Small Heat Transfer Research Articles

Expected mechanism and characteristics of aqua-float process

A new process for the manufacture of flat glass, which consists of pouring a glass melt onto a water-containing substrate and stretching it on the steam, is studied in terms of heat transfer and energy balance, steam flow, and behavior of glass in order to understand the fundamental features of the process. Small heat transfer to steam and wet substrate from the glass defines the process and the sliding of substrate to glass together with adequate steam drain is critically important for the process to achieve flatness of product. The process is characterized by energy and resource saving; it is clean, simple and versatile with many possible applications; the apparatus is small and convenient.

A study on the development of the wire woven heat exchanger using small diameter tubes

This research focused on the experimental study of the performance characteristics of the wire woven heat exchanger with small diameter tubes. First, the wire woven heat exchangers were composed of small diameter tubes and thin wire fins: inner diameter of tube=1.3 mm, thickness of tube=0.25 mm, thickness of Al wire fin=0.5 mm, and tube length=295 mm. There were straight-fin type and spring-fin type wires. The experiments were carried out under the following conditions; evaporation pressure=0.6 MPa, air velocity=0.7–1.7 m/s, superheating=6–8 °C and working fluid=HCFC-22. The pressure drop and heat transfer coefficient of the heat exchangers were experimentally evaluated at various air velocities. The experimental results indicated that the pressure drop in the refrigerant side was lower than the typical fin-tube heat exchangers. This is due to the short tube length and many branch tubes. In spite of the small heat transfer surface, the wire woven heat exchanger had a high heat transfer coefficient. These results lead us to the conclusion that the wire woven heat exchanger using small diameter tubes (ID: 1.3 mm) is the compact heat exchanger with high performance and flexibility.

A mechanism for differential frost heave and its implications for patterned-ground formation

AbstractThe genesis of some types of patterned ground, including hummocks, frost boils and sorted stone circles, has been attributed to differential frost heave (DFH). However, a theoretical model that adequately describes DFH has yet to be developed and validated. In this paper, we present a mathematical model for the initiation of DFH, and discuss how variations in physical (i.e. soil/vegetation properties) and environmental (i.e. ground/air temperatures) properties affect its occurrence and length scale. Using the Fowler and Krantz multidimensional frost-heave equations, a linear stability analysis anda quasi-steady-state real-time analysis are performed. Results indicate that the following conditions positively affect the spontaneous initiation of DFH: silty soil, small Young’s modulus, small non-uniform surface heat transfer or cold uniform surface temperatures, and small freezing depths. The initiating mechanism for DFH is multidimensional heat transfer within the freezing soil. Numerical integration of the linear growth rates indicates that expression of surface patterns can become evident on the 10–100 year time-scale.

Onset of convection in the Rayleigh-Bénard flow under non-Boussinesq conditions: an asymptotic approach

The effect of temperature dependent fluid properties on the onset of convection in a horizontal fluid layer heated from below is investigated. Based on asymptotic expansions of all fluid properties with respect to temperature final results are deduced that are independent of specific property laws. They are general in nature and hold for all Newtonian fluids and all (small) heat transfer rates. A special point of interest is the widely used Boussinesq approximation. Our asymptotic results clearly show how this approximation affects the stability calculations of the flow under investigation.

HEAT AND MASS TRANSFER DURING SAPWOOD DRYING ABOVE THE FIBRE SATURATION POINT

ABSTRACT Pine sapwood was dried in an air convection kiln at temperatures between 60-80 °C. Temperature and weight measurements were used to calculate the position of the evaporation front beneath the surface. It was assumed that the drying during a first regime is controlled by the heat transfer to the evaporation front until irreducible saturation occurs. Comparisons were made with CT-scanned density pictures of the dry shell formation during initial stages of drying of boards. The results indicate a receding evaporation front behaviour for sapwood above approximately 40-50% MC when the moisture flux is heat transfer controlled. After that we finally reach a period where bound water diffusion is assumed to control the drying rate. The heat transfer from the circulating air to the evaporation front controls the migration flux. In many industrial kilns the heating coils therefore have too small heat transfer rates for batches of thin boards and boards with high sapwood content.

Onset of convection in the Rayleigh-Bénard flow with temperature dependent viscosity: An asymptotic approach

In this study it is investigated how variable viscosity affects the onset f instability in the Rayleigh-Benard convection. An asymptotic approach provides results that are independent of specific property laws. They are compared to those of other studies and to direct solutions of the non-expanded stability equations for particular property laws. It is demonstrated that one can also get the asymptotic results from solutions of the non-expanded equations by use of a so-called combined method. The asymptotic results are general in nature and hold for all Newtonian fluids and all (small) heat transfer rates.

Experimental study on boiling heat transfer with an impinging jet on a hot block

Previous studies on boiling heat transfer by impinging jets were mainly concerned with the impinging point by using small heat transfer surfaces of about 20 mm. An experimental study was made of the boiling heat transfer to an impinging water jet on a massive hot block. The upward heating surface was made of copper, its diameter and the nozzle diameter being 80 and 2.2 mm, respectively. The velocity of the impinging jet was varied between 0.6 and 2.1 m/s. Saturated water impinged normally on the heating surface, flowed radially, and subsequently dispersed into the atmosphere. It is clarified in the present study that heat transfer characteristics vary with the temperature of the heat transfer surface, and also with the distance from the impinging point. © 1999 Scripta Technica, Heat Trans Asian Res, 28(5): 418–427, 1999

Nonlinear stability theory of channel flow with heat transfer - an asymptotic approach

A fully developed laminar Poiseuille flow subject to constant heat flux across the wall is analysed with respect to its stability behavior by applying a weakly nonlinear stability theory. It is based on an expansion of the disturbance control equations with respect to a perturbation parameter e. This parameter is the small initial amplitude of the fundamental wave. This fundamental wave which is the solution of the linear (Orr-Sommerfeld) first order equation triggers all higher order effects with respect to e. Heat transfer is accounted for asymptotically through an expansion with respect to a small heat transfer parameter eT. Both perturbation parameters, e and eT, are linked by the assumption eT=O(e2) by which a certain distinguished limit is assumed. The results for a fluid with temperature dependent viscosity show that heat transfer effects in the nonlinear range continue to act in the same way as in the initial linear range.

Thermal receptivity of unstable laminar flow with heat transfer

In this study, open questions about the temperature disturbances in linear stability theory are addressed. Temperature effects on flow stability have been investigated previously either by assuming a time independent shape for the temperature disturbance or by neglecting temperature fluctuations completely. Treating temperature fluctuations as an initial value problem can show the limits in which these assumptions are justified. By means of an asymptotic approach, based on small heat transfer rates, the various effects can be well separated from each other.

Calculation of non-steady-state thermal conduction for low Fourier numbers (Fo<0.001)

Assuming that for small Fourier numbers heat transfer is determined by the specific heat of a heated layer of thickness \(\delta = \sqrt {a \cdot \tau } \), an equation is derived for the temperature field, whose solution is satisfied in finite quadratures and has a fairly simple form. The results of calculations made using the proposed dependence are compared with the accurate solutions obtained by A. V. Lykov. This suggests that acceptable calculation accuracy may be achieved for Fo<0.001 and Bi<20. In this case the values of the dimensionless temperature do not depend on the shape of the body, and the proposed dependence can be used for calculations of plates, cylinders, or spheres.

Local heat transfer, solids concentration and erosion around membrane tubes in a cold model circulating fluidized bed

Measurements of local solids concentration, heat transfer and erosion were obtained in a 152 mm diameter x 9.3 m tall circulating fluidized bed operated at room temperature with 200 μm sand particles at a superficial gas velocity of 7.0 m s −1 with different solids circulation rates. Local solids concentrations were found to be higher in the fin region than on the crests of membrane tubes. For the small heat transfer surfaces investigated, this led to higher local heat transfer coefficients in the fin region, a trend which is the reverse of that for long heat transfer surfaces. Erosion rates were higher on the tube crests than on the fins.

The effect of heat transfer on the stability of laminar boundary layers

Classical linear stability theory is extended to include the effects of temperature dependent viscosity and density. From an asymptotic point of view, i.e. after a Taylor series expansion of all properties with respect to temperature and pressure, they turn out to be the leading order variable property effects for forced convection at low speeds. In an asymptotic approach assuming small heat transfer rates, the two property effects acting on the basic flow and its perturbations are well separated from each other. The asymptotic solutions hold for all Newtonian fluids. Examples are given for air and water. The numerical results are in good agreement with experimental data from the heat transfer literature.

A small artery heat transfer model for self-heated thermistor measurements of perfusion in the kidney cortex.

A small artery model (SAM) for self-heated thermistor measurements of perfusion in the canine kidney is developed based on the anatomy of the cortex vasculature. In this model interlobular arteries and veins play a dominant role in the heat transfer due to blood flow. Effective thermal conductivity, kss, is calculated from steady state thermistor measurements of heat transfer in the kidney cortex. This small artery and vein model of perfusion correctly indicates the shape of the measured kss versus perfusion curve. It also correctly predicts that the sinusoidal response of the thermistor can be used to measure intrinsic tissue conductivity, km, in perfused tissue. Although this model is specific for the canine kidney cortex, the modeling approach is applicable for a wide variety of biologic tissues.

Effect of temperature dependent viscosity on the flow and heat transfer over an accelerating surface

The effect of temperature dependent viscosity on the boundary layer flow over a linearly stretching surface is investigated. This solid elastic flat surface remains at a constant temperature higher than ambient, and moves in its own plane at a velocity varying linearly with the distance from the discharge slit. In many liquids, such as water and oils, the variation in viscosity due to temperature change is more dominant than other effects. The authors adopt two approaches to deal with the effect of temperature dependent viscosity by (1) setting a known function describing the mathematical modelling of the viscosity-temperature relation into the governing equations (direct method) and (2) using the perturbation expansion technique for small heat transfer rates (perturbation method). In the direct method the viscosity-temperature relationship follows an exponential function. In the perturbation method a Taylor expansion is used on viscosity, velocity and temperature on a small quantity that is defined as the ratio of temperature differences between the moving surface and the ambient to the ambient temperature. The perturbation expansion method is independent of any choice of-the viscosity-temperature function. Following the similarity transformation, the governing partial differential equations reduce to ordinary equations. The results obtained by the direct method indicate that the velocity and temperature distributions depend upon the Prandtl number as well as the viscosity ratio that implicitly represents the temperature difference between the moving surface and the ambient. The results by the perturbation method can effectively describe the flow and temperature fields with perturbation series truncated after linear terms even though the perturbation quantity is not so small.

A computer simulation program for evaluation of the continuous heat treatment of particulate food products. Part 2: Utilisation

A computer program for calculation of temperatures in a liquid containing particles during continuous heat treatment has been developed at the SIK. The program facilitates the study of the influence of processing on product quality in an aseptic processing system. The calculated F value is related to the safety, and the cook value (C value) is related to the quality of the product. In this paper, results of some calculations using the program are presented. They concentrate on the influence of the processing conditions on the process design. These results indicate that factors such as particle heat transfer coefficient, both in the holding tube and in the scraped surface heat exchangers (SSHEs), flow conditions, particle diameter and sterilisation temperature have consequences for the holding tube length, i.e. the processing time, for a given lethality. For example, for small particle heat transfer coefficients (< 100 W m 2 K), a small change will have a large effect on the required processing time (i.e. the holding tube length). However, at particle heat transfer coefficients > 150–200 W m 2 K a small change does not greatly affect the processing time (i.e. holding tube length). The program can thus be used to examine whether the surface heat transfer coefficient is the rate-limiting factor, or whether the heat conduction inside the particles is more important in the design of the process.

Experimental study of bed-to-wall heat transfer in a circulating fluidized bed

Heat transfer between the riser wall and particle bed in a circulating fluidized bed (CFB) of fluid catalytic cracking (FCC) particles has been studied in terms of the local bed densities and solid particle velocities near the heat transfer surface, which were measured by reflection-type optical-fiber probes. The results showed that the bed-to-wall heat transfer coefficients for a small heat transfer surface used in this work were well estimated using the packet model of Mickley and Fairbanks (1955) with several assumptions.

A fluidized bed membrane reactor for the steam reforming of methane

AbstractIn the present investigation a realistic two‐phase model accounting for the change in the total number of moles accompanying the reaction is utilized to explore a novel reactor configuration suggested for the methane steam reforming process. The suggested design is basically a fluidized bed reactor equipped with a bundle of membrane tubes. These tubes remove the main product, hydrogen, from the reacting gas mixture and drive the reaction beyond its thermodynamic equilibrium. The proposed novel design is also equipped with sodium heat pipes which act as a thermal flux transformer to provide the large amount of heat needed by the endothermic reaction through a relatively small heat transfer surface, assuring better reactor compactness. Two options for fluid routing through the membrane tubes are proposed; each is suitable for a certain industrial application. The performance of this novel configuration is compared with that of an industrial fixed bed steam reformer and the comparison shows the potential advantages of the suggested configuration.

The mould-filling capacity of two casting alloys

The mould-filling capacities of an Au-Ag-Cu alloy and a Ni-Cr-Be alloy for dental use have been studied by measuring the lengths of cast helices of a constant cross-section as a function of the supertemperature of the melt. A vacuum-pressure casting machine was applied in the experiments. Assuming that the conduction of heat through the investment is rate-controlling for the heat flow, the heat of fusion was calculated for the two alloys. These values were found to be close to those obtained by differential thermal analysis measurements. The lengths of the helices are strongly influenced by the deliberated heat of fusion during solidification. The substantially higher mould-filling capacity of the Ni-Cr-Be alloy compared with that of the Au-Ag-Cu alloy can be explained to a large extent by the corresponding difference in their latent heat of fusion. A calculation of the lengths of the helices requires a knowledge of the speeds of the melts. So far there are only indications of a higher speed for the Ni-Cr-Be alloy than for the Au-Ag-Cu alloy with the casting machine employed. The highest slope for the length of helix against supertemperature curve was observed for the Au-Ag-Cu alloy, indicating a smaller heat transfer coefficient for this alloy than for the Ni-Cr-Be alloy.

Influence of cooling characteristics on glass formation of FeB and NiSiB metallic alloys

One common approach to the glass-forming process of rapidly quenched metallic alloys is to prevent the formation and growth of crystalline nuclei in the undercooled melt. Homogeneous nucleation is the dominant mechanism for moderately high cooling rates. In the frequency of a kinetic model, glass-forming ability is defined in terms of a critical cooling rate to produce amorphous foils with quenched-in crystals with volume fractions less than a given value. In a preliminary paper a heat flow model for the formation of amorphous foils by cooling a melt film of given thickness on a heat conducting substrate with constant heat transfer coefficient was presented allowing for a more realistic description of the cooling process as well as spatial differences in the as-quenched state in the amorphous foils. Practically the thermal contact may be limited to a rather short time in certain rapid solidification techniques as in twin-roller experiments or may, according to recent results on single-roller experiments, undergo a sudden change in a smaller heat transfer coefficient during the ribbon-wheel adherence period. Therefore, in this work, the influence of time-dependent foil-substrate heat transfer conditions on the glass formation process and the as-quenched state of the amorphous foils is considered.

Transient Thermal Load Effects on Coatings Bonded to Cylindrical Substrates and Containing Circumferential Cracks

The effect of a transient thermal load on a coating which is bonded to a cylindrical substrate is analyzed using fracture mechanics by considering the presence of a circumferential edge crack normal to the inner boundary of the coating. The solution is obtained using the finite element method and is compared to the exact solution of the problem. The analysis is then used to show that smaller heat transfer rates at the boundary result in smaller stress intensity factors. For three different materials combinations, including two ceramic coatings on metal, the nondimensional stress intensity factor has a similar magnitude for short crack lengths, but varies appreciably as the crack length becomes longer. It is also determined that inner coatings result in smaller or comparable stress intensity factors than thicker ones.