Abdul Aziz

Extended Surface Heat Transfer

Preface. Convection with Simplified Constraints. Convection with Real Constraints. Convective Optimizations. Convection Coefficients. Linear Transformations. Elements of Linear Transformations. Algorithms for Finned Array Assembly. Advanced Array Methods and Array Optimization. Finned Passages. Compact Heat Exchangers. Longitudinal Fin Double-Pipe Exchangers. Transverse High-Fin Exchangers. Fins with Radiation. Optimum Design of Radiating and Convecting-Radiating Fins. Multidimensional Heat Transfer in Fins and Fin Assemblies. Transient Heat Transfer in Extended Surfaces. Periodic Heat Flow in Fins. Boiling From Finned Surfaces. Condensation on Finned Surfaces. Augmentation and Additional Studies. Appendix A: Gamma and Bessel Functions. Appendix B: Matrices and Determinants. References. Author Index. Subject Index.

Convection–radiation from a continuously moving fin of variable thermal conductivity

Abstract The homotopy analysis method (HAM) is applied to generate an analytic solution for heat transfer in a moving fin of variable thermal conductivity which is losing heat by simultaneous convection and radiation to its surroundings. The accuracy of the analytic solution is validated by comparing it with the direct numerical solution of the problem. The analytic solution is found to be accurate to at least three places of decimal for a wide range of values of the parameters that are commonly encountered in thermal processing application. Graphs displaying the results are interpreted in physical terms.

Viscous Flow with Second-Order Slip Velocity over a Stretching Sheet

In this paper, viscous flow with a second-order slip condition over a permeable stretching surface is solved analytically. The current work differs from the previous studies in the application of a new second-order slip velocity model. The closed form solution reported is an exact solution of the full governing Navier-Stokes equations. The effects of slip and mass transfer parameters are discussed.

Optimum Design of Radiating and Convecting-Radiating Fins

The design of fins of optimum dimensions of specified shapes has been pursued by numerous investigators, and a significant body of literature has accumulated over the past 70 years. Of this, the literature pertaining to purely convecting fins has been systematically organized in a review article by Aziz. At that time, it was felt that there was a need for a similar review covering the design of radiating and convecting-radiating fins with optimum dimensions. The present article has been prepared to fulfill this need. Like its predecessor, the article seeks to achieve three objectives. The first objective is to provide an overview of the literature and to identify future research needs. The second objective is to provide a convenient design reference for the practicing engineer. The third objective is to create an instructional resource on the topic. To meet the last two objectives, several design examples are interspersed throughout the article.

Transient Heat Transfer in Extended Surfaces

This paper attempts to provide a comprehensive, coherent, and methodical review of the existing literature on the transient performance of extended surfaces (fins). With the exception of very few experimental studies, the work described is theoretical involving either analytical approaches or numerical computations. For both longitudinal and radial convecting fins, the shapes analyzed include fins of rectangular, trapezoidal, concave parabolic, and convex parabolic profiles. The boundary conditions considered are those of time-dependent base temperature or time-dependent base heat flow, or time-dependent temperature of the fluid on the unfinned side of the primary surface. Other studies discussed consider the transient responses of radiating and convecting-radiating fins, fins with stochastic base temperature and fins in which conduction, natural convection, and radiation are coupled. The paper also provides an in-depth consideration of two-dimensional analyses of a cylindrical spine (pin fin) and a composite longitudinal fin. All of the important results pertaining to the transient effect in extended surfaces are presented and these effects are illustrated with several examples. The paper concludes with an attempt to identify future investigative efforts.

Homotopy Analysis Method for Variable Thermal Conductivity Heat Flux Gage with Edge Contact Resistance

The homotopy analysis method (HAM) has been used to develop an analytical solution for the thermal performance of a circular-thin-foil heat flux gage with temperature dependent thermal conductivity and thermal contact resistance between the edge of the foil and the heat sink. Temperature distributions in the foil are presented illustrating the effect of incident heat flux, radiation emission from the foil, variable thermal conductivity, and contact resistance between the foil and the heat sink. The HAM results agree up to four places of decimal with the numerical solutions generated using the symbolic algebra package Maple. This close comparison vouches for the high accuracy and stability of the analytic solution.

The Effects of Internal Heat Generation, Anisotropy, and Base Temperature Nonuniformity on Heat Transfer from a Two-Dimensional Rectangular Fin

Abstract A finite-element approach is used to study the two-dimensional performance of a straight fin of rectangular profile operating in a convecting environment. The analysis includes the effects of internal heat generation, anisotropy of fin material, base temperature elevation (depression), and unequal heat transfer coefficients for tip and main convection surfaces. Numerical results are presented showing the impact of these effects on the heat removal capability of the fin. The graphical information provided is believed to be useful for predicting the performance of a two-dimensional rectangular fin under more general and realistic conditions.

The Critical Thickness of Insulation

The theory of critical thickness of insulation for cylindrical and spherical geometries is discussed in a comprehensive and methodical manner. The article begins with the introduction of the classical analysis, which assumes surface convection with a constant heat transfer coefficient, h. Next, various modifications of the basic theory are discussed in detail. These modification allow for: The variation of h with outside radius, ro (constant-property forced convection) The variation of h with ro, with temperature-dependent fluid properties (variable-property forced convection) Circumferential variation of h with forced convection The variation of with outside radius and the temperature difference between the outside surface and the surroundings (natural convection) Surface radiation Combined radiation and natural convection Combined radiation, natural convection, and surface heat release due to change of phase of the surrounding fluid Effects of radiation, inclination, and insulation opacity The last thre...

Transient response and entropy generation minimisation of a finite size radiation heat shield with finite heat capacity and temperature–dependent emissivities

The paper presents a numerical study of the transient response of a rectangular radiation heat shield inserted between two planes, grey, diffuse, parallel, rectangular surfaces. The radiation shield is assumed to have different emissivities on its top and bottom surfaces, and both are assumed to be linear functions of temperature. A specific configuration is investigated in detail to highlight the transient as well as the steady state thermal characteristics of the system. The paper derives an equation to calculate the steady state shield temperature for minimum entropy generation. Results are presented in graphical or tabular forms.

Thermal Stresses in a Hollow Cylinder with Convective Boundary Conditions on the Inside and Outside Surfaces

Analytical solutions for thermal stresses (radial, tangential, and axial) in a hollow cylinder with uniform internal heat generation for the thermal boundary condition of convective heating on the inside surface and convective cooling on the outside surface are derived. The analysis assumes the ends of the cylinder to be clamped, the axial strain to be negligible, and the radial stresses on the inside and the outside surfaces to be zero. Results are presented to illustrate the effects of internal heat generation parameter Q, convective environment temperatures ratio θ*, Biot number for convection on the inside surface Bi 1, Biot number for convection on the outside surface Bi 2, and the radii ratio ρ on thermal stresses distribution in the cylinder. The analytical solutions should serve as benchmarks for validating the numerical codes for dealing with more complicated cases.