Convective Fins Research Articles

Analysis and optimization of convective trapezoidal profile pin fins with internal heat generation

An analysis of trapezoidal profile convective pin fins, with internal heat generation density is presented. The solution of the optimal problem is also given, when either the desired heat dissipation rate or the volume of the pin is specified. The results are presented graphically and in polynomial forms that are particularly useful for computerized calculations. The effect of the fin's profile and thermal conductivity upon the optimum dimensions is discussed. An example serves to demonstrate the usefulness of the method.

Local Convective Behavior and Fin Efficiency in Shallow Banks of In-Line and Staggered, Annularly Finned Tubes

Local mass transfer data for high-profile fins in the second row of in-line and staggered, circular-finned tubes are presented for Reynolds numbers from 5000 to 28,000 based on hydraulic diameter and velocity at the minimum flow area. The data, obtained using an optical adaptation of the naphthalene sublimation technique, show that local variations in heat transfer do not cause significant fin efficiency deviations from the analytical solution of Gardner (contrary to earlier reports). Average heat transfer and pressure drop data indicate that the thermal performance of the in-line arrangement is comparable to the staggered configuration.

Analysis and Optimization of Convective Trapezoidal Profile Longitudinal Fins

The paper presents an analysis of convective trapezoidal-profile longitudinal fins, which describes their thermal performance. In addition, an improved solution of the optimal problem is derived using the Razelos (1979, 1983) method. 8 refs.

Performance analysis and optimization of convective annular fins with internal heat generation

An analysis of the thermal performance for convective annular fins, having a general trapezoidal profile and internal heat generation, is presented. The solution of the optimal problem is also given when either the heat dissipation rate or the volume of the fin is specified. The results are expressed in suitable nondimensional variables that are specified by the problem, and presented graphically. The effect of the fin's profile and thermal conductivity upon the optimum dimensions is discussed. It is shown that the presence of heat generation reduces the ability of the fin to convect heat. Furthermore, certain limiting values of the heat generation that may be imposed on the fin for a feasible optimization are also derived.

Optimization of convective fin with temperature-dependent thermal parameters

The method of temperature-correlated profiles is used to obtain the solution of optimum convective fin when the thermal conductivity and heat transfer coefficient are functions of temperature. The profile is shown to be convenient to obtain an analytical solution of the resulting nonlinear heat transfer equation. It is shown that the profile correctly predicts the optimization problems with spatial variation of the heat transfer coefficients reported in the literature. The effect of temperature dependence on heat transfer coefficients is found to be important in the design of optimum fins. Using the profile, an approximate solution for the optimum fin, including the effect of temperature dependence on convection heat transfer coefficient (useful for parametric study and design analysis), is obtained. The exact solution, using numerical integration of the resulting equations, is compared with the approximate solutions. The results are reported in terms of dimensionless quantities convenient in design analysis. The method is shown to be very useful for parametric study where the optimization problem is given in terms of two parameters: the tip temperature and a profile parameter.

Effect of thermal stratification on free convection within a porous medium

Free convection over a vertical flat plate embedded in a thermally stratified porous medium is analyzed by exploiting the similarity transformation procedure. Numerical integration results are presented for a series of wall and ambient temperature distributions which permit similarity solutions. The conjugate conduction connection problems of a free convection fin embedded in a thermally stratified porous medium is examined, and it is shown that the influence of the thermal stratification on the heat transfer is quite significant. 8 references.

Free convection around a heated fin embedded in a thermally stratified porous medium.

A theoretical analysis is presented for the conjugate conduction-convection problems of a free convection fin with an infinite length, embedded in a porous medium of infinite extent. In view of practical applications, the analysis takes account of a possible thermal stratification within the surrounding porous medium. An integral procedure is exploited to solve the boundary layer equations for the Darcian fluids, while the thin-fin approximation is evoked for the quasi-one-dimensional heat conduction equation for the fin. Similarity solutions re obtained for a class of the fins in which the conduction-thickness product varies according to the power function of the distrance form the origin. Some of the results are compared with available exact solutions. It will also be shown that the presence of thermal stratification within a porous medium can significantly displace the isotherms around the fin.

Closure to “Discussion of ‘The Optimum Dimensions of Convective Pin Fins’” (1984, ASME J. Heat Transfer, 106, pp. 256–257)

Closure to “Discussion of ‘The Optimum Dimensions of Convective Pin Fins’” (1984, ASME J. Heat Transfer, 106, pp. 256–257)

Erratum: “The Optimum Dimensions of Convective Pin Fins” (Journal of Heat Transfer, 1983, 105, pp. 411–413)

Erratum: “The Optimum Dimensions of Convective Pin Fins” (Journal of Heat Transfer, 1983, 105, pp. 411–413)

Thermally Optimum Arrays of Cards and Fins in Natural Convection

Recently derived analytic relations for natural convection heat transfer coefficients along isothermal or isoflux channel surfaces are applied to the thermal optimization of printed circuit cards and fin arrays. The procedure used and the governing relations, for both thermally symmetric and asymmetric card arrays, are presented. A similar development for arrays of natural convection fins, addressing the influence of fin thickness on the optimum fin spacing and maximum array heat dissipation, is also shown.

The Optimum Dimensions of Convective Pin Fins

The Optimum Dimensions of Convective Pin Fins

Minimum mass convective fins with variable heat transfer coefficients

Pontryagin's maximum principles are applied to obtain the solution of minimum mass convective fins with variable heat transfer coefficients. It is shown that the volume and the width of the fin are uniquely related to the specified heat transfer rate and the properties of the material. For a power law spatial variation of the heat transfer coefficient, the results are set forth in a dimensionless form and they are given in tables or graphs, in order to aid design procedures. Several properties relating to the optimum volume, base thickness and the width of the fins with the properties of the material are also discussed. The method can also be used to solve problems of minimum mass fins having restricted width, often encountered in practice.

Optimal linearization and variational embedding solutions for convective fins with variable thermal conductivity

The optimal linearization method is used to obtain an approximate analytical solutions for steady state of convective fins with variable thermal conductivity. Furthermore, an approximate analytical solutions for transient state of convective fins with variable thermal conductivity is achieved by using the variational embedding method.

A Natural Convection Fin with a Solution-Determined Nonmonotonically Varying Heat Transfer Coefficient

A conjugate conduction-convection analysis has been made for a vertical plate fin which exchanges heat with its fluid environment by natural convection. The analysis is based on a first-principles approach whereby the heat conduction equation for the fin is solved simultaneously with the conservation equations for mass, momentum, and energy in the fluid boundary layer adjacent to the fin. The natural convection heat transfer coefficient is not specified in advance but is one of the results of the numerical solutions. For a wide range of operating conditions, the local heat transfer coefficients were found not to decrease monotonically in the flow direction, as is usual. Rather, the coefficient decreased at first, attained a minimum, and then increased with increasing downstream distance. This behavior was attributed to an enhanced buoyancy resulting from an increase in the wall-to-fluid temperature difference along the streamwise direction. To supplement the first-principles analysis, results were also obtained from a simple adaptation of the conventional fin model.

Convective fin of minimum mass

The problem of reducing to a minimum the mass of a convective annular/circular fin at the prescribed magnitude of the heat flux is considered. The limiting case of minimization is obtained at the temperature of the outer edge of the fin differing from the temperature of the environment surrounding. The mass of the ideal fin examined differs but little from the mass of the fin of a triangular profile.

Optimization of convective circular fins

The volume of a circular fin whose thickness is inversely proportional to the square of the radius is optimized.

The optimization of longitudinal convective fins with internal heat generation

The solution of the optimization problem for longitudinal convective fins of constant thickness, triangular or parabolic profile, and uniform internal heat generation, is presented. The cases considered are those of a given heat generation density, total heat generation, and heat generation per unit width of the fin, when either the heat dissipation or the width of the fin is prescribed. The results are set forth in a nondimensional form, which are presented graphically. The effect of the fin's thermal conductivity upon the optimum dimensions is discussed, and limiting values for the heat generation and the heat dissipation, which may be imposed on the fin for a feasible optimization, are also obtained.

A note on the heat transfer in convective fins

In this paper a generalized approach to the problem of heat transfer through convective fins is given. The proper dimensionless variables, which specify the general problem are identified, and upper bounds of the values of the dimensionless number Nr defined as “the ratio of the heat transferred by the fin to that of the corresponding bare surface” are derived. It was shwon that these limiting values of the Nr are 1/√B1 and √2/B1 for longitudinal fins and spines respectively, where B1 is the Biot number hb/k, while for annular fins of constant thickness and hyperbolic profile, Nr⩽ K(β)/√Bi, where K(β) is a number determined by the profile of the fin and the ratio β=x2/x1 of the outside to the inside radii. It was also shown that for longitudinal fins and spinces the possible adverse insulating effect by the use of the fin is avoided, if one selects the value of √hA/KC < 1, which is a rather stricter criterion than the one reported in the literature, namely that of hA/kC < 1 [2–5]. An example is given to show how one may utilize the appropriate value of Nr and the fin effectiveness e, to obtain the dimensions of the fin.

Perturbation solution for convective fin with internal heat generation and temperature dependent thermal conductivity

Perturbation solution for convective fin with internal heat generation and temperature dependent thermal conductivity

Closure to “Discussion of ‘Approximate Solution for Convective Fins With Variable Thermal Conductivity’” (1977, ASME J. Heat Transfer, 99, p. 692)

Closure to “Discussion of ‘Approximate Solution for Convective Fins With Variable Thermal Conductivity’” (1977, ASME J. Heat Transfer, 99, p. 692)