Antonio Campo

Analytic solutions of the temperature distribution in Blasius viscous flow problems

We apply a new analytic technique, namely the homotopy analysis method, to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate. An explicit analytic solution of the temperature distributions is obtained in general cases and recurrence formulae of the corresponding constant coefficients are given. In the cases of constant plate temperature distribution and constant plate heat flux, the first-order derivative of the temperature on the plate at the 30th order of approximation is given. The convergence regions of these two formulae are greatly enlarged by the Pade technique. They agree well with numerical results in a very large region of Prandtl number 1[les ] Pr [les ]50 and therefore can be applied without interpolations.

Effects of a Thick Plate on the Excess Temperature of Iso-Heat Flux Heat Sources Cooled by Laminar Forced Convection Flow: Conjugate Analysis

A conjugate analysis via the finite volume approach is performed to study the effects of a thick plate on the excess (peak) temperature of an iso-heat flux heat source cooled by laminar forced convection flow. A thick plate of temperature-dependent thermal conductivity is placed between the heat sources and the cooling fluid. A cooling fluid flows over the thick plate and removes the heat by laminar forced convection. On account of the two-dimensional heat redistribution in the finite thick plate with one face subjected to iso-heat flux and the other face exposed to forced flow, the interface ceases to be an iso-heat flux and, consequently, reduces the excess temperature of the heat sources. In the numerical analysis, the thickness of the plate is relaxed one by one to search for the optimal thickness that minimizes the excess temperature. It is shown that the reduction in the excess temperature due to the insertion of the thick plate with optimal thickness depends upon the Reynolds number of the fluid flow and the fluid-to-solid thermal conductivity ratio.

NUMERICAL ANALYSIS OF PARTIALLY HEATED VERTICAL PARALLEL PLATES IN NATURAL CONVECTIVE COOLING

This paper addresses the significance of adding insulated extensions to a parallel-plate channel in which the plates receive a uniform heat flux and a natural convection airflow is responsible for the cooling. The wall temperatures may decrease or increase, depending on whether the channel extensions are appended at the inlet or at the exit of the channel. The full elliptic conservation equations are solved numerically in an I-type composite computational domain. For the two cases treated, the pertinent results are reported in terms of wall temperature profiles, induced mass flow rates, and pressure profiles. The insulated extension placed downstream of the heated part implies a reduction of the maximum wall temperature. This effect is less relevant as the Rayleigh number increases. In addition, correlations have been obtained between the induced mass flow rate as well as the maximum wall temperatures and the Rayleigh number and the extension ratio in the investigated range of parameters.

Formation of a pitchfork bifurcation in thermal convection flow inside an isosceles triangular cavity

Transient, laminar thermal convection of air confined to an isosceles triangular cavity heated from the base and symmetrically cooled from the upper inclined walls has been investigated numerically. The system of conservation equations, subject to the proper boundary conditions, along with the equation of state assuming the air behaves as a perfect gas are solved with the finite volume method. In the conservation equations, the second-order-accurate QUICK scheme was used for the discretization of the convective terms and the SIMPLE scheme for the pressure-velocity coupling. The maximum height-to-base aspect ratio A is fixed at 0.5, while the Grashof number extends from a low Gr=103 to a high Gr=106. The influence of Gr on the flow and temperature patterns is analyzed and discussed for two opposing scenarios, one corresponding to increasing Gr and the other corresponding to decreasing Gr. It is found that two steady-state solutions are possible, excluding their solution images through a vertical mirror pla...

Optimum plate separation in vertical parallelplate channels for natural convective flows: incorporation of large spaces at the channel extremes

Abstract This paper addresses the problem of optimizing the plate separation of an open, parallel-plate channel that is cooled by natural convection air flow. The plates are symmetrically heated by uniform heat flux. The I-shaped computational domain comprised two subdomains: the actual physical domain between the plates, and two large rectangular reservoirs placed upstream of the entrance and downstream of the exit. The aggregate subdomains accommodated the diffusion phenomena by momentum and energy that occur outside the channel. The full elliptic Navier-Stokes and energy equations are solved numerically in the composite domain. Correlations of the optimal values of the plate spacing as a function of the GrL number and of the induced mass flow rate, as well as thermal and velocity profiles, are presented for air.

BENEFITS DERIVABLE FROM CONNECTING THE BOTTOM AND TOP WALLS OF ATTIC ENCLOSURES WITH INSULATED VERTICAL SIDE WALLS

ABSTRACT This article addresses buoyant air circulation inside attic spaces of houses and buildings with sloped roofs and horizontally suspended ceilings. Depending on the season of the year, two different heating/cooling scenarios may occur. In order to counteract the excessive heat transmission that takes place during the winter and summer seasons, heavily insulated, vertical side walls of variable height h are placed at the hot/cold intersection between the active walls. As a result, the shape of the enclosure switches from an isosceles triangular enclosure to a trapezoidal enclosure, but having two insulated side walls. The finite-volume method is employed to perform the numerical computations.

Irreversibility phenomena associated with heat transfer and fluid friction in laminar flows through singly connected ducts

Abstract The main objective of this study is to explore the existence of thermodynamic irreversibility extrema for laminar fluid flow with heat transfer under fully developed conditions through different cross-sectional, free-flow area ducts. The evaluation of thermodynamic trade-offs caused by simultaneous heat transfer at a finite temperature difference and fluid friction will be emphasized in terms of the dimensionless entropy generation as a performance criterion. A set of duct geometries under investigation included circular, rectangular, square, triangular, sine and a set of longitudinal finned circular tubes. One of the pragmatical goals of the analysis is to establish the mutual relationship between the hydrodynamic and thermal aspects using, from one side, the conventional area goodness factor, and from the other side, the thermodynamic performance evaluation criterion. The quantitative results for the set of parameters under investigation show that the improvement and/or the deterioration of the performance of one geometry with respect to another depend on the duct geometry, the Reynolds number and the inlet wall temperature ratio for a given fluid and a certain duct length.

Natural Convection Patterns in Right-Angled Triangular Cavities with Heated Vertical Sides and Cooled Hypotenuses

The present investigation deals with the numerical computation of laminar natural convection in a gamma of right-angled triangular cavities filled with air. The vertical walls are heated and the inclined walls are cooled while the upper connecting walls are insulated from the ambient air. The defining apex angle α is located at the lower vertex formed between the vertical and inclined walls. This unique kind of cavity may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method is used to perform the computational analysis encompassing a collection of apex angles α compressed in the interval that extends from 5° to 63°. The height-based Rayleigh number, being unaffected by the apex angle α, ranges from a low 103 to a high 106. Numerical results are reported for the velocity field, the temperature field and the mean convective coefficient along the heated vertical wall. Overall, the matching between the numerically predicted temperatures and the experimental measurements of air at different elevations inside a slim cavity is of ordinary quality. For purposes of engineering design, a Nu¯H correlation equation was constructed and also a figure-of-merit ratio between the Nu¯H and the cross sectional area A of the cavity was proposed.

EXPERIMENTAL-BASED CORRELATIONS FOR THE CHARACTERIZATION OF FREE CONVECTION OF AIR INSIDE ISOSCELES TRIANGULAR CAVITIES WITH VARIABLE APEX ANGLES

The archival literature contains an abundance of correlations for the characterization of laminar-free convection in rectangular, square, and annular cavities, but unfortunately does not disclose a single correlation for triangular cavities. A prominent application of triangular cavities specialized to isosceles shapes arises in air-filled attic spaces of houses and buildings with sloped roofs and horizontal suspended ceilings. In this work, two contrasting situations are considered embodying three apex angles and several Grashof numbers: a hot base and symmetrically cold inclined sides for winter conditions, and a cold base and symmetrically hot inclined sides for summer conditions. The goal of this article is to construct two dependable correlations, one for the mean convective coefficient at the air/wall interface, and the other for the temperature variation of the ascending air along the center plane of attic spaces. The input data was taken from precise measurements available in the specialized literature.

A new minimum volume straight cooling fin taking into account the length of arc

Abstract The problem of determining the shape of a straight cooling fin of minimum volume without the “length of arc” assumption is addressed. Proceeding from the conventional assumptions of one-dimensionality of the temperature distribution and its linearity for the minimum volume fin we found the profile of the optimum fin to be a circular arc and computed its geometric parameters. The volume of the optimum circular fin found in this paper is 6.21–8 times smaller than the volume of the corresponding Schmidt’s parabolic optimum fin. The optimum circular fin tends to be shorter and to have a larger base height than Schmidt’s fin.