F. Méndez

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.

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.

Laminar film condensation along a vertical fin

Abstract We study the conjugate condensation-heat conduction process of a saturated vapor in contact with a vertical fin, including both longitudinal and transversal heat conduction effects. The momentum and energy balance equations are reduced to a nonlinear system of partial differential equations with four parameters: the Prandtl number, Prc, Jakob number, Ja, a nondimensional fin thermal conductivity α and the aspect ratio of the plate e. Using the small Jakob limit and the boundary layer approximation, the total mass flow rate of condensed fluid has been obtained for all possible values of the involved parametric space.

Film condensation induced by a natural convective flow : steady-state analysis

Abstract In this paper we study the laminar condensation process of a saturated vapor in contact with one side of a vertical thin plate, caused by a natural laminar boundary layer flow on the other surface of the plate. The effects of both longitudinal and transversal heat conduction in the plate are considered. The momentum and energy balance equations are reduced to a system of differential equations with five parameters. Asymptotic and numerical solutions for the temperature and condensed film thickness distributions are presented for all possible values of the nondimensional plate thermal conductance α.

Heat transfer across a vertical wall separating two fluids at different temperatures

Abstract In this paper we study the conjugate heat transfer across a vertical wall separating two fluids at different temperatures. We present a classification of the solutions of the problem in terms of two main parameters; e, the ratio of thickness to height of the wall and α, measuring the ratio of the thermal resistance of one of the boundary layers to the thermal resistance of the wall. Numerical and asymptotic solutions are presented for all possible values of α. We show that a maximum average Nusselt number or non-dimensional overall heat flux is attained for values of α much smaller than one, but still large compared with e2.

Boundary layer separation by a step in surface temperature

Abstract The free-interaction influence of thermal expansion process in the boundary layer gas flow is analysed in this paper, using the formalism of the Triple-Deck theory. The physical model considered herein is the forced convection of a gas flowing over a flat plate subject to a step change in the surface temperature, taking place at a certain distance from the leading edge. There is a fundamental parameter T w , defined as the ratio of the wall temperature to the free stream temperature. For values of T w close to one, the governing equations can be linearized and solved with the aid of the Fourier transform method. However, for values of this parameter not close to one, a numerical treatment is required to solve the governing equations. Using finite-difference methods, the numerical results for the pressure, skin friction, thickness displacement and Nusselt number are presented for different values of T w . Finally, for a critical value of this temperature ratio, the boundary layer separates.

Transient conjugate condensation process on a vertical plate with finite thermal inertia

Abstract In this paper we analyse the transient condensation process of saturated vapor in contact with one surface of a vertical thin plate, caused by a uniform cooling rate on the other surface of the plate, applied at a time t = 0. The effects of longitudinal and transversal heat conduction, as well as the thermal inertia for the plate, are considered. The nondimensional governing equations are reduced to a system of four partial differential equations with six nondimensional parameters. The transient evolution of the condensed layer thickness and the temperature of the plate are obtained using different realistic limits, including the cases of very good and poor conducting plates.

Transient analysis of carbon combustion in stagnation flow

The early history of a carbon particle is studied as it is suddenly injected into a hot oxidizing atmosphere. In this early phase, a high Reynolds number approach is appropriate. Five stages characterize the processes: (1) inert stage, (2) transition stage (ignition of the heterogeneous reaction), (3) heterogeneous diffusion controlled stage, (4) homogeneous ignition, and (5) overall diffusion-controlled stage. In this last stage, the surface temperature and the regression rate reach the final equilibrium values. Using correlations for the quasi-steady gas-phase response and Greens function for the solid phase, the evolution of the surface temperature as well the regression rate are obtained.

Effect of longitudinal heat conduction on the catalytic ignition of carbon monoxide in a boundary layer

The catalytic ignition of dry carbon monoxide and air in a boundary layer flow over a palladium plate is studied in this paper. The heterogeneous reaction mechanism is modelled with the dissociative adsorption of the molecular oxygen and the non-dissociative adsorption of CO, together with a surface reaction of the Langmuir-Hinshelwood type and the desorption reaction of the adsorbed product, CO2(s). The critical condition for catalytic ignition, represented by the ignition Damköhler number, has been deduced using high activation energy asymptotics of the desorption kinetics of the most efficiently adsorbed reactant, CO(s). Longitudinal heat conduction along the plate has been considered and its influence on the ignition temperature has been evaluated. This influence is rather weak, indicating that the flat plate boundary layer flow configuration is a robust device to determine the critical conditions for catalytic ignition.