Integral transforms in the two‐dimensional non‐linear formulation of longitudinal fins with variable profile

Abstract

IntroductionExtended surfaces (or fins) play a major role in the design of heat exchange devices within different fields of application, aimed at providing a heat transfer enhancement effect through an increase in the total exchange area. Although fins of uniform longitudinal profile are more commonly employed, owing to the obvious advantages in manufacturing and installation, extended surfaces of variable profiles are also of great practical interest, in connection with optimized designs towards the minimization of the fin weight and consequent reduction on the fin material utilization (Kern and Kraus, 1972;Snider and Kraus, 1983).

Analytical and hybrid solutions of diffusion problems within arbitrarily shaped regions via integral transforms

“…The extension of this analysis to the computation of the potential field itself, is now a straightforward task and particularly computationally effective for linear problems, when the integral transformation procedure yields decoupled ordinary differential equations for the transformed potentials, and the inversion formula provides a fully analytical solution for the original potential in all independent variables. Nevertheless, the approach is similarly applicable to nonlinear situations, as previously considered [19,20].…”

“…Since 1989, a number of contributions have appeared in the integral transform solution of elliptic and parabolic diffusion problems within irregularly shaped domains [14][15][16][17][18][19][20]. All these contributions have in common the procedure of directly integral transforming the original partial differential system, starting from chosen one-dimensional eigenvalue problems which carry the information on the irregular shape through their own domain bounds, written as functions of the coordinate variables.…”

Steady Thermal Analysis of Two‐Dimensional Cylindrical Pin Fin with a Nonconstant Base Temperature

“…Here, K a is the thermal conductivity of the fin at ambient temperature, β is the thermal conductivity gradient, n is an exponent, and B is the thermal conductivity parameter. Applying the Kirchoff's transformation see, e.g., 16 ,…”

“…Two-dimensional transient analysis have been carried out for fins without heat source or sink in 12 . Solutions for two-dimensional fin models exist for the constant thermal conductivity see e.g., [13][14][15][16] . Recently, heat transfer and entropy generation in two-dimensional orthotropic pin fin has been studied in 17 .…”

An appropriate analysis for optimum design of wet fins based on modified 1-D and 2-D approaches

“…In a parallel work, Razelos and Krikks [20] concluded that the heat transfer from the tip could be neglected without introducing any appreciable error. A negligible heat loss from the tip is only true for very thin and long fins investigated by Kundu and Das [21]. On the other hand, the presence of fins induced transverse 2-D effects within the supporting surface had been studied by Sparrow and Lee [22], and these may in turn produce 2-D variations within the fin itself.…”