Heat transfer in unsteady MHD couette flow of an electrically conducting,viscous, incompressible rarefied gas

An analytical study is performed to examine the heat transfer characteristics on the flow of a viscous, incompressible rarefied gas in a parallel plate channel under the action of transverse magnetic field when (i) suction velocity normal to the plate is constant, (ii) the second plate oscillates in time about a constant non-zero mean, (iii) fluid is subjected to a constant heat source of absorption type. Apprximate solutions for velocity, temperature, phase, and amplitude of skin-friction and rate of heat transfer are evaluated. Mean temperature profiles, phase and amplitude of rate of heat transfer at both plates are discussed graphically followed by a quantitative discussion. Mean rate of heat transfer is tabulated in Table I.     

Radiative transfer in an infinite cylinder

The problem of radiation transfer in a cylinder with diffuse reflectivity and containing an energy source is connected with the source-free radiation transfer problem with isotropic boundary condition. Equation for the radiation heat flux is obtained for a polynomial source. In the special case of isotropic scattering, the radiation heat flux is given in terms of the albedo of the second problem. An expression is also given for the net radiation heat flux.     

Hydromagnetic free convection and mass transfer flow of non-Newtonian fluid through a porous medium bounded by an infinite vertical limiting surface with constant suction

An analysis of a two-dimensional steady-free convection and mass transfer flow of an incompressible, viscous, and electrically conductive non-Newtonian fluid through a porous medium bounded by a vertical infinite limiting surface (plane wall) has been presented in the presence of a transverse magnetic field. Approximate solutions to the coupled nonlinear equations governing the flow are derived and expression for the velocity, temperature, concentration, the rate of heat transfer, and the skin-friction are derived. Effects of Gr (Grashof number), Gm (modified Grashof number),M ^* (non-Newtonian parameter),N (magnetic parameter), and permeabilityK of the porous medium on the velocity, the skin-friction and the rate of heat transfer are discussed when the surface is subjected to a constant suction velocity.     

Nonlinear Rayleigh-Taylor instability in the presence of magnetic field and mass and heat transfer

The nonlinear Rayleigh-Taylor instability in the presence of magnetic field and mass and heat transfer is studied using a simplified formulation. The method of multiple scale expansion is employed for the investigation. It is found that the nonlinear effects of magnetic field and mass and heat transfer stabilize the classically unstable system. A simple non-dimensional parameter is also found to characterize the stability of the system.     

Application of the superconvergence properties of the Galerkin approximation to radiative transfer

The superconvergence Galerkin approximation is introduced to calculate some functionals arising in radiative transfer problems. Forward and backward radiation heat fluxes are calculated for comparison.     

Padé approximant calculations for dispersive,isotropic scattering,homogeneous media

Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.     

On disk accretion

A simple but sufficiently accurate method for calculating an accretion disk structure is developed. The detailed analysis of the accretion disk is fulfilled by using this method. The effect of turbulent heat transfer on the disk structure is taken into account along with the effect of radiative transfer. The turbulent heat transfer is shown to play an important role, and may be even predominant in the inner disk region. The dependence of temperatureT and density on thez-coordinate is found. Simple analytic expressions are proposed for the run of the density in all the disk zones. It is shown that the inner disk region is convectively stable. The main parameters of all the zones are derived. The geometry of regular motions is studied; the regular hydrodynamical flows are found to appear directed both toward and outside the central object. A detailed comparison is made with the results of other authors.     

A self-similar flow behind a shock wave in a gravitating or non-gravitating gas with heat conduction and radiation heat-flux

The propagation of a spherical shock wave in an ideal gas with heat conduction and radiation heat-flux, and with or without self-gravitational effects, is investigated. The initial density of the gas is assumed to obey a power law. The heat conduction is expressed in terms of Fourier’s law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density, and the total energy of the wave to vary with time. Similarity solutions are obtained and the effects of variation of the heat transfer parameters, the variation of initial density and the presence of self-gravitational field are investigated.     

Thermal history of the Jovian satellite Io

The discovery of large volcanic eruptions on Io suggests that Io is one of the most geologically active planetary bodies. The energy source of this geologic activity is believed to be tidal heating induced by Jupiter. A number of thermal history calculations were done to investigate the effect of tidal heating on the thermal history of Io taking into account solid state convection and advective heat transfer. These simulations show that the total tidal heating energy in Io is almost equal to the advectively transferred heat, indicating that the observed heat flow from Io is nearly equal to the total tidal heating energy. Since total tidal heating energy is dependent on the radius of the liquid mantle and the internal dissipation factor (Q), the radius of the liquid mantle can be estimated for a given value of Q. Some reasonable thermal history models of Io were obtained using a model with Q ≈ 25–50 in which the magma source of Ionian volcanism is at a depth of 100–300 km. The models satisfy the heat flow data and the existence of a thick lithosphere. Using a model with Q = 25 and L = 300 km (thickness of the advective region) as the standard model (model II), we then studied the effect of convective heat transfer and the initial temperature distribution on the Ionian thermal history. In these calculations, the other parameters are the same as in the standard model (model II). These calculations show that although the temperature distribution in the central region reflects the difference in the efficiency of convective heat transfer and initial temperature distribution, the temperature distribution in the outer region does not changes appreciably.     

Comparative effect of viscous dissipation on heat transfer in mixed convection flow: UWT and UHF cases

The effect of viscous dissipation on mixed convection flow about a rotating sphere with a prescribed uniform surface heat flux (UHF) has been investigated analytically. Merk's type of series expansions is used to obtain the heat transfer rate and the skin-friction coefficients. The results are presented for Pr=1;B=0, 1; ^*0, 0.5, 1 and various values of the dissipation parameter Ec^* at various angular positions. As in the case of uniform wall temperature (UWT), the heat transfer rate decreases with viscous dissipation. It is also observed that for an equivalence viscous dissipation effect, heating by UHF yields larger Nusselt number than heating by UWT.     

Anisotropic radiation transfer in a sphere with internal source

In this work we connect the problem of anisotropic radiation transfer in a sphere with diffuse reflectivity and containing an energy source with the problem of source free amisotropic radiation transfer with isotropic boundary condition. Exact equation for radiation heat flux for the first problem is obtained in terms of the source, the flux and the albedo of the second problem. Modeled kernel is used to represent the anisotropy of the phase function. Numerical results are given.     

Effects of mass transfer on an oscillating free-convection flow in the Stokes's problem past an infinite porous vertical limiting surface with heat sources and variable suction

An analysis of the effects of the mass transfer on the unsteady free-convection flow of a viscous incompressible fluid, past an impulsively started infinite porous vertical limiting surface with heat sources is presented, when the free-stream velocity and the suction velocity, are oscillating in the time about constant mean values. Approximate solutions for the coupled nonlinear equations are derived for the mean velocity, the mean temperature, the mean skin-friction, and the mean rate of heat transfer. All the above quantities are shown graphically followed, by a discussion.     

Inferred heat transfer mechanisms and tectonic development of planets and satellites

A schematic diagram showing the relative importance of conduction, convection and hotspots as heat transfer mechanisms on planets has been previously described by Solomon and Head (1982). In their construction they assumed that the majority of heat transfer on Earth involved mantle convection (and hence, plate recycling), with Io and Mercury dominated by hotspot and conduction, respectively. This diagram is here quantified and used to deduce the tectonic regime of Jovian and Saturnian satellites.     

Surface heat current in an inhomogeneous slab with reflecting walls

The problem of radiative transfer in an inhomogeneous finite medium with boundary surfaces which reflects both diffusely and specularly is connected with a source-free specular boundary condition radiation tramsfer. Numerical results are obtained for the partial heat flux using the bi-variational technique.     

Laminar convection in binary mixture of hydromagnetic flow with radiative heat transfer,II

The hydromagnetic flow in a vertical channel with heat and mass transfer is studied when chemical reaction is present. For the general integral equation for radiative flux and in the absence of the Dufour term, the problem is reduced to a set of coupled integral equations which are solved iteratively. The results are compared with the solutions obtained when chemical reaction is absent.     

Solar heating and internal heat flow on Jupiter

Models of convection in Jupiter's interior are studied to test the hypothesis that internal heat balances the absorbed sunlight at each latitude. Such a balance requires that the ratio of total emitted heat to absorbed sunlight be above a critical value 4/π ≈ 1.27. The necessary horizontal heat transport then takes place in the interior instead of in the atmosphere. Regions of stable stratification can arise in the interior owing to the effects of solar heating and rotation. In such regions, upward heat transfer takes place on sloping surfaces, as in the Earth's atmosphere, provided there are horizontal temperature gradients. Potential temperature gradients are found to be small, and the time constant for the pattern to reach equilibrium is found to be short compared to the age of the solar system. It is suggested that Jupiter and Saturn owe their axisymmetric appearance to internal heat flow, which eliminates differential heating in the atmosphere that would otherwise drive meridional motions.     

Heat and mass transfer of a viscous heat generating fluid with Hall currents

A study of natural convection in hydrodynamic flows of a viscous heat generating fluid in the presence of Hall currents and variable suction has been carried out. The governing equations for the magnetohydrodynamic fluid flow and heat transfer are solved. The effects of Hall currentm and heat source parameter on the velocity and temperature distributions are discussed.     

Modeling of the Turbulent Transport Coefficients in a Gas–Dust Accretion Disk

An heuristic way of modeling the turbulent exchange coefficients for Keplerian accretion disks surrounding solar-type stars is considered. The formulas for these coefficients, taking into account the inverse effects of dust transfer and potential temperature on the maintenance of shear turbulence, generalize to protoplanetary gas–dust clouds the expression for the turbulent viscosity coefficient in so-called a-disks which was obtained in a classic work by Shakura and Syunyaev (1973). The defining relationships are derived for turbulent diffusion and heat flows, which describe, for the two-phase mixture rotating differentially at an angular velocity O(r, z), the dust and heat transfer in the direction perpendicular to the central plane of the disk. The regime of limiting saturation by small dust particles of the layer of “cosmic fluid” located slightly above (or below) the dust subdisk is analyzed.     

Outgassing of icy bodies in the Solar System – II: Heat transport in dry,porous surface dust layers

In this work, we present a new model for the heat conductivity of porous dust layers in vacuum, based on an existing solution of the heat transfer equation of single spheres in contact. This model is capable of distinguishing between two different types of dust layers: dust layers composed of single particles (simple model) and dust layers consisting of individual aggregates (complex model). Additionally, we describe laboratory experiments, which were used to measure the heat conductivity of porous dust layers, in order to test the model. We found that the model predictions are in an excellent agreement with the experimental results, if we include radiative heat transport in the model. This implies that radiation plays an important role for the heat transport in porous materials. Furthermore, the influence of this new model on the Hertz factor are demonstrated and the implications of this new model on the modeling of cometary activity are discussed. Finally, the limitations of this new model are critically reviewed.     

Heat transfer in the corona and transition region

Thermal transfer in closed magnetic tubes in the corona and transition region is described on the basis of a static model in which all heat generated is radiated away, though conduction transfers much of the heat to the transition region prior to emission. The rate of conductive transfer depends on the cross-section of the magnetic tube as it passes through the chromosphere and transition region. This is derived from the pressure in the normal chromosphere. There is then only one main parameter to establish conditions in the corona and transition region, viz. the heating per unit area of the Sun's surface, which must equal the observed radiation from corona and transition region. The density adjusts itself so as to radiate away all heat generated within the tube; conditions in the tube below the transition region have little influence other than to decide where the base of the transition region lies and the width of the region particularly in its lower parts. For the observed rate of heating, the computed densities (or pressures), the ratio of coronal to transition region emissions, and the distribution of radiation in the EUV spectrum agree closely with those observed. The optimum maximum temperatures are found with heating concentrated in the highest regions of the flux tubes. It is only in the lowest 20–40 km of the transition region, where T<10⁵K, that any additional heating is needed to explain EUV line intensities. The equation of heat transfer also has solutions in which the temperature is oscillatory with disance. These do not apply to the normal corona, but may be relevant to prominences.