Kinetic-Theory Description of Conductive Heat Transfer from a Fine Wire

Abstract

The Maxwell mome nt method utilizing the two-sided Maxwellian distribution function is applied to the problem of conductive heat t ransfer between two concentric cylinders at rest. Analytical solutions are obtained for small temperature differences between the cylinders.The predicted heat transfer agrees very well with experiments performed by Bomelburg, Sch!tfer-Rating and Eucke n . Comparison with res ults given by Gra d 1 s thirte e n moment equ ations, and with t h ose given by Fourier 1 s " l aw" p l us the M axwell-Smoluchowski temperaturejump boundary condition shows that the two-side d character in the distribution function is a crucial factor in proble m s inv olving surface c urvatur e .ii PART I. II. III.IV. 1 7) parameter defined by Eq. (23) non-dimensional radial distance of Knudsen layer from surface of heated wire angle between plane of the orbit and plane containing the original relative velocity and the x-axis in a binary collision (See Reference 13.)Maxwell mean free path correction factor used in Dickins 1 work (See Section I.)"classical" viscosity coefficient vector particle velocity dsi d~j dsk planar velocity vector, S = p velocity components of particle velocity in R, Q, Z directions mean mass density angle between particle planar velocity vector lt "F" and radius ">pThe subscripts "I" and "II" refer to quantities given at the inner and outer cylinders, respectively. The subscript "oo" denotes quantities evaluated at the continuum limit. The bar ( -) superscript refers to non-dimensional quantities.The pre sent p r oble m deals with the conductive heat transfer from a metallic wire to a monatorn ic gas at rest. A fine wire is placed coaxially in a large cylindrical bell jar and is electrically heated. The wire temperature i s kno w n from its electrical resistance, while the heat input is found by meas ur ing t h e current. A t nor m al g as density, heat conduction from the w ir e is clearly independent of th e gas pressure; while at very lo"\v gas den s ity t h e h e a t loss is proportional t o gas pressure .When the gas density i s i n t he t ransition range , t h e relation between heat conduction and press ur e i s not as simple, but the t w o limiting regimes are joined smoothly (Figure 1). Thi s simple de v ic e ha s long been used by many inv estigators 1 • 2 • 3 • 4 • 6 t o d ete rmine the t h e r m al conductiv ity of gases and to study the pheno m ena of temperature j ump and energy accomn10dation at the wi r e surface. Som e authors h a v e also approached the problem analytically, but they a r e all forced t o introduce certain ad hoc assumptions, w hi c h re s t rict their results t o s mall values of the ratio of the mean free pat h to the wire radius.It is easy to see t hat this type of instrument enj oy s the privilege of simplicity. Up u ntil ver y r e cently e xperiment s wit h such a heated wire furnished one o f t h e f ew se t s of data for the full range of gas densities from the free molecu lar re g ime t o the continuum regime. Moreover, the present prob...

Theoretical and experimental behaviour of a thermal conductivity detecter for the determination of the ortho/para hydrogen composition of gas mixtures in the temperature-jump region

“…On the other hand, the integrand (i3K/i3Xp), and the term @ T I '/a X,),, in [20] are approximately proportional to N,,,. This can be seen from [22] and [29] and noting that the ratio DO,,,,,,/~O,,LH, ranged from 1.06 a t 3 0 0 K t o 1.11 a t 7 7 K .…”

“…appearing in [20] a n d [22] it was necessary to utilize a theoretical and semi-empirical approach since few relevant experimental data are available (30,31 For personal use only.…”

“…The values of T, ' were then determined by an iterative procedure. From these, all of the nonelectrical quantities in [20] were evaluated using [21], [22], and [29]. Values of C, for H, were calculated directly from spectroscopic data (33) and diffusion coeficients were obtained from a recent literature survey P T , ' (34).…”

“…A drawback of the oil-line technique is that heat conduction is pressure dependent at the pressures ( I to 30 Torr) used in these experiments. This effect, attributed to the phenomenon of the "temperaturejump", has been recognized for lnany years (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25). It can be avoided by internal calibration ( I I ) or by using relative concentration lneasure~nents at fixed pressure (4,5).…”

Thermodynamic Study of the Unsteady BGK Model for a Binary Gas Mixture Affected by a Nonlinear Thermal Radiation Field

“…Lee's moment method [23][24] is employed here to obtain the solution of the BGK equation. When the application of heat to a gas.…”