C. Treviño

The toroidal thermosyphon with known heat flux

Abstract This paper discusses the behavior of a toroidal thermosyphon with known heat flux around the loop. Criteria are first established for steady state solutions. The transient governing equations are then transformed to an infinite set of ordinary differential equations. The flow velocity, however, can be determined from a set of three equations which decouple from the rest. The existence and stability of the critical points of these equations are examined, and typical numerical solutions for different values of the governing parameters are presented. Chaotic solutions are shown to be possible.

The conjugate conduction-natural convection heat transfer along a thin vertical plate with non-uniform internal heat generation

Abstract The steady state heat transfer characteristics of a thin vertical strip with internal heat generation is studied in this work. The nondimensional temperature distribution in the strip is obtained as a function of the following parameters: (a) the intensity and distribution of the internal heat sources, (b) the aspect ratio of the strip, (c) the longitudinal heat conductance of the strip and (d) the Prandtl number of the fluid. Both the thermally thin and the thick wall approximations are considered in this paper. The total thermal energy or averaged temperature of the strip is found to decrease as the influence of the longitudinal heat conduction effects in the strip decreases in the thermally thin wall regime. After reaching a minimum, it increases again in the thermally thick wall regime.

Velocity field measurements in granular gravity flow in a near 2D silo

Abstract Using particle image velocimetry (PIV) we studied experimentally the whole velocity field during the discharge of monodisperse granular material from a flat-bottomed 2D silo. We have characterized important quantities of this flow such as the transversal flow oscillations, the mean velocity field and the velocity fluctuations.

A steady-state analysis for variable area one- and two-phase thermosyphon loops

Abstract Multiple solutions for closed thermosyphon loops have been previously found for single-phase, constant area, one-dimensional models. In this paper, this result is further extended to variable area loops. The phase-change thermosyphon is also considered, first with a finite two-phase zone and then using a sharp interface approximation. For entirely different reasons, multiple solutions are also found in this case. The physical basis for multiple solutions in the two-phase loop is discussed in detail with the aid of a particular example.

Catalytic Flat Plate Boundary Layer Ignition

Abstract An analysis is performed of the influence of a catalytic surface reaction on the gas phase ignition of a premixed combustible gas flowing past a hot catalytic flat plate. It is assumed that the catalytic surface reaction is infinitely fast so that chemical equilibrium is reached along the whole length of the plate surface. In the gas phase a finite-rate chemical reaction with a large activation energy is considered. The analysis makes use of the boundary layer approximation to describe the gas flow and of first order matched asymptotic expansions to define ignition. Explicit expressions are derived for the critical gas phase Damkohler number for ignition and for the distance from the plate leading edge to the onset of ignition. The ignition distances for a catalytic and a non-catalytic plate are compared. Longer ignition distances for the former case are predicted. The results of the analysis agree qualitatively with previous experimental observations.

External heating of a flat plate in a convective flow

Abstract The steady-state and transient processes of the external heating of a flat plate under a convective flow is studied in this paper, with inclusion of the axial heat conduction through the plate. The balance equations reduce to a single integro-differential equation with only one parameter, a, denoting the ratio of the ability of the plate to carry heat in the streamwise direction to the ability of the gas to carry heat out of the plate. The two limits of a good conducting plate (α a ∞) and a bad conducting plate (α → 0) are analysed through the application of a regular perturbation procedure for the first case and a singular perturbation technique for the latter. The existence of two boundary layers at both edges of the plate is shown and their structure are analysed. The evolution of the temperature of the plate is then obtained for a constant external energy flux input.

Gas-phase boundary layer ignition on a catalytic flat plate with heat loss

Abstract The gas-phase ignition of a premixed boundary layer flow by a nonisothermal plate with very large catalytic efficiency is studied. The catalytic upper side of the plate is in contact with the premixed gas while the lower side is held at constant temperature. The catalytic reaction is assumed to be ignited and diffusion controlled. The temperature on this side changes from the adiabatic equilibrium temperature at the leading edge to reach asymptotically the constant temperature of the lower surface far downstream. Matched asymptotic expansions are used to analyze the gas-phase ignition for different limiting cases. When the constant temperature of the lower surface is less than the adiabatic equilibrium temperature an S-shaped response curve is obtained showing different ignition branches.

Asymptotic analysis of the ignition of hydrogen by a hot plate in a boundary layer flow

Abstract In this paper we have analyzed the steady-state process leading to ignition of a combustible mixture of hydrogen, oxygen and nitrogen by a hot flat plate in a boundary layer flow. For plate temperatures larger than the crossover temperature dictated by the competition between the chain branching reaction H + 02 → OH + O and the chain breaking reaction H + 02 + M → H02 + M, the ignition event corresponds to a typical chain branching explosion with negligible heat release, in a first approximation. The boundary layer equations are solved using the fact that the activation energy of the chain branching reaction H + 02 → OH + O is relatively large, employing the reduced kinetic mechanism appropriate for this regime. The equations reduce to a single integro-differential equation for the concentration of atomic hydrogen. The ignition condition can be assumed to be reached when one of the shuffle reactions reaches partial equilibrium. On the other hand, for low plate temperatures, the ignition event is ...

Conjugated heat transfer in circular ducts with a power-law laminar convection fluid flow

Abstract This work deals with the study of the steady-state analysis of conjugated heat transfer process for the thermal entrance region of a developed laminar-forced convection flow of a power-law fluid in a circular tube. A known uniform heat flux is applied at the external surface of the tube. The energy equation in the fluid is solved analytically using the integral boundary layer approximation by neglecting the heat generation by viscous dissipation and the axial heat conduction in the fluid. This solution is coupled to the Laplace equation for the solid, where the axial heat conduction effects are taken into account. The governing equations are reduced to an integro-differential equation which is solved by analytical and numerical methods. The results are shown for different parameters such as conduction parameter, α , the aspect ratio of the tube, e and the index of power-law fluid, n .

The classical problem of convective heat transfer in laminar flow over a thin finite thickness plate with uniform temperature at the lower surface

Abstract In this paper we study the longitudinal heat conduction effects on the classical problem of forced laminar convection from a flat plate with an uniform temperature on the opposite surface. We found that small but noticeable differences when including the longitudinal heat conduction through the wall for the thermally thin wall regime as compared with the thermally thick wall regime solution.