Search

A Naylor transform is employed to determine the axisymmetric steady-state temperature distributions in finite spherical cones where the boundary conditions include a variety of conditions at the spherical surface (insulation or heat loss in accordance with Newton's law) and an assigned temperature variation on the conical surface (in particular,f(r)=rm,m≧0). Solutions are obtained in terms of inversion integrals and in Fourier-Legendre expansions. Computations based on the inversion integrals are carried out for cones of half-angles, α=π/6 and π/2, and with several combinations of parameters relating to the boundary conditions.

The fundamental cooling parameters, the cooling constant k, the heat transfer coefficient h, and the ultimate steady state temperature T′, are explained and the methods for their determination are described. The conversion of k to a percentage, r%(T − Ta)/t, provides an understandable number which is useful for comparing the relative rates of cooling of different systems under different conditions. h is indispensable for coefficient calorimetry and T′ can be used to calculate separately the heat input from local generation and from blood circulation.

The nonlinear differential equation controlling the steady state temperature variation in a fin is solved, using a substitution that is valid within previous experimental knowledge of the problem. The temperature distribution is given in terms of Jacobian elliptic functions. Plots illustrating the agreement between theory and experiment are shown for an aluminum fin and a steel fin. Fin effectiveness equations are included in the Appendix.

The steady-state temperature distribution about heat sources possessing axial symmetry is presented in two cases, the right circular source cylinder and the cylindrical column of thin circular source discs of random orientation. In both cases, the source strength is assumed to decrease exponentially from the one end of the cylinder to the other. Application of the results to the problem of optically produced burns, such as the retinal burn obtained in sun-gazing, is discussed. A brief comparison is made of the steady-state model with that employed in studies of transient temperature distributions in systems with time-dependent source strengths.

Temperature gradients in the region around the solid-liquid interface are critical parameters in determining the nature of a solidification process. A procedure for calculating temperature distributions in the interface region should therefore be useful. In the present work, it is demonstrated that, for the case of unidirectional solidification in a silica tube, a fairly simple analysis can give calculated temperature profiles in good agreement with experiment. Resume Les gradients de temperature au voisinage de l'interface solide-liquide sont des parametres critiques qui servent a determiner la nature d'un procede de solidification. Il est donc utile de posseder une methode de calcul de ces gradients. L'auteur demontre la validite d'une methode relativement simple pour un cas de solidification uniaxiale dans un tube de silice.

The molal steady-state temperature differences δ for a number of solvents have been determined by the Hill-Baldes technique, using a precision thermistor bridge. The values of δ obtained in the present investigation as well as those available in the literature have been explained on the basis of the theory of evaporation of droplets after introducing a thermal efficiency factor, which is characteristic of the experimental method employed. The application of this technique for the determination of molecular weights in solution is also discussed.

A steady-state, mathematical model for the human heat transfer system has been developed. This model includes the following factors: a) the distribution of metabolic heat generation, b) conduction of heat in tissue, c) convection of heat by flowing blood, d) loss of heat by radiation, convection and evaporation at the surface, e) loss of heat through the respiratory tract, and f), countercurrent heat exchange between large arteries and veins. Computed results were compared with experimental results for the nude basal man and found to be satisfactory. Submitted on August 1, 1960

On the basis of previously measured rates, rate-temperature coefficient and heat of the reaction between oxygen and palm-kernel fat, the steady-state temperature distribution in uniform columns of palm kernels due to atmospheric oxidation is determined theoretically using a uni-dimensional model. Temperature rise may be controlled by three factors; (i) conduction loss, (ii) oxygen deficiency and (iii) convection loss. In practice (i) and (ii) or (i) and (iii) usually operate together; however, they may be considered separately in order to define the lengths of column, external temperatures and ventilation rates at which the column is certainly safe from spontaneous ignition; but the margin of safety cannot be determined by this simplified method.

The steady state temperature distribution of a relay winding depends upon the power supplied and upon the rates of heat removal at the inner and outer surfaces. This is analyzed in terms of a more general form of the temperature distribution relation discussed by Emmerich (Journal of Applied Physics)1. This analysis is used to determine empirical constants far the rates of heal removal at the surfaces. Illustrative data are given for a stepping magnet.

The mixed problem with axial symmetry is solved approximately, with boundary conditions of the third kind specified at the disc surface.

A method is described for the calculation of the steady state temperature difference between a drop of solvent and a drop of solution suspended in a solvent saturated atmosphere. The procedure is used to discuss the influence of different parameters on the performance of an apparatus for the thermoelectric routine determination of molecular weight.

This article deals with the effect of couple-stresses on thermal stress distribution in a square cylinder with a central circular hole under steady state temperature distribution. The analysis is developed by the point-matching technique. From our calculation, it may be concluded that stress concentration around a circular hole, taking couple-stress into account, results in lower values than those accepted heretofore.

An integral equation is obtained which describes the steady-state temperature field in a semi-infinite body with internal cylindrical heat sources (for cylinders of an arbitrary shape). For practical calculations a simplified equation is obtained by replacing the integral by a sum of a finite number of terms. The equations were used by the author to develop new methods of calculating the temperature in disc and drum rotors of heat turbines cooled by blowing-off the working fluid through distributed slots.

An analytic solution has been obtained for the steady-state temperature field of two coaxial finite cylinders, the inner of which is a rotor. Two cases corresponding to different conditions of cooling of the outer cylinder, or housing, are considered.

We propose to investigate the following boundary value problem: (1) Wx,.+W,,v = O. O sup supP(f1(x),f2(x)), (6) G[x; u] is continuous in x and u jointly. Physically, w is the temperature, and the condition (4) with G satisfying (5) and (6) is a generalization of Newton's law of cooling; -wy(x, 0) = I(co-w(x, 0)), I and co being constants. Mann and Blackburn [I ] investigated a particular case of the foregoing problem corresponding to fi = O=f2, c = 1, and G independent of the first argument x. The reason we consider this problem again is two-fold: first, the argument given in [I ] in the proof of the existence theorem (loc. cit. Theorem 3) does not directly carry over to the present more general case, and second, we wish to present a method for constructing the solution in certain particular cases, whereas the authors in [1] were more concerned with existence theorems. Our main tool is a fixed point theorem of H. Schaefer [2]. By a solution of the boundary value problem (1)-(6), we mean a function w harmonic in the open strip, satisfying (2)-(6), continuous in 0< x r, 0< y < oo, and vanishing at infinity. We postulate w to be of the form (7) w=W1+W2, where w1, w2 are harmonic in the open strip, and (8) wi (0, y) = w, (7r, y)=O, O