Optimization of heat transfer through finned dissipators cooled by laminar flow

In the present work, the problem of optimizing the shape and the spacing of the fins of a thermal dissipator cooled by a fluid in laminar flow is studied. For a particular finned conduit, the velocity and temperature distributions on the transversal section are determined with the help of a finite element model and a global heat transfer coefficient is calculated. A polynomial lateral profile is proposed for the fins and the geometry is optimized in order to make the heat transfer coefficient as high as possible with the smallest dimensions or the lowest hydraulic resistance to the flow. The optimum fin profile and spacing, obtained by means of a genetic algorithm, are finally shown for different situations. Increases of 45% are obtained in the heat transfer coefficient referring to the maximum values which can be obtained with rectangular fin profiles.     

Viscous incompressible flow in a narrow channel with one free wall and fluid supply through a porous insert

The problem investigated relates the plane unsteady flow of a viscous incompressible fluid in a narrow channel one of whose walls is free and acted upon by a given load, while the other is rigidly fixed. The fluid enters the channel through a porous insert in the stationary wall. A model of the flow of a thin film of viscous incompressible fluid and Darcy's law for flow in a porous medium are used to find the distribution of fluid pressure and velocity in the channel and the porous insert in the two-dimensional formulation for fairly general boundary conditions in the case where the length of the porous insert exceeds the length of the free wall. In the particular case where the length of the porous insert is equal to the length of the free wall an exact stationary solution of the problem is obtained for a given value of the channel height. The stability of the equilibrium position of the free wall supported on a hydrodynamic fluid film is examined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–24, January–February, 1986.     

Flow past an axisymmetric body embedded in a saturated porous mediumÉcoulement derrière un corps à symétrie axiale plongé dans un milieu poreux saturé

The problem of viscous fluid past an axisymmetric body embedded in a fluid saturated porous medium is studied using the Brinkman's extension. A general formula for the drag on the body is derived in the form of a limit of an expression involving the stream function characterizing the flow. The flow past an axisymmetric approximate sphere is also considered. The stream function in this case is obtained in terms of Bessel functions and Gegenbauer's functions. The drag acting on the body is evaluated by using the formula derived. Its variation is studied with respect to geometric and permeability parameters. The special cases of flow past a sphere and a spheroid are obtained from the present analysis. To cite this article: D. Srinivasa Charya, J.V. Ramana Murthy, C. R. Mecanique 330 (2002) 417–423.     

Linearized equations of motion of a viscous fluid in a porous medium of periodic structure

The investigation of flow in essentially inhomogeneous porous systems through the analysis of model periodic structures [1] is considered. In the acoustic approximation, an integrodifferential equation is obtained that describes the motion of a viscous fluid in a rigid porous medium of periodic structure. The velocity vector and pressure are represented in the form of asymptotic series with respect to a small parameter that characterizes the size of the periodicity cell, and the well-known procedure for averaging linearized hydrodynamic equations with small coefficients of viscosity [2, 3] is also used. A solution is presented to the local problem in the periodicity cell for a structure consisting of a doubly periodic system of infinitely long rods of circular section and a compressible viscous fluid that fills the space between them, and also for a structure formed by a system of orthogonal rectilinear channels, filled with viscous fluid, in a solid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 123–130, March–April, 1988.     

Metal foam and fin implementation into a triple concentric tube heat exchanger over melting evolution

It is believed that it is going to be a sizeable mismatch between supply and demand when it comes to renewable resources. Lately, researchers are on course to compensate for the unpredictabilityof such resources by the employment of phase change materials (PCMs). Having multiple advantages, PCMs generally suffer from inadequate thermal conductivity which causes prolonged transition procedures. To tackle this issue, this study is fixated on two parameterswhich are linked to fins addition and porous media incorporation in a melting process within a triple concentric tube heat exchanger (TCTHX). The results provided by multiple cases underlined the significance of natural convection in the bare system, although finned and copper-metal-foam cases outshine buoyancy forces by roughly 45% and 97%, respectively. Material is a major determent when it comes to the selection of porous media as Al₂O₃ registered the weakest performance among SiC, Ni and Cu, however, it managed to speed up the process by 75% which still is much higher than the finned system, implying that porous media is of higher priority over fins. The best scenario transpiredwhile fins and copper metal foam were integrated as 26% and 97% soars in efficacy have been obtained compared to individual incorporation of porous media and fins, respectively.     

Heat transfer for non-Newtonian laminar flow in internally finned pipes with uniform temperature

An analysis is presented for fully developed laminar convective heat transfer of non-Newtonian power-law fluids in pipes with internal longitudinal fins and uniform outside wall temperature. The governing momentum and energy equations have been solved numerically, with the influence of fin conductance. The distributions of fin temperature, fluid temperature and local heat flux (both at finned and unfinned surfaces) are presented. These are shown to be strongly dependent on finned pipe geometry, fluid flow behavior index and the fin conductance. Values of overall Nusselt number indicated significant heat transfer enhancement over finless pipes. The flow behavior index affects the no. of fins which maximizes the overall Nusselt number.     

Effect of viscous dissipation on the heat transfer in sinusoidal profile finned dissipators

In the present work, the efficiency of finned heat dissipators cooled by laminar flow is studied. The analysis is carried out by varying certain sizing parameters in correspondence with different viscous dissipation conditions. The velocity distribution in the fluid and the temperature distribution in the dissipator and in the fluid are determined by means of a finite element method. The model allows to study the variation of the heat transfer coefficient due to the fluid dynamic conditions imposed by the fin profile. Lastly, a comparison between the optimum fin shapes obtained under different viscous dissipation effects is carried out.     

Pressure drop and heat transfer characteristics of turbulent flow in annular tubes with internal wave-like longitudinal fins

Measured were pressure drop and heat transfer characteristics with uniform axial heat input using air as the working fluid in both the entrance and fully developed regions of annular tubes with wave-like longitudinal fins. Five series of experiments were performed for turbulent flow and heat transfer in the annular tubes with number of waves equal to 4, 8, 12, 16 and 20, respectively. The test tube has a double-pipe structure with the inner blocked tubes as an insertion. The wave-like fins are in the annulus and span its full width. The friction factor and Nusselt number in the fully developed region were obtained. The friction factor and Nusselt number can be well corrected by a power-law correction in the Reynolds number range tested. In order to evaluate the thermal performance of the longitudinal finned tubes over a plain circular tube, comparisons were made under three conditions: (1) identical pumping power; (2) identical pressure drop and (3) identical mass flow. It was found that under the three constraints all the wave-like finned tubes can enhance heat transfer with the tube with wave number 20 being superior. Finally, discussion on the enhancement mechanism is conducted and a general correlation for the fully developed heat transfer is provided, which can cover all the fifty data of the five tubes with a mean deviation of 9.3%.     

Use of the curvature hypothesis for calculating supersonic flow past a rotating finned body

Three-dimensional supersonic ideal-gas flow past axisymmetric finned bodies rotating about the longitudinal axis is considered. A calculation method based on the numerical solution of the Euler equations by finite differences is described. The effect of the rotation of the body is taken into account within the framework of the curvature hypothesis [1], which provided that the dimensionless rate of rotation is small reduces the solution of the unsteady three-dimensional problem of supersonic flow past a rotating body to the solution of the steady-state problem of flow past a nonrotating body with specially curved fins. The problem of the rotation of a finned body in a free stream is solved.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 109–114, July–August, 1988.     

Unsteady flow of a dusty Bingham fluid through a porous medium in a circular pipe

A time-varying flow through a porous medium of a dusty viscous incompressible Bingham fluid in a circular pipe is studied. A constant pressure gradient is applied in the axial direction, whereas the particle phase is assumed to behave as a viscous fluid. The effect of the medium porosity, the non-Newtonian fluid characteristics, and the particle phase viscosity on the transient behavior of the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is investigated. A numerical solution is obtained for the governing nonlinear momentum equations by using the method of finite differences.     

Investigation of the Relative Motion of a Viscous Fluid and a Porous Medium Using the Brinkman Equations

Exact solutions are obtained for the following three problems in which the Brinkman filtration equations are used: laminar fluid flow between parallel plane walls, one of which is rigid while the other is a plane layer of saturated porous medium, motion of a plane porous layer between parallel layers of viscous fluid, and laminar fluid flow in a cylindrical channel bounded by an annular porous layer.     

A Simple Hysteretic Constitutive Model for Unsaturated Flow

The present study covers the problem of rotation of a porous disk under a viscous incompressible fluid that fills the half-space above the disk, which is the generalization of the von Karman’s problem. It is found that, instead of solving the exact problem, which is rather complicated by coupling the motions of the free fluid and that contained inside the permeable disk, it is sufficient to solve a much simpler problem of the motion of the free fluid placed onto a permeable plane. Assuming the flow in the permeable disk is described by the Brinkman equations, we obtain a self-similar formulation of the problem. Employing this formulation, we also show that the boundary condition associated with continuity of the tangential strains and tangential velocity components is satisfied at the fluid–porous body interface. The coefficient for the vertical velocity component is furthermore obtained. Various extreme cases are identified.     

Fins and turbulence promoters for heat transfer enhancement in latent heat storage systems

One of the serious problems associated with the operation of PCM storage system is the heat transfer in and out of the element containing the PCM. This paper presents the results of an experimental investigation of the effects of radial fins and turbulence promoters on the enhancement of phase change heat transfer external to a horizontal tube submersed in the PCM with the working fluid flowing through it. The experimental measurements were realized on a bare cupper tube and an identical cupper tube fitted with radial fins. The fins investigated are 40, 60, 120 and 180 mm diameters. A turbulence promoter made of stainless steel wire of 1.0 mm diameter coiled in a helical form with a pitch of 25.0 mm was inserted into the cupper tubes. The tests were realized on bare tubes, finned tubes and finned tubes with the turbulence promoter inserted into the finned tubes. The measurements were realized for the working fluid temperatures in the range of −10 °C, to −25 °C and six values of the mass flow rate ranging from 0.013 to 0.031 kg/s. The position of the phase interface was photographed by a high resolution digital camera and scanned to determine the real interface position by comparison with a precision measuring scale. The results of the phase interface position, velocity of the interface, solidified mass fraction and the time for complete solidification are presented in function of the working fluid temperature, the working fluid mass and the tube arrangements. The results are presented and discussed.     

Hydrodynamic action of the fluid slowly flowing around a spheroidal particle covered by a viscous film

A steady problem of a slow axisymmetric flow of a viscous incompressible fluid around an oblate spheroid covered by a viscous film is solved analytically with the use of the Stokes approximation. Surface tension on the interface between the fluids is taken into account. Expressions for velocity components and stream functions are presented. A formula for determining the force action of the incoming flow onto the oblate spheroid is derived.     

Stability of viscous flow in a rotating porous medium in the form of an annulus: The small-gap problem

The paper deals with the linear stability analysis of laminar flow of a viscous fluid in a rotating porous medium in the form of an annulus bounded by two concentric circular impermeable cylinders. The usual no-slip condition is imposed at both the boundaries. The resulting sixth order boundary value, eigenvalue problem has been solved numerically for the small-gap case by the Runge-Kutta-Gill method, assuming that the marginal state is stationary. The results of computation reveal that the critical Taylor number increases with decreasing permeability of the medium. The problem is found to reduce to the case of ordinary viscous flow in the annulus obtained by Chandrasekhar,¹ when the permeability parameter tends to zero.     

The effect of an additional boundary condition on the plane creeping flow of a second-order fluid

A similarity solution is obtained for the two-dimensional creeping flow of a second-order fluid with non-parallel porous walls. The resulting ordinary differential equation is fifth order. Thus, an additional velocity boundary condition is needed, the other four being due to the usual no-slip conditions. Having chosen to prescribe the rate of shear at the wall, the problem is solved by a standard numerical routine. A singular perturbation analysis is developed for small values of the Deborah number. A type of boundary layer forms for which the viscous Newtonian case is the outer solution.     

Viscous fluid flow induced by rotational-oscillatory motion of a porous sphere

Viscous fluid flow induced by rotational-oscillatorymotion of a porous sphere submerged in the fluid is determined. The Darcy formula for the viscous medium drag is supplementedwith a term that allows for the medium motion. The medium motion is also included in the boundary conditions. Exact analytical solutions are obtained for the time-dependent Brinkman equation in the region inside the sphere and for the Navier–Stokes equations outside the body. The existence of internal transverse waves in the fluid is shown; in these waves the velocity is perpendicular to the wave propagation direction. The waves are standing inside the sphere and traveling outside of it. The particular cases of low and high oscillation frequencies are considered.     

Experimental studies of model porous media fluid dynamics

The three-dimensional, steady flow velocity components of a viscous, incompressible, Newtonian fluid in model porous media were measured. The model porous geometries were constructed from 3 mm glass rods. A laser Doppler anemometer was used to measure two of the velocity components and the third was calculated by integrating the continuity equation. The effects of viscous drag, inertial flow fields and eddy losses in the model were studied. The results showed that the measured flow was laminar and stable such that micromixing of the fluid was absent. Inertial flow effects were absent due to high viscous drag coefficients.