A. Aziz

Two-dimensional performance of convecting-radiating fins of different profile shapes

A finite element approach is used to investigate the two-dimensional performance of convecting-radiating fins of rectangular, trapezoidal, triangular, and concave parabolic shapes. The heat transfer rate depends on fin size parameter α, Biot numberBi, radiation-conduction parameterNr, and environment temperatures θ∞ and θr. Numerical results for the heat transfer rate and the error due to one-dimensional assumption are presented and discussed for each geometry. The highest heat dissipation is achieved with the concave parabolic shape and the lowest with the rectangular shape with the trapezoidal and triangular shapes falling in between. The maximum error of +144 percent is noted for a short and thick rectangular fin (α=1) and −47 percent for a long thin triangular fin (α=20).ZusammenfassungMit Hilfe der Methode der Finiten Elemente wird das zweidimensionale Übertragungsverhalten bezüglich Konvektion und Strahlung von Rippen mit rechteckigem, trapezförmigem, dreieckförmigem und konkav-parabolischem Querschnitt untersucht. Der übertragbare Wärmestrom hängt von dem Rippenparameter 2L/W, der BiotzahlBi, dem StrahlungskonvektionsparameterNr und von den Umgebungstemperaturen θW und θr ab. Für jede Geometrieform werden der übertragene Wärmestrom und der bei eindimensionaler Behandlung auftretende Fehler angegeben und diskutiert. Der höchste Wärmeübergang wird mit dem Parabelprofil, der niedrigste mit dem Rechteckprofil erzielt. Trapez- und Dreiecksform liegen dazwischen. Für eine kurze und dicke Rechtecksrippe (2L/W=1) erhält man einen Maximalfehler von +144% und für eine lange dünne Dreiecksrippe (2L/W=20) von −47%.

Mixed Convection From a Convectively Heated Vertical Plate to a Fluid With Internal Heat Generation

A numerical approach has been adopted to study steady mixed convection from the right face of a vertical plate of finite thickness. Cold fluid flowing over the right face of the plate contains a heat generation that decays exponentially with a dimensionless distance from the wall. The left face of the plate is in contact with a hot flowing fluid. The heating process on that side is characterized by a convective boundary condition that takes into account the conduction resistance of the plate as well as a possible contact resistance between the hot fluid and the left face of the plate. Using a pseudo similarity approach, the continuity, momentum, and energy equations for mixed convective flow over the right face of the plate are transformed into a set of coupled ordinary differential equations. It is found that for a true similarity solution, the convective heat transfer coefficient associated with the hot fluid must be proportional to x ―1/2 , and both the thermal expansion coefficient and the internal heat generation rate for the cold fluid must be proportional to x ―1 , where x is the upward distance along the plate. The equations give local similarity solutions. The effects of local Grashof number (defined to represent a mixed convection parameter), Prandtl number, Biot number, and the internal heat generation parameter on the velocity and temperature profiles are illustrated and interpreted in physical terms. The present results agree closely with the existing results for the special cases of the problem. This close agreement lends support to the validity of the present analysis and the accuracy of the numerical computations. The paper also contains a table in which the data for the local skin friction and local Nusselt number are provided for various combination values of the parameters that govern the momentum and energy transport in the mixed boundary layer.

On inherent irreversibility in Sakiadis flow of nanofluids

The problem of entropy generation and inherent irreversibility in the steady boundary layer shear flow of nanofluids over a moving flat plate is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation and then solved numerically by a Runge–Kutta–Fehlberg method with the shooting technique. Two types of nanofluids, namely, Cu–water and TiO2–water, are used. The effects of nanoparticle volume fraction, the type of nanoparticles, group parameter, and the local Reynolds number on the entropy generation rate, irreversibility ratio and the Bejan number are discussed. It is found that the entropy generation rate at the plate surface decreases with increasing nanoparticle volume fraction and the group parameter. Moreover, the heat transfer irreversibility at the plate surface with TiO2–water nanofluid is slightly higher than that at the plate surface with Cu–water nanofluid.

Second law analysis for a variable viscosity plane Poiseuille flow with asymmetric convective cooling

A second-law analysis of a pressure-driven variable viscosity fluid flow through a channel with asymmetric convective cooling at the walls is investigated. Flow is assumed to be steady, laminar and fully-developed. The effect of heat generation due to viscous dissipation is included. The resulting equations and boundary conditions are solved numerically, by using an efficient numerical shooting technique with a fourth order Runge-Kutta algorithm. The effect of variable viscosity parameter, the Brinkman number and the Biot numbers on the velocity, temperature and entropy generation profiles are provided and discussed with appropriate physical explanations.

Analysis of Entropy Generation and Thermal Stability in a Slab

This study investigates the inherent irreversibility in a rectangular slab with temperature-dependent internal heating. It is assumed that the slab external surfaces are subjected to asymmetric heat exchange with the surrounding medium. The simplified governing equation for energy balance in Cartesian coordinates is solved analytically and expedites to obtain expressions for the temperature field, thermal stability criterion, volumetric entropy generation number, and irreversibility distribution ratio. Graphical results are presented and discussed quantitatively. It is found that the local and total entropy generation rates in the slab can be minimized for certain combinations of the heat transfer parameters.

Heat transfer and entropy generation in a two-dimensional orthotropic convection pin fin

The paper uses a two-dimensional heat conduction model to obtain the thermal performance and entropy generation in an orthotropic pin fin used in advanced light weight heat sinks. The analytical expressions for the distribution and heat transfer rates are used to generate the thermal performance graphs that are of general applicability unlike the results for specific cases reported so far. The same information is subsequently used to generate graphs of local and total volumetric entropy generation rates in the fin. The results clearly delineate the effect of radial Biot number, fin aspect ratio, and the ratio of radial to axial thermal conductivities on temperature distribution, heat transfer rate, and local and total entropy generation rates. A procedure is discussed to illustrate the simultaneous realisation of the least material and minimum entropy generation pin fin designs.

Laminar Natural Convection From an Isothermal Vertical Surface to Pseudoplastic and Dilatant Fluids

This paper reports the results of a numerical study of natural convective heat transfer from a vertical isothermal surface to pseudoplastic and dilatant fluids. The analysis calculates the average Nusselt number in the laminar regime when the surface is exposed to an otherwise quiescent fluid. Because the solution utilizes constitutive equations that are valid over the entire shear rate range, the results map the behavior regardless of the shear rates that exist in the flow field. The Nusselt number is shown to approach Newtonian values when the shear rates throughout the flow field are predominantly either in the zero or in the high shear rate Newtonian regions of the flow curve. When they are principally in the power law regime, and if the fluid is also strongly non-Newtonian, then the Nusselt number approaches power law values. For all other cases, it is seen to attain intermediate values. Furthermore, a shear rate parameter is identified that determines the shear rate regime where the system is operating. The average Nusselt number is presented in both graphical and tabular forms over a broad range of system parameters.

Heat transfer from convecting-radiating fins of different profile shapes

A finite difference method is used to predict the performance of convecting-radiating fins of rectangular, trapezoidal, triangular, and concave parabolic shapes. The analysis assumes one-dimensional, steady conduction in the fin and neglects radiative exchange between adjacent fins and between the fin and its primary surface. For the range of thermal and geometrical parameters investigated, the variation of heat transfer rate and the fin efficiency with other profile shapes was found to be within 11 percent of the rectangular shape. The effect of profile shape is most pronounced when the Biot number,Bi, and radiation number,Nr, are small compared to unity. Because of several limiting assumptions, the results would be used only for preliminary analysis and design particularly when a fin assembly is involved rather than an individual fin.ZusammenfassungEin Finite-Differenzen-Verfahren findet Anwendung zur Berchnung der Wärmeübertragungsleistung mittels Konvektion und Strahlung an Rippen, die rechteckige, trapezförmige, dreieckige und konkav-parabolische Formen besitzen. Die Berechnungen setzen eine eindimensionale, stetige Wärmeleitung in den Rippen voraus und vernachlässigen den Strahlungsaustausch zwischen aneinandergrenzenden Rippen und zwischen den Rippen und ihrer Oberfläche. Für den betrachteten Bereich der thermischen und geometrischen Parameter wurde herausgefunden, daß die Veränderung der Wärmeübertragungsrate und des Rippenwirkungsgrades der anderen Profilformen im Bereich von 11 Prozent im Vergleich zur Rechteckform liegen. Der Einfluß der Profilform ist am stärksten, wenn die Biot-ZahlBi und die StrahlungszahlNr im Vergleich zu 1 klein sind. Aufgrund einiger einschränkender Annahmen sollten die Ergebnisse nur für die Voruntersuchungen und den Vorentwurf benutzt werden, insbesondere wenn es sich um eine Rippenanordnung und nicht um eine Einzelrippe handelt.