic Optimization of a Sensible-Heat Thermal-Energy-Storage System: A Complete Storage Cycle

An analytical model for the second-law-based thermoeconomic analysis and optimization of a sensible-heat-storage system is derived and discussed, in which the storage element is both heated and cooled by flowing streams of gases. In this analysis, monetary values are attached to the irreversible losses caused by the finite temperature difference heat transfer and pressure drop in the storage system. Important dimensionless parameters are identified and the results are presented in terms of the optimum dimensionless charging time θS,opt as a function of a dimensionless temperature difference τ, as well as the optimum number of heat transfer units NTUS,opt, as a function of the dimensionless unit cost per unit heat conductance γUA and τ of the storage systems. The systems analyzed are optimized by introducing a new performance criterion described as the cost rate number, Γ*. Several example problems are also presented and the results are compared with that obtained from Krane’s analysis to illustrate the usefulness of the present approach. The influence of important unit cost parameters on NTUS,opt and θS,opt, are also studied in somewhat more detail.

Interpretation of Crown Radiation Temperatures of a Dense Douglas fir Forest with Similarity Theory

Infrared crown radiation temperatures as observed over a dense Douglas fir forest are analyzed in the context of similarity theory and the concept of transport resistances. As such we obtain a rather high value of the roughness length for heat, which is about equal to the roughness length for momentum. This value can be explained by the more efficient transport of heat relative to momentum in the roughness sublayer of the forest. Correcting for this effect we arrive at the classic value for homogeneous terrain of about 0.1 times the roughness length for momentum. For unstable cases the presence of enhanced mixing of heat in the roughness sublayer leads to a modified integral stability function for the dimensionless potential temperature difference between the surface and the top of the roughness sublayer. The observations give some evidence for this different stability behaviour. The analysis suggests that during daytime the radiative surface temperature and the aerodynamic surface temperature are not significantly different when used to estimate fluxes. Daytime trunk space air temperature is satisfactory parameterized with the concept of gusts and with surface renewal analysis. As such it is related to the sensible heat flux and the storage heat flux. Night time radiation temperatures at times strongly deviate from the expected behaviour based on similarity theory and the roughness length for heat, suggesting that the concept of a single surface temperature is too simple for such cases.

96/05421 HCFC22-based absorption cooling systems. Part III: Effects of different absorber and condenser temperatures

The aim of this study is to investigate the economic performance of the waste heat recovery (WHR) system for a marine diesel engine. Four waste heat sources, which are exhaust gas, cylinder cooling water, scavenge air cooling water and lubricating oil of a marine diesel engine, are first applied to drive the transcritical Rankine cycle (TRC). R1234yf, R1234ze, R134a, R152a, R236fa and R290 are employed in the system as working fluids. The effects of expander inlet pressure and temperature on net power output, thermal efficiency, total cost, mass flow rate, and available efficiency of the WHR system are analyzed. The levelized energy cost is used to evaluate the economic optimizations and their corresponding optimal parameters in the WHR system. The results show that the optimal levelized energy cost of R236fa is the most excellent and is lower than that of R1234ze, R134a, R152a, R1234yf or R290 by 5.07%, 6.25%, 7.42%, 9.77% or 12.11%, respectively. The payback period, fuel oil saving, and CO2 emission reduction are applied to assess the suitability of these working fluids. Furthermore, the economic optimization correlations in terms of dimensionless optimal pressures and temperature difference ratios are proposed for the system design of the optimal operating conditions.

Analysis of non-isothermal heterogeneous autocatalytic reactions

This paper presents a general model for autocatalytic heterogeneous reactions in non-isothermal particles. We consider both quadratic and cubic autocatalysis and determine the effects of particle geometry, relative reaction rates, bulk fluid-phase composition, dimensionless temperature differences, and Arrhenius numbers on the catalyst effectiveness factor. In general, diffusion limitations within the heterogeneous phase can lead to effectiveness factors much greater than unity for both exothermic and endothermic autocatalytic reactions. Furthermore, multiple steady states can exist for exothermic reactions in a quadratic autocatalytic system, or for any reaction with a cubic autocatalytic system.

Unsteady Thermal Stratified Flow and Heat Transfer in a Horizontal Feedwater Pipe

In this paper, the unsteady state calculational model is proposed for the thermal stratification analysis in the feedwater line of the PWR plant. By defining dimensionless parameters in the two-dimensional polar coordinate system and applying SIMPLE algorithm, the temperature and flow profiles due to the thermal stratification are obtained. Base on the fact that the most significant condition occurs when the fluid temperature difference between the piping ends reaches as high as 166.deg. C, the present result shows that max. Dimensionless temperature difference of 0.6 (about l00.deg. C) obtained between hot and cold sections of pipe wall at dimensionless time 47.0.

Thermal stratification in a horizontal pipe of pressurizer surge line

In this paper, the unsteady two dimensional model for the thermal stratification in the pressurizer surge line of PWR plant has been proposed to numerically investigate the heat transfer and flow characteristics. The dimensionless governing equations are solved by using the Control Volume Formulation and SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The temperature profile of fluids and pipe wall with time are shown when the thermal stratification occurs in the horizontal pipe. The numerical result shows that the maximum dimensionless temperature difference is about O.514 between hot and cold section of pipe wall at dimensionless time 1,632.

Transient and steady bouyancy-driven flow in a horizontal cylinder

The ASTEC code is used to simulate both transient and steady two-dimensional, compressible, bouyancy-driven laminar flow and heat transfer in a horizontal cylinder full of air. Calculations cover Rayleigh numbers from 10 4 to 10 8 . The local and average Nusselt numbers, the velocity and temperature profiles along the vertical and horizontal diameters, and the velocity vector plots and temperature fields are presented for both the transient and steady-state cases. Results show that a near-stagnant, thermally stratified core exists only at moderately high Rayleigh numbers (>10 5) , the dimensionless temperature difference vertically across the core decreases with increasing Rayleigh number, and the time evolution of the flow and thermal fields is quite complicated. Numerical predictions are in good agreement with available experimental data.

Reconcentration of Aqueous Solutions in a Packed Bed: A Simple Approach

In recent years attempts have been made to use packed beds in open-cycle liquid desiccant cooling systems for the dehumidification process and/or for regenerating weak aqueous solutions. The possibility of reconcentrating the aqueous solution in a packed bed by means of solar-heated air was investigated. The schematic of the reconcentration process is shown. The weak absorbent solution, which leaves the absorber, is pumped to the top of the packed bed after passing through a solution-to-solution heat exchanger where it is preheated by the strong solution. solar-heater air enters the packed bed at the bottom. Since the weak solution vapor pressure exceeds the vapor pressure of water in air, the moisture transfer takes place from the solution to the air. Cooled and humidified air exists at the top and warm, concentrated solution leaves the bottom of the packed bed. For each kilogram of water evaporated from the solution in the packed bed, one kilogram may be absorbed in the absorbed and thus evaporated in the evaporator to provide cooling. Hence, the performance of the cooling system is directly related to the amount of water evaporated from the weak solution in the packed bed. A step-wise heat and mass balance across themore » bed is used to determine the performance of the reconcentration process. In this paper dimensionless vapor pressure and temperature difference ratios suitable for application in the reconcentration of aqueous solutions are defined. Further, a closed-form analytical solution is obtained to predict the mass of water evaporated from the weak absorbent solution, through a simplified vapor pressure correlation and the dimensionless vapor pressure correlation and the dimensionless vapor pressure and temperature difference ratios.« less

Heat Transfer in the Flow of Gases Around Oil Sand Spheres

An experimental study was conducted for the combined free and forced convection heating of preshaped molded spherical particles of Athabasca oil sands in hot gaseous streams of air at low Reynolds numbers. Based on a quasi-steady system, the lumped-heat-capacity approximation was employed to estimate the heat transfer coefficient of the transient convective system for each prescribed set of experimental stream conditions. Correlation of the results was made in terms of the dimensionless Nusselt number as a function of the particle Reynolds number and a dimensionless temperature difference. The simple closed-form analytical expression of the correlation was shown to fit the experimental data well.

On the structure of the flow due to the collision of opposed, vertical, free convection, boundary layers

Preliminary experimental results are reported for the structure of the flow due to the collision of a pair of boundary layers driven towards each other by buoyant forces along a vertical wall. Of the possible parameters characterizing the flow, a Rayleigh number ratio, R, and a dimensionless temperature difference, n, emerge as important. When 0.6 < R 2.0: if n < 0.20, the approaching streams merge in a two-dimensional streamlined manner; if n > 0.20 “fingering” of fluid between the streams and cross-stream secondary flows occur.

The Critical Conditions in a Reactive Slab with Slowly Varying Surface Temperature

Liouville's non-linear partial differential equation is considered for an infinite rectangular strip domain with a slowly varying boundary condition. The equation describes a layer of chemically reactive material under conditions where the resistance to surface heat transfer is negligible and the ambient temperature varies slowly along the surface. Symmetrical heating by a zero order exothermic reaction is assumed. If ε is a small dimensionless temperature difference between regions where the surface temperature is effectively constant, a perturbation series solution in δ may be determined provided the Frank-Kamenetskii parameter δ satisfies δ ≤ δc(ε). It is shown that a plausible value for the critical parameter is δc(ε) = δc(0) e−e,where δc(0) = 0.878. The corresponding critical temperature distribution is shown to have a dependence on ε different from that for subcritical cases.

Thermal performance of radiative cooling panels

The performance of panels which cool by.means of thermal infrared heat transfer to the sky is calculated from basic principles. The efficiency of a radiative cooling panel is defined. Computer calculations with the full heat transfer equations are performed for horizontal surfaces with infrared-transparent covers. Plots of efficiency versus a dimensionless temperature difference are shown to be insensitive to variations in air temperature, wind speed, and sky radiance, resulting in plots analogous to standard efficiency curves for solar panels. Experimental measurements show that, for most applications, white paint is a better radiator than aluminized polyvinyl fluoride film.

The Effect of Wall Conduction on the Stability of a Fluid in a Right Circular Cylinder Heated From Below

The onset of natural convection in a cylindrical volume of fluid bounded above and below by rigid, perfectly conducting surfaces and laterally by a wall of arbitrary thermal conductivity is examined. The critical Rayleigh number (dimensionless temperature difference) is determined as a function of aspect (radius to height) ratio and wall conductivity. The first three asymmetric modes as well as the axisymmetric mode are considered. Two sets of stream functions are employed to represent a velocity field that satisfies the no-slip boundary condition on all surfaces and conservation of mass everywhere. The Galerkin method is then used to reduce the linearized perturbation equations to an eigenvalue problem. The results for perfectly insulating and conducting walls are compared with the work of Charlson and Sani[9].

BUOYANCY-DRIVEN FLUID FLOW AND HEAT TRANSFER IN A PAIR OF INTERACTING VERTICAL PARALLEL CHANNELS

Abstract Consideration is given to a system consisting of two parallel vertical channels that share a common wall across which heat is transferred from one channel to the other. The other walls of the system are characterized by prescribed surface temperatures that exceed the ambient temperature, and this induces a buoyancy-driven upflow in the channels. To cope with the strong interaction between the channels, a solution scheme was employed in which each channel was visited successively and iteratively. The single-channel solutions that were performed at each visitation were also iterative in character, with the computations carried out with a parabolic finite-difference method. Three parameters were varied during the course of the computations. These Included the dimensionless channel height, a dimensionless temperature difference, and the dimensionless position of the common wall between the channels. Results are presented for the surface-integrated heat transfer at each channel wall, the total system ...

Vapor heat transfer in post-CHF region including the effect of thermodynamic non-equilibrium

Vapor phase heat transfer in the post-CHF region is modelled using momentum-transfer analogy and allowing for thermodynamic non-equilibrium. The vapor heat transfer coefficient is determined by momentum-transfer analogy, using an appropriate two-phase friction factor. The degree of thermodynamic non-equilibrium, denoted by the ratio of actual quality to equilibrium quality, is correlated in terms of a dimensionless temperature difference which includes the superheated vapor temperature. This correlation is solved simultaneously with a heat balance equation to determine the actual quality and the vapor temperature. Post-CHF vapor heat flux, calculated by this method, is compared to experimental tube data from eight different sources at pressures up to 2830 psia and over a wide range of mass fluxes. Results indicate an average deviation of 14.9% between measured and predicted heat fluxes for 2854 data points.