Constant Heat Transfer Coefficient Research Articles

Rewetting of a solid cylinder with precursory cooling

A model for the rewetting of a solid cylinder is solved by the Wiener-Hopf technique. A constant heat transfer coefficient is assumed in the wetted part of the cylindrical rod, whereas an exponentially decaying heat flux is assumed in that part of the solid which is cooled by a mixture of vapor and liquid droplets (the precursory cooling). Accurate predictions of the rewetting velocity are obtained for a wide range of model parameters. The results of the present solution are found to compare favorably with a separation of variables solution obtained by Olek (1987). Values of the rewetting velocity where precursory cooling is neglected are recovered as a particular case. The decomposition in the form of infinite products presented here is shown to yield results which agree well with those derived from a decomposition by Evans (1984), employing the Cauchy theorem.

Performance evaluation of crossflow compact heat exchangers using finite elements

An analysis of a crossflow compact heat exchanger is carried out using a finite element model. The predictions are in good agreement with analytical solutions available for cases with constant heat transfer coefficients. The analysis is extended to variable heat transfer coefficient cases and the results compared with constant heat transfer coefficient cases. In addition to thermal analysis, the pressure drops are calculated for all cases.

Solution to a fuel-and-cladding rewetting model

A solution by the Wiener-Hopf technique is derived for a model for the rewetting of a nuclear fuel rod. The gap between the fuel and the cladding is modelled by an imperfect contact between the two. A constant heat transfer coefficient is assumed on the wet side, whereas the dry side is assumed to be adiabatic. The solution for the rewetting temperature is in the form of an integral whose integrand contains the model parameters, including the rewetting velocity. Numerical results are presented for a large number of these parameters. It is shown that there are such large values of the rewetting temperature and the gap resistance, or such low values of the initial wall temperature, for which the rewetting velocity is unaffected by the fuel properties.

Methods for calculating the conduction-controlled rewetting of a cladded rod

A theory is presented for the conduction-controlled rewetting of a cladded water-reactor fuel rod. It is assumed that there is no heat loss from the dry part of the rod and that a constant heat transfer coefficient obtains over the wetted part. The analysis, which employs the Wiener-Hopf technique, yields an explicit expression for the logarithm of the sputtering temperature in the form of an integral, the integrand depending upon the speed of the quench front, the dimensions, and physical properties of the composite rod, the fuel-to-clad thermal resistance, and the magnitude of the heat transfer coefficient in the wetted zone. An alternative expression in terms of an infinite product, the terms of which are evaluated by locating the interlacing zeros of a pair of oscillatory functions, is also developed.

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.

Heat Transfer From a Flat Surface to an Oblique Impinging Jet

Experiments are conducted to determine the heat transfer to a jet impinging at different oblique angles to a plane surface. The main portion of the test plate contains a composite sheet of temperature-sensitive liquid crystal, which is sandwiched between a thin metallic-foil heater and a specially designed liquid bath. The results indicate a displacement of the peak heat transfer from the geometric center of the jet origin, the displacement being a function primarily of impingement angle. Contours of constant heat transfer coefficient are obtained and correlated with an empirical equation that permits determination of average Nusselt numbers over areas of interest.

Thermoelastic analysis of radiation-heating thermal shock

AbstractA thermoelastic model consisting of an infinite slab-type rectangle symmetrically heated on two faces with a constant heat transfer coefficient is used to interpret radiationheating thermal shock experimental results. The solution of the maximum principal tensile stress of the model is presented in dimensionless form, and a graphical method of inverting the stress solution is described and used to construct the loci of fracture initiation curves that highlight the transient aspect of the thermal stress fracture problem. A solution for the total strain energy is also presented and a method for computing the elastic strain energy at fracture is described. Previously reported thermal shock data are interpreted in terms of a thermoelastic damage-resistance parameter that accounts for the combined effects of material properties, geometry and thermal loading.

ANALYTICAL TEMPERATURE DISTRIBUTION FOR MULTIDIMENSIONAL BODIES EXPOSED TO A CONSTANT SURFACE HEAT FLUX

For many decades, solutions for transient temperature distributions in multidimensional objects were determined by combining as a product the solutions of one-dimensional objects necessary to delimit the contour of these multidimensional objects. These product solutions are usually restricted to two types of boundary conditions: a constant wall temperature and a constant heat transfer coefficient This paper considers the case of an object exposed to a constant surface heat flux. It is shown that when the surface of multidimensional object is submitted to a constant heat flux density, its temperature distribution can be obtained by the simple addition of one-dimensional temperature distributions. Only three one-dimensional solutions are necessary to solve all possible multidimensional problems. These are the solutions for a semi-infinite slab, an infinite plate and an infinite cylinder. The equations describing the temperature profile within each of these one-dimensional objects are presented as well as th...

CONJUGATE HEAT TRANSFER WITH TURBULENT FLOW IN A CIRCULAR TUBE

A steady heat transfer problem has been analyzed as a conjugate problem with turbulent flow in a circular tube. The three kinds of thermal boundary conditions considered here are specified as constant temperature, constant heat flux and constant heat transfer coefficient at the outer surface of the wall. From the results of numerical calculation for Prandtl numbers in the range 0.01 ≤ Pr ≤ 10 and for Reynolds numbers in the range 104 ≤ Re ≤ 105, it was confirmed that the dimensionless parameter Rc could have significant effects on the heat transfer and the temperature field in the fluid adjacent to the wall.

Boundary Perturbation Method for Free Boundary Problem in Convectively Cooled Continuous Casting

Novel mathematical techniques are here used to treat general boundary conditions in convectively cooled continuous ingot casting problems, applying a constant convective heat transfer coefficient at the ingot sides (so that the temperature distribution along the sides is unknown). The problem is first inverted to treat the physical coordinates as dependent variables of temperature and heat flow, mapping the ingot into a region that is nearly rectangular. A boundary perturbation method is then used to obtain an analytical solution in this near-rectangular region. Solidification interface shapes depend on two dimensionless parameters: one is a function of the casting velocity, while the other is dependent on the convective heat transfer coefficient at the cooled wall.

Adiabatic Film Cooling Effectiveness From Heat Transfer Measurements in Compressible, Variable-Property Flow

A variable property correction is given for turbulent boundary layers that are film-cooled using staggered rows of injection holes inclined at 35 deg. With the correction, a relation is provided between the adiabatic film cooling effectiveness for constant property flow and heat transfer coefficients for variable property flow, which are based on the difference between the freestream recovery temperature and wall temperature. The variable property correction was determined from heat transfer measurements for a range of injection parameters at different values of the nondimensional coolant temperature and from results in the literature. Because the flow is compressible, the importance of the injection mass flux ratio, momentum flux ratio, and velocity ratio are considered in the determination of effectiveness.

Thermal stability of superconducting magnets: dynamic criteria

The stability of a specific forced convection cooled conductor is analysed with two dynamic models of different complexity. We compare the dynamic analysis with static criteria. First we introduce a dynamic model of the conductor where the coolant is modelled as a constant temperature bath. A constant heat transfer coefficient is assumed. We found a critical energy that is not a function of the disturbed length for small sizes, and is proportional to the disturbed length for larger sizes. To introduce transient effects in the helium flow we solved a two dimensional flow and thermal model of the coolant. We present some characteristics of the transient behaviour. Critical energy appears to increase from 4 mJ to 15 mJ when transient effects are considered.

COMPARISON OF NINE THREE-DIMENSIONAL NUMERICAL METHODS FOR THE SOLUTION OF THE HEAT DIFFUSION EQUATION

The literature contains a large number of three-dimensional numerical methods that can be used to solve the heat diffusion equation. Users of numerical methods are often at a loss when faced with the selection of one method for their particular problem. To facilitate this task, a practical comparison of the nine more common three-dimensional methods is presented. Each numerical method is used to obtain the temperature distribution within a parallelepiped exposed to three very important boundary conditions: constant surface heat flux density, a sudden cooling of the wall temperature, and a sudden immersion in a fluid of constant heat transfer coefficient. A general discussion of each numerical method is given.

Comparison of Nine Three-Dimensional Numerical Methods for the Solution of the Heat Diffusion Equation

The literature contains a large number of three-dimensional numerical methods that can be used to solve the heat diffusion equation. Users of numerical methods are often at a loss when faced with the selection of one method for their particular problem. To facilitate this task, a practical comparison of the nine more common three-dimensional methods is presented. Each numerical method is used to obtain the temperature distribution within a parallelepiped exposed to three very important boundary conditions: constant surface heat flux density, a sudden cooling of the wall temperature, and a sudden immersion in a fluid of constant heat transfer coefficient. A general discussion of each numerical method is given.

乱れ促進体による，狭い二重管内強制対流熱伝達の改善

Enhancement of forced convective heat transfer in a narrow concentric annulus was performed by turbulence promoters in order to improve the heat removal from High Temperature Gas-cooled Reactor, Gas-cooled Nuclear Fusion Reactor and other narrow flow passages. Present experiments, which were different from the conventional research, were carried out to examine the effect of the turbulence promoters on the inner insulated wall opposite the outer smooth heated wall by changing the ratio of the pitch and the height P/ε (from 5 to 60), the ratio of the height and the space ε/ε' (from 0.2 to 2) and the type of turbulence promoters. Experimental results were arranged for the local heat transfer coefficient distribution on the smooth outer tube, the average heat transfer coefficient, the friction factor and the thermal performance. Five kinds of evaluation for thermal performance were presented: The ratio of heat transfer coefficient with and without turbulence promoters at three conditions, (1) constant Reynolds number, (2) constant pressure drop and (3) constant pumping power, additionally, (4) pumping power reduction at constant heat transfer coefficient and (5) working ratio. An example of a fuel element of HTGR with turbulence promoters was indicated as an application of present results.

Heat conduction in eccentric annuli

Under the assumption of constant properties and negligible axial effects, heat conduction in the radial direction through concentric annuli is a straightforward, 1-dim. problem. However, when the annular region is shifted from the centerline, the analysis must be made in two dimensions. A theoretical, experimental, and numerical study has been made of the 2-dim. temperature distributions for a system of eccentric annuli. Two boundary conditions are examined. The first is an angular temperature function on the outer boundary. The second is a convective boundary condition with a constant heat transfer coefficient and a constant ambient temperature. The general solutions are described which are valid for any size annular region and any degree of eccentricity. The evaluation of the analytical solutions are verified by an appropriate experiment. Several numerical approximations are examined for their suitability in handling the eccentric problem.

Visualization of heat transfer from arrays of impinging jets

A visualization technique is used to measure the heat transfer coefficient distribution on a flat plate on which either a single jet or an array of jets impinges. Liquid crystals coated on a mylar sheet are used to locate isotherms on a heated surface. By adjusting the surface heat flux, contours of constant heat transfer coefficient are obtained.

蒸気の液中凝縮に伴う圧力変動 Ｉ 現象の分類及びチャギング現象

The experiments are performed to know the character of pressure variations caused by steam condensation when vapor are discharged downward from the vertical vent tube into subcooled liquid. The phenomena are classified into five types based on the experiments in which liquid temperature, vapor flow rate, vent tube length and vent tube inner diameter are parametrically changed. The phenomena diagram is made by using two parameters, vapor mass flow flux and liquid temperature which are main parameters to decide each type. The experiments are also performed to know the character of chugging phenomenon which is caused at small vapor mass flow flux. The observation by high speed cine camera shows that the occurrence of chugging Phenomenon needs sudden collapse (several milli seconds order) of vapor mass around the vent tube outlet.Furthermore, the condition that makes vapor sphere unstable with constant vapor flow supply and constant heat transfer coefficient in subcooled liquid is analytically solved. This condition agrees very well with the character of upper limit temperature of the liquid for occurrence of chugging.

Effect of bath and specimen temperature on the thermal stress resistance of brittle ceramics subjected to thermal quenching

The effect of specimen and bath temperature on the failure of brittle ceramics in a thermal quench experiment was studied by quenching glass and alumina rods in water and silicon oil baths at different temperatures. The results were discussed in terms of the variation of heat transfer coefficient of the quenching media and the change in material properties as a function of temperature. It was found that the usual assumption of constant heat transfer coefficient and material properties may lead to considerable errors in the quantitative interpretation of the results of thermal quench experiments. Effective values for the film coefficient of heat transfer for water and oil baths were estimated as a function of film temperature from thermal quench data. Recommendations were made for the selection of quenching media and for the procedure to be followed in reporting the results.

Analyse en regime thermique periodique du couplage conduction-convection entre un fluide en ecoulement laminaire et une paroi de stockage

This paper deals with the laminar flow in a storage unit in thermal periodic regime. Energy equations are solved simultaneously in both elements with boundary conditions of the fourth kind. The solution found is then confronted with a solution using a constant and uniform heat transfer coefficient. It is found that this simplified model is satisfactory with Nu = 12. This result is then used to compare the performances of both storage units, the first one in turbulent flow (with air), the second one in laminar flow (with an organic oil).