Unequal Heat Research Articles

Heat transfer in the thermal entrance region with turbulent flow between parallel plates at unequal temperatures

For steady one-dimensional flow between parallel plates at unequal temperatures solutions are given for the Nusselt number in the entrance region, as well as for the fully developed flow with unequal temperatures and heat flux.

An analytical and experimental study of turbulent gas flow between two smooth parallel walls with unequal heat fluxes

This paper contains the results of a theoretical and experimental study of asymmetric heat transfer to air in fully developed turbulent flow between two smooth parallel plates. The heat fluxes at the plate surfaces were of different magnitude; in the theoretical analysis, each surface heat flux was assumed to be uniform in the flow direction. In the experimental work, two-dimensional flow was simulated by means of long ducts of large aspect ratio. Velocity distribution and friction data in adiabatic flow were recorded, and these showed good agreement with accepted relationships. Heat-transfer measurements were made firstly with one wall insulated and then with heat transfer at both walls. In the latter series of experiments, the wall fluxes were unequal and of opposite sign. The experimental heat-transfer coefficient for the wall through which heat was transferred to the fluid was observed to be less than the accepted value for the case of symmetrical heat transfer and to decrease as the degree of asymmetry increases. A decrease in heat transfer coefficient of up to about 40 per cent was measured. The theory, which is based on the analogy between the transfers of heat and momentum, is more rigorous than that published by the author in a previous paper and is adequately supported by the experimental data. It is concluded that the heat-transfer coefficient is dependent on the heat-flux distribution around the circumference of the flow section.

Convection heat transfer coefficients for turbulent flow between parallel plates with unequal heat fluxes

This paper contains a semi-theoretical analysis of asymmetric heat transfer in fully developed two dimensional turbulent flow between parallel walls. An extension of the analogy between the transfer of heat and the transfer of momentum (due to Mizushina), is used to determine the heat transfer coefficients for the respective boundaries. The results of the analysis are presented in the form of working formulae from which the relative magnitudes of the heat transfer coefficients may be determined. The formulae may be applied to practical engineering problems, but care is necessary because the assumptions made in the theory impose restrictions on the Prandtl and Reynolds number ranges for which the predictions are acceptable. It is immediately obvious from the graphical presentation of the results for a particular fluid, that the heat flux ratio is an important additional parameter, and that cognizance of this should be taken in cases of non-uniform heating. By its nature, the present analysis is preliminary, and an experimental programme has been devised to study the general problem of asymmetric heat transfer and to test the theory. While channel flow has been considered, the results are thought to be valid for axisymmetric flow in annuli with small outside diameter/inside diameter ratios.

Asynchronous and single-phase operation of synchronous machines

ASYNCHRONOUS operation of synchronous machines has been the subject of numerous articles in the technical literature, for example, the articles of Fechheimer, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> Hay and Mowdawalla, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> Putman, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> Park, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> Linville, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> Lauder <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> . The fact that articles on this subject continue to be of primary interest to design and operating engineers is attributable to the importance of satisfactory operation at asynchronous speeds. It is only through a precise knowledge of the conditions present in asynchronous operation that machines can be designed for and operated through these asynchronous periods satisfactorily. As examples of the extreme conditions which can arise during asynchronous operation, it should be noted that stalling a synchronous machine with the field voltage applied can result in pulsating torques greater than those obtained by inadvertent synchronizing 180° out of phase; <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> or that the currents in the damper bars on the trailing half of a pole can be considerably greater than the currents in the corresponding bars on the leading half of the pole, and the resulting unequal heating will influence the design of the damper winding to a considerable degree. Because of the importance of these and similar phenomena, the problem of asynchronous operation must be studied continuously until a complete, easily visualized, and easily applied solution is obtained.

Asynchronous and Single-Phase Operation or Synchronous Machines

ASYNCHRONOUS operation of synchronous machines has been the subject of numerous articles in the technical literature, for example, the articles of Fechheimer,1 Hay and Mowdawalla,2 Putman,3 Park,4 Linville,5 Lauder6. The fact that articles on this subject continue to be of primary interest to design and operating engineers is attributable to the importance of satisfactory operation at asynchronous speeds. It is only through a precise knowledge of the conditions present in asynchronous operation that machines can be designed for and operated through these asynchronous periods satisfactorily. As examples of the extreme conditions which can arise during asynchronous operation, it should be noted that stalling a synchronous machine with the field voltage applied can result in pulsating torques greater than those obtained by inadvertent synchronizing 180° out of phase;6 or that the currents in the damper bars on the trailing half of a pole can be considerably greater than the currents in the corresponding bars on the leading half of the pole, and the resulting unequal heating will influence the design of the damper winding to a considerable degree. Because of the importance of these and similar phenomena, the problem of asynchronous operation must be studied continuously until a complete, easily visualized, and easily applied solution is obtained.

Dynamics of thunderstorms

The development of a thunderstorm which is essentially a convective phenomenon needs a cause for initial convection and then conditions for its maintenance once started. The possibility of the inherent instability due to potentially colder air superposed on potentially warmer air or the analogous case of extra injection of moisture in the lower layers in shown to be not applicable in nature and that causes for initial convection must be found elsewhere than in the potential density distribution. Some of the causes are non-horizontality of surfaces of equal temperature and equal humidity; and gradient of wind velocity. It is shown that upward rise of air produced by unequal heating of the ground, does not stop where the rising mass of air attains a density equal to that of the environment (hydrostatic equilibrium), but continues to rise higher till the momentum developed is reduced to zero. The extent of over-shooting is nearly of the same order as the height between the initial level and the level of hydrostatic equilibrium. Once the condensation level is reached, it is well known that the convection will become regenerative due to the evolution of the latent heat of condensation. In the usual treatment of the problem, the ascending parcel of air is expected to condense at or before it reaches the level of hydrostatic equilibrium if it is to develop into a thunderstorm. The dynamical treatment outlined in this paper takes into consideration the overshooting of the parcel of air and thereby allows much drier air to reach condensation and thereafter maintain convection: and can thus account for a larger number of thunderstorms.

The Thermal Stress in a Strip Due to Variation of Temperature Along the Length and Through the Thickness

The thermal stress developed by unequal heating of a flat strip is investigated, the temperature varying along the length and through the thickness, but not across the width. The problem is reduced to one of edge tractions only, for which general solutions are already known. From the properties of these solutions it is shown that for heating local to a narrow transverse band across the width, as might occur in welding processes, there is a concentration of stress near the edge of the strip, at the hottest part, and a maximum tensile stress of magnitude EαTmax., when the temperature is constant through the thickness. The corresponding quantity is found also for temperatures varying through the thickness. For steel EαTmax,= lim ··350Tmax, pounds per in.2, the temperature being measured in centigrade degrees above that of the cool parts of the strip, and this approaches the yield point of mild steel for a maximum temperature (rise) of the order of 150°C. For a given maximum temperature, the maximum stress is reduced by about 40 percent by keeping one face cold.

Heterotaxia in Chick Embryos

DURING the second day of incubation a rotation of the embryo begins which normally results in the turning of the chick to lie on its left side. A reverse movement causing the chick to lie on its right side is known as heterotaxia and is often associated with inversion of the viscera (Lillie1).Fol and Warynski2 experimentally produced reversal of the unequal development of the two sides of the body and an assumption of the heterotaxic position by application of heat from a cauter held above exposed 36-hour chick embryos. Dareste3 stated that heterotaxia normally was extremely rare but cites evidence for its production by unequal heating of parts of the embryo. Taylor, Gunns, and Moses4 experimenting on the effect of interrupted incubation found heterotaxia in 0.20 and 0.08 percent of dead embryos from chilled and control lots respectively. In terms of fertile eggs, the incidence was 0.115 and 0.029 .

Flow Distribution in Forced-Circulation Once-Through Steam Generators

Abstract Forced-circulation, once-through steam generators of large capacity are constructed of several parallel circuits connected between inlet and discharge headers. Unequal flow distribution between these circuits, possibly resulting in tube failure, may be due to unequal frictional resistances, unequal heat absorption, or improper arrangements of circuits. The investigation which is reported in this paper was undertaken in order to determine the effect of unequal heat absorption, unequal circuit resistances, and the location of equalizers upon the flow distribution in the circuits of forced-circulation steam generators. Pressure-drop calculations were based on the measurement of friction factors of water at temperatures between 57 and 694 F; also, of superheated steam at pressures between 1120 and 3578 lb per sq in abs with a maximum temperature of 806 F. Head-loss measurements were made with a special glass manometer for pressures up to 2200 lb per sq in., and for higher pressures by radiographs of the mercury level in a steel-tube manometer. An analysis of flow distribution between parallel circuits leads to the following conclusions: (1) Parallel circuits connected between the feedwater header and the superheater outlet header are unstable, the pressure drop being nearly independent of the flow rate. Consequently, slight variations in frictional resistance or heat-transfer rates may result in decreased flow and in overheated tubes. (2) The flow in unstable circuits can be controlled by the use of an inlet resistance such as a section of small-diameter tube. (3) The use of a common header or equalizer on each side of the evaporating zone will stabilize the flow in parallel circuits. (4) Superheater and economizer circuits are more stable than evaporating-zone circuits. (5) If only one equalizer is used, it should be placed at the end of the economizer section rather than at the end of the evaporating surface. (6) The stability of circuits is independent of their capacity. (7) The stability of superheater circuits is independent of pressure. Combined evaporating zone and superheater circuits are more stable at high pressures. Curves are presented to show the extent to which the enthalpy of the steam and of the water delivered from parallel circuits will vary as a result of unequal circuit resistances and unequal heat absorption.

A Hypothesis of Mountain Building

The following paper is an attempt to contribute to the solution of the problem of mountain building. It is here suggested that the folding of mountain ranges may be produced by the frictional drag of moving portions of the asthenosphere, and that these movements may be convective and result from its unequal heating by radio-active elements.

The Effect of Temperature and Altitude of Aerodrome in the Taking off of Aeroplanes

The Cairo-Cape flights of 1920 brought into prominence many peculiarities of conditions arising from the high temperature combined with high altitude ot the aerodromes on the route. The conditions were for the most part new, for flight from elevated aerodromes in Europe and the United States has been made as a rule in temperate climates, where the temperature at such altitude was low. These peculiarities, which led to great difficulties for the pilots, may be divided into two classes :—(1) Engine peculiarities, especially defects of carburation and unequal heating of the cylinder jackets owing to the high temperature of the air.(2) Aerodynamical peculiarities, owing to the tenuity of the atmosphere. In the former class the difficulties were not to be foreseen, and much valuable information has been obtained as a result of these flights.The latter class of difficulty, on the other hand, was one that could have been predicted with certainty by anyone who has had experience in the testing of the performance of aeroplanes under varying conditions of the atmosphere.

不同熱に因て緊張されたる鋼鐵の彈力

不同熱に因て緊張されたる鋼鐵の彈力

XV. On the stresses in solid bodies due to unequal heating, and on the double refraction resulting therefrom

(1901). XV. On the stresses in solid bodies due to unequal heating, and on the double refraction resulting therefrom. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 1, No. 2, pp. 169-178.

South Polar Depression of the Barometer

MR. CLEMENT LEY, writing in NATURE (vol. xv. p. 157), thinks that the great depression of the barometer throughout the region round the South Pole as compared with that round the North Pole, is “mainly due to superior evaporation in the water hemisphere generally.” This seems an inadequate cause, for evaporation must be small in the very low temperatures which appear to be constant at all seasons in high southern latitudes. I am convinced that the cause of the barometric depression round the South Pole is the centrifugal force of the west winds which revolve round the Pole, forming, in Maury's words, “an everlasting cyclone on a great scale,” A similar cyclone is formed round the North Pole also, but less perfectly, and consequently the North Polar barometric depression, though decided, is much less than the South Polar. The reason of this difference I believe to be, that the North Polar cyclone is broken up by local air-currents due to the unequal heating of land and sea—a cause which scarcely exists in the South Polar regions, where almost all is sea or snow-covered land.

XXXIII. On the unequal heating effect of a galvanic current while entering and emerging from a conductor

"XXXIII. On the unequal heating effect of a galvanic current while entering and emerging from a conductor ." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 4(24), pp. 224–225

On the Laws of Development of Existing Vegetation and the application of these laws to certain Geological Problems

The author's remarks are chiefly founded on the excentrical position of the pith of exogenous trees, which he states are caused by unequal heat afforded to the north and south side. He supposes that a north and south line drawn through the central axis in a transverse section of a tree will generally bisect the section, while an east and west line divides it into two unequal parts; but that at the equator and poles such section will be bisected by either line. He then alludes to the prevailing wind as a disturbing cause, not however obliterating the action of the sun, and concludes that contemporaneous plants, whether fossil or not, being in their upright position with their roots downwards, and having lines of like development parallel to each other, have grown in the place where they are found and are in their original position. He also concludes that if the lines of development are not parallel in beds of different ages, the line of action of the cause of that development has changed. He considers that many important geological conclusions may be deduced by applying these propositions. The author next proceeds to the subject of internal heat, and considers that since it would tend to produce an equality of development, we may determine its former extent of action by examining the trunks of exogenous trees. Although at first he only applied this theory to exogenous vegetables, he afterwards considered that the central pith of Stigmaria and some other fossil