Solvabilitity of a model problem of heat and mass transfer in thawing snow

A model problem of the motion of water and air in thawing snow is examined using the Masket-Leverett equations of two-phase filtration. The theorem of existence of a self-similar solution is proved. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 13–23, July–August, 2008.     

Validation of Thermal Equilibrium Assumption in Transient Forced Convection Flow in Porous Channel

The validity of the local thermal equilibrium assumption in the transient forced convection channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion which insures the validity of the local thermal equilibrium assumption. It is found that four dimensionless parameters control the local thermal equilibrium assumption. These parameters are the porosity , the volumetric Biot number Bi, the dimensionless channel length _max and the solid to fluid total thermal capacity ratio C _R. The qualitative and quantitative aspects of the effects of these four parameters on the channel thermal equilibrium relaxation time are investigated.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Numerical modeling of thermophysical processes in laser-beam welding with formation of a vapor channel

A quasi-two-dimensional mathematical model of laser welding of plates made of a binary alloy with allowance for metal vaporization and formation of a vapor channel is developed. A difference algorithm and a computer code are designed on the basis of this model. Processes of melting, vaporization, and solidification of the alloy of butt-welded aluminum plates are considered numerically as an example. The shape and depth of the vapor channel and welding bath are calculated for given conditions of the radiation power and welding velocity. Based on semi-empirical relations and numerical data obtained, the characteristic size of the dendritic structure of the solidified melt is estimated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 88–96, September–October, 2006.     

The Convective Boundary-Layer Flow on a Reacting Surface in a Porous Medium

The convective boundary-layer flow on an impermeable vertical surface in a fluid-saturated porous medium is considered where the flow results from the heat released by an exothermic catalytic reaction on the surface converting a reactive component within the convective fluid to an inert product. The reaction is modelled by first-order kinetics with an Arrhenius temperature dependence. Numerical solutions of the governing equations are obtained for a range of parameter values. These show, for large activation energies, that localized rapid changes in wall temperature and localized high reaction rates occur a little way from the leading edge. Asymptotic expansions, valid at large distances from the leading edge, are derived, the form that these expansions take is qualitatively different depending on whether or not reactant consumption is included in the model.     

Radiative and Thermal Dispersion Effects on Non-Darcy Natural Convection with Lateral Mass Flux for Non-Newtonian Fluid from a Vertical Flat Plate in a Saturated Porous Medium

The problem of natural convective heat transfer for a non-Newtonian fluid from an impermeable vertical plate embedded in a fluid-saturated porous medium has been analyzed. Non-Darcian, radiative and thermal dispersion effects have been considered in the present analysis. The governing boundary layer equations and boundary conditions are cast into a dimensionless form and simplified by using a similarity transformation. The resulting system of equations is solved by using a double shooting Runge–Kutta method. The effect of viscosity index n, the conduction–radiation parameter R, the non-Darcy parameter Gr*, the thermal dispersion parameter Ds and the suction/injection parameter f_w on the fluid velocities, temperatures and the local Nusselt number are discussed.     

Numerical Simulation of Thermal and Concentration Natural Convection in a Porous Cavity in the Presence of an Opposing Flow

Two-dimensional steady-state thermal concentration convection in a rectangular porous cavity is simulated numerically. The temperature and concentration gradients are horizontal and the buoyancy forces act either in the same or in opposite directions. The flow through the porous medium is described by the Darcy-Brinkman or Forchheimer equations. The SIMPLER numerical algorithm based on the finite volume approach is used for solving the problem in the velocity-pressure variables.Numerous series of calculations were carried out over the range Ra _t =3·10⁶ and 3·10⁷, 10^-6 < Da < 1, 1 < N < 20, Le=10 and 100, where Ra, Da, Le, and N are the Rayleigh, Darcy, and Lewis numbers and the buoyancy ratio, respectively. It is shown that the main effect of the presence of the porous medium is to reduce the heat and mass transfer and attenuate the flow field with decrease in permeability. For a certain combination of the Ra, Le, and N numbers the flow has a multicellular structure. The mean Nusselt and Sherwood numbers are presented as functions of the governing parameters.     

Stability of triple diffusive convection in a viscoelastic fluid-saturated porous layer

The triple diffusive convection in an Oldroyd-B fluid-saturated porous layer is investigated by performing linear and weakly nonlinear stability analyses. The condition for the onset of stationary and oscillatory is derived analytically. Contrary to the observed phenomenon in Newtonian fluids, the presence of viscoelasticity of the fluid is to degenerate the quasiperiodic bifurcation from the steady quiescent state. Under certain conditions, it is found that disconnected closed convex oscillatory neutral curves occur, indicating the requirement of three critical values of the thermal Darcy-Rayleigh number to identify the linear instability criteria instead of the usual single value, which is a novel result enunciated from the present study for an Oldroyd-B fluid saturating a porous medium. The similarities and differences of linear instability characteristics of Oldroyd-B, Maxwell, and Newtonian fluids are also highlighted. The stability of oscillatory finite amplitude convection is discussed by deriving a cubic Landau equation, and the convective heat and mass transfer are analyzed for different values of physical parameters.