Stokes problem for infinite vertical plate with constant heat flux

An exact solution for the Stokes problem for an infinite vertical plate has been derived on taking into account the constant heat flux at the plate. It has been observed that the velocity of the fluid increases with increasingt (time) orG (the Grashof number).     

Self-inhibiting heat flux

Heat transfer through weakly magnetized diffuse astrophysical plasmas excites whistlers. This leads to electron whistler resonant scattering, a reduction of the electron mean free path, and heat flux inhibition. However, only whistlers propagating at a finite angle to the magnetic field (off-axis) can scatter the heat flux carrying electrons. Thus the level of heat flux inhibition along the magnetic field lines depends on the presence of off-axis whistlers.   We obtain a solution of the Boltzmann equation with the whistler wave equation and show that if εthβe ≫ 10⁻⁴, where ε^th is the thermal collisional Knudsen number and β_e is the ratio of the electron pressure to the magnetic energy density, then scattering of heat flux carrying electrons by off-axis whistlers, which are shown to propagate at about 65δ, is efficient enough to lead to heat flux inhibition along field lines. The inhibition so obtained is proportional to (ε^thβ_e)⁻¹.     

The calculation of force-free fields from discrete flux distributions

This paper presents particularly simple mathematical formulas for the calculation of force-free fields of constant α from the distribution of discrete sources on a flat surface. The advantage of these formulas lies in their physical simplicity and the fact that they can be easily used in practice to calculate the fields. The disadvantage is that they are limited to fields of ‘sufficiently small α’. These formulas may be useful in the study of chromospheric magnetic fields by the comparison of high-resolution Hα photographs and photospheric magnetograms.     

Quasi-exospheric heat flux of solar-wind electrons

Density, bulk-velocity, and heat-flow moments are calculated for truncated maxwellian distributions representing the cool and hot populations of solar-wind electrons, as realized at the base of a hypothetical exosphere. The electrostatic potential is thus calculated by requiring charge quasineutrality and the absence of electrical current. Plasma-kinetic coupling of the cool-electron and proton bulk velocities leads to an increase in the electrostatic potential and a decrease in the heat-flow moment. If the velocities differ by the Alfvén speed along the magnetic field, for example, the potential rises to 72.6 V and the heat flux falls to 2.72×10^–2 erg cm^–2 s^–1. In each case the heat flux is carried mainly by the quasi-exospherichot electrons.     

Shear-free homogeneous cosmological model with heat flux

We present the condition of vanishing shear in a spatially homogeneous spacetime in terms of the Ricci rotation co-efficients corresponding to an orthonormal tetrad (ν ^α. _A η ^α) (whereν ^α is the unit vector along the time axis and _A η ^α are the three independent reciprocal group vectors). Assuming that the velocity vector can be expanded in the direction ofν ^α and any one of the _A η ^α’s it is shown that shear-free motion is possible only in case of some special Bianchi types, and these cases are studied assuming the velocity vector to be geodetic and that there may be a nonvanishing heat flux term.     

Stability of the ordinary mode to an electron heat flux

Stability equations for the low frequency ordinary mode propagating perpendicular to a homogeneous magnetic field in the presence of a heat flux in a collisionless plasma are derived by working within an appropriate velocity reference frame. Solutions indicate the ordinary mode is stable under average solar wind conditions at 1 AU.     

Self-similar cylindrical shock waves with radiation heat flux

Similarity solutions describing the flow of a perfect gas behind cylindrical shock waves with radiation heat flux are investigated. The total energy of the expanding wave has been supposed to remain constant. The solution, however, is only applicable to a gaseous medium where the undisturbed pressure falls as the inverse square of the distance from the line of explosion.     

In situ methods for measuring thermal properties and heat flux on planetary bodies

The thermo-mechanical properties of planetary surface and subsurface layers control to a high extent in which way a body interacts with its environment, in particular how it responds to solar irradiation and how it interacts with a potentially existing atmosphere. Furthermore, if the natural temperature profile over a certain depth can be measured in situ, this gives important information about the heat flux from the interior and thus about the thermal evolution of the body. Therefore, in most of the recent and planned planetary lander missions experiment packages for determining thermo-mechanical properties are part of the payload. Examples are the experiment MUPUS on Rosetta's comet lander Philae, the TECP instrument aboard NASA's Mars polar lander Phoenix, and the mole-type instrument HP³ currently developed for use on upcoming lunar and Mars missions. In this review we describe several methods applied for measuring thermal conductivity and heat flux and discuss the particular difficulties faced when these properties have to be measured in a low pressure and low temperature environment. We point out the abilities and disadvantages of the different instruments and outline the evaluation procedures necessary to extract reliable thermal conductivity and heat flux data from in situ measurements.     

Aram Chaos and its constraints on the surface heat flux of Mars

The surface heat flux of a planet is an important parameter to characterize its internal activity and to determine its thermal evolution. Here we report on a new method to constrain the surface heat flux of Mars during the Hesperian. For this, we explore the consequences for the martian surface heat flux from a recently presented new hypothesis for the formation of Aram Chaos (Zegers, T.E., Oosthoek, J.H.P., Rossi, A.P., Blom, J.K., Schumacher, S. [2010]. Earth Planet. Sci. Lett. 297, 496-504. doi:10.1016/j.epsl.2010.06.049.). In this hypothesis the chaotic terrain is thought to have formed by melting of a buried ice sheet. The slow sedimentation and burial of the ice sheet led to an increased thermal insulation of the ice and subsequently to a temperature increase high enough to trigger melting and the formation of the subsurface lake. As these processes highly depend on the thermal properties of the subsurface and especially on the surface heat flux, it is possible to constrain the latter by using numerical simulations. Based on the hypothesis for the formation of Aram Chaos, we conducted an extensive parameter study to determine the parameter settings leading to sufficient melting of the buried ice sheet. We find that the surface heat flux in the Aram Chaos region during the Hesperian was most likely between 20 and 45 mW m⁻² with a possible maximum value of up to 60 mW m⁻².     

A study of the expansin of the solar corona with radiation heat flux

The expansion of the solar corona, with the aid of hydrodynamic blast wave theory using the concept of the Roche model, is studied here when both the solar gravity and radiation heat flux are taken into consideration.     

Electromagnetic lower hybrid instability driven by solar wind heat flux

Under a fully electromagnetic treatment, the threshold for excitation of the lower hybrid instability driven by solar wind electron heat flux is found to be much higher than that predicted by electrostatic approximation. For average solar wind conditions at 1 AU, the fully electromagnetic lower hybrid instability is excited when the core electron drift speed is about 8V _A, whereV _A is the Alfvén speed. The region between the Sun and 1 AU is expected to be more favourable than 1 AU for this instability.     

Cylindrical magnetohydrodynamic model of shock waves with radiation heat flux

Similarity solutions have been obtained for a cylindrical piston advancing with constant speed into a uniform plasma of infinite electrical conductivity and uniform axial magnetic field with heat radiation. The total energy of the expanding wave has been supposed to remain constant. The plasma is assumed to be a perfect grey gas in local thermodynamic equilibrium. To make the discussions less complicated the simplifying assumptions include transparent shock, cool piston neither an emitter nor a reflector and negligible radiation pressure and energy.This research was partially supported by a grant from U.G.C., India.     

Regulation of solar wind heat flux by ordinary mode instability

The ordinary mode can frequently become unstable in the solar wind at 1 AU provided the ratio of halo to core electrons density does not exceed the value 0.05. The growth rates corresponding to the average conditions are typically 10 _P ( _P being the proton cyclotron frequency). Because of low threshold for onset of instability for _C 1 (where _C is the transverse beta for the core electrons), the mode is expected to play an important role in regulating the solar wind heat flux at 1 AU.     

Mechanical modeling of thrust faults in the Thaumasia region, Mars, and implications for the Noachian heat flux

Insight into the state of the early martian lithosphere is gained by modeling the topography above surface breaking thrust faults in the southern Thaumasia region. Crater counts of key surface units associated with the faulting indicate a scarp emplacement in the late Noachian-early Hesperian periods between 4.0 and 3.7 Gyr. The seismogenic layer thickness at the time of faulting is constrained to 27-35 km and 21-28 km for the two scarps investigated, implying paleo geothermal gradients of 12-18 and 15-23 K km⁻¹, corresponding to heat flows of 24-36 and 30-46 mW m⁻². The heat flow values obtained in this study are considerably lower than those derived from rift flank uplift at the close-by Coracis Fossae for a similar time period, indicating that surface heat flow is a strong function of regional setting. If viewed as representative for magmatically active and inactive regions, the thermal gradients at rifts and scarps span the range of admissible global mean values. This implies , with the true value probably being closer to the lower bound.     

Albedo,internal heat flux,and energy balance of Saturn

Full-disk and high-resolution measurements recorded during the Voyager 1 flyby of Saturn by the radiometer of the infrared instrument, IRIS, indicate a geometric albedo of 0.242 ± 0.012, which is lower than previous estimates. The given error is largely due to uncertainties in systematic corrections; random effects are small. Combining this measurement with the Pioneer-derived phase integral yields a Bond albedo of 0.342 ± 0.030. Infrared spectra recorded at the same time by the Michelson interferometer, along with a model extrapolation to wavenumbers not covered by the instrument, yield an effective temperature of 95.0 ± 0.4°K. As in the case of the radiometer, random instrumental errors are small, and the quoted error in the effective temperature reflects primarily uncertainties in systematic corrections. The rings of Saturn significantly affect both the short- and long-wavelength fluxes. From these measurements the internal heat flux of Saturn is 2.01 ± 0.14 10^?4W cm^?2, and the energy balance, defined as the ratio of total emitted to total absorbed energy, is 1.78 ± 0.09.     

Some aspects related to the asymptotic solutions of the laminar boundary-layer equations with heat flux

The oscillatory, conjugate and asymptotic behaviours of the principal and non-principal solutions of the Blasius and corresponding heat transfer equations governing the compressible laminar boundary-layer flow over a semi-infinite flat plate with heat flux have been studied; the results of the discussion being based on the asymptotic integrations of second-order linear differential equations.     

The Roche coordinates for the rotational problem

Curvilinear coordinates in three dimensions associated with the Roche model distorted by centrifugal force alone constitute a Lamé family, of which one (-) coordinate can be defined by equipotential surfaces which are known in closed algebraic form; the other () becomes identical with the meridional planes of the rotationally distorted Roche model; while the third () then follows from the requirements of orthogonality to the others. The explicit form of such coordinates in terms of the polar or cartesian systems has already been established by the author (Kopal, 1970) correctly to quantities of the first order in superficial distortion of the respective Roche model. In the present paper this latter restriction on accuracy will be removed, and expressions constructed for the -coordinate in the form of infinite series which are exact and converge rapidly for any distortion below that which entails equatorial break-up.     

Finite difference analysis of unsteady hydromagnetic free-convection flow with constant heat flux

A numerical solution for unsteady hydromagnetic free-convection currents of a viscous incompressible and electrically conducting fluid induced by a vertical moving infinite plate is considered for constant heat flux at the plate. Velocity and skin-friction have been worked out for various values of the parameters occuring into the problem. It is found that magnetic parameter has a retarding effect on the velocity of air and water, while skin-friction increases with it.