Transient natural convection flow over vertical cylinder with variable surface temperatures

An analysis is made for transient natural connective flow over a vertical cylinder with surface temperature of the cylinder varying as x ⁿ , a power function of distance from the leading edge. A Crank-Nicolson type of implicit finite difference method is used to solve the governing non-linear set of equations. Numerical results are obtained and presented for air and water with various n. The transient velocity and temperature profiles, local and average skin-friction and Nusselt numbers are shown graphically. The effects of exponent n on velocity and temperature profiles, skin-friction and rate of heat transfer have been analysed. The velocity and temperature profiles are compared with the available results in the literature and it is found to be in good agreement.     

On the solution of diffusion—convection equations by the space—time finite element method

A functional has been developed for the finite element solution of diffusion—convection problems. This functional is suitable for the application of the variational principle on discretization schemes in the space—time domain. This algorithm has shown to be computationally efficient over the conventional finite element discretization in the space domain alone. Numerical examples on one-dimensional energy transport have been included to illustrate the merit of this technique.     

Analysis of early-stage frost formation in natural convection over a horizontal cylinder

Frost growth process on a cold surface consists of two stages: The early-stage or one-dimensional growth of ice columns and multidimensional growth in the form of a porous structure. The transition time which marking these two stages is important for any numerical modeling of frost formation. This paper proposes a mathematical model to predict the transition time and frost properties in natural convection of frost formation over a cooled horizontal cylinder in the first stage of growth period. Comparison is performed among the results of this model and experimental observations reported in the literatures. It is observed that the presented model can be used more efficiently to determine transition time and frost properties in the early-stage of frost formation. Based on the obtained results a new correlation is developed for the duration time of early-stage of frost formation process (transition time) in natural convection.     

Some problems of the hydrodynamics of a horizontal cylinder with natural convection

The article examines the special features of vortex flow in the vicinity of the upper critical point, and approximating dependences are obtained for the point of detachment from the data of numerical solution and experiments.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 6, pp. 905–909, December, 1982.     

Heat transfer from a horizontal cylinder under mixed convection conditions

An investigation has been made of special features of heat transfer from horizontal wires under combined forced and free convection. It is shown that in counterflow, in contrast with auxiliary flow, the dependence of Nu(Re)_Ra=const bas a minimum. Near the minimum in the range 0.15 < Re²/Ra√Re < 1.5 there is a region where the heat transfer conditions are oscillatory.     

Natural convection from a vertical cylinder at very large Prandtl numbers

Summary The natural convection from a vertical cylinder, is determined in the limiting case of very large Prandtl number, the Grashof number remaining finite.     

Transient free convection flow past an impulsively started isothermal vertical cylinder with mass flux

This paper concern with the laminar flows, which arise in fluids due to the interaction of the force of gravity and density differences, caused by temperature differences and material or phase constitution for both air and water. A solution of laminar boundary layer equations has been obtained for the transient free convective flow past an impulsively started semi-infinite isothermal vertical cylinder with uniform mass flux. The solutions of the dimensionless, unsteady, coupled and non-linear governing partial differential equations are obtained by a more accurate, unconditionally stable and fast converging implicit finite difference scheme. The results show many interesting effects on velocity, temperature and concentration profiles and local as well as average shear stress, rate of heat and mass transfer. It is observed that there is a rise in the velocity due to the presence of mass diffusion.     

Free convection from a heated vertical cylinder embedded in a fluid-saturated porous medium

Summary We consider the free convection boundary layer flow induced by a heated vertical cylinder which is embedded in a fluid-saturated porous medium. The surface of the cylinder is maintained at a temperature whose value above the ambient temperature of the surrounding fluid varies as then ^th power of the distance from the leading edge. Asymptotic analyses and numerical calculations are presented for the governing nonsimilar boundary layer equations and it is shown that, whenn<1, the asymptotic flowfield far from the leading edge of the cylinder takes on a multiple-layer structure. However, forn>1, only a simple single layer is present far downstream, but a multiple layer structure exists close to the cylinder leading edge. We have shown that the fully numerical and asymptotic calculations are in stisfactory agreement, especially for exponentsn close to zero. Comparisons of the present numerical solutions obtained using the Keller-box method with previous numerical solutions using local methods are also given.List of symbols a radius - scaled streamfunctions - f ₀,f ₁,f ₂ inner zone streamfunctions whenn<1 - leading order streamfunctions inn>1, 1 asymptotic solution - F ₀,F ₁ outer zone streamfunctions whenn<1 - G large parameter satisfyingG=X ² lnG - g gravitational acceleration - K permeability of the porous medium - n exponent in prescribed temperature law - r radial co-ordinate - r rescaled radial co-ordinate - R Darcy-Rayleigh number - T temperature of convective fluid - T _w temperature of cylinder at leading edge - T ambient temperature of fluid - u velocity in axial direction - v velocity in azimuthal direction - w velocity in radial direction - x axial co-ordinate - x escaled axial co-ordinate - X dimensionless axial co-ordinate - thermal diffusivity of the saturated medium - coefficient of thermal expansion - constant in the boundary conditions forF ₀ - dimensionless radial co-ordinate - co-ordinate for the outer zone in then<1 solution - scaled radial co-ordinates - scaled fluid temperature - similarity variable for then=1 problem - nondimensionalisation constant (Eq. (9)) - viscosity of fluid - scaled axial co-ordinates - density of fluid - co-ordinate for the inner zone in then<1 solution - azimuthal co-ordinate - similarity variables for then>1 problem - streamfunction     

Prediction of frost deposition on a horizontal circular cylinder under natural convection using artificial neural networks

In the present work Artificial Neural Network is used to predict frost thickness and density around a cooled horizontal circular cylinder having constant surface temperature under natural convection for different ambient conditions. The database for ANN generated from the experimental measurements. In the present work a multilayer perceptron network is used and it is found that the back-propagation algorithm with Levenberg-Marquardt learning rule is the best choice to estimate frost growth due to accurate and faster training procedure. Experimental measurements are used for training and testing the ANN approach and comparison is performed among the soft programming ANN and experimental measurements. It is observed that ANN soft programming code can be used more efficiently to determine frost thickness and density around a cold horizontal cylinder. Based on the developed ANN wide range of frost formation over various cylinder diameters are determined and presented for various conditions.     

Nonlinear instability of mixed convection flow over a horizontal cylinder

Vortex shedding and instability of the mixed convection flow over a horizontal cylinder have been studied numerically for different flow directions with respect to the direction of buoyancy—with emphasis on assisting and opposing flows. Nonlinear instability and vortex shedding have been investigated with the help of the Landau equation—that is modified to identify critical Reynolds and Richardson numbers. Effects of flow direction are studied for a representative Richardson number. The average Nusselt number is estimated for all the cases to represent average heat transfer.     

Rubber covered rolls—the thermoviscoelastic problem. A finite element solution

The coupled thermomechanical behaviour of a layer of thermorheologically simple material bonded to a uniformly rotating rigid cylinder and indented by another rigid cylinder is studied by the finite element method. The various approximations necessary to reduce the problem to one of tractable size and the computational methods used are discussed in some detail. The complete thermal, deformation and stress fields may be computed. Some results, computed for a grid using ‘rectangular’ elements, presented graphically include the temperature distribution, the stress distribution near the bond surface, the contact pressure distribution and the asymmetric surface deformation of the rubberlike layer.     

Experimental study of laminar natural convection heat transfer from a vertical cylinder to slush nitrogen under constant heat flux conditions

Natural convection heat transfer from a vertical cylinder immersed in slush and subcooled liquid nitrogen and subjected to constant heat fluxes was investigated in order to determine the relative merits of slush nitrogen (SlN₂) for immersion cooling. A glass dewar was used as a test vessel in which a cylindrical heater was mounted vertically, and heat transfer measurements were carried out for SlN₂ and subcooled liquid nitrogen (LN₂) in the laminar flow range. The results revealed advantages of SlN₂ over subcooled LN₂ in natural convection cooling. The local temperatures of the heated surface surrounded by solid nitrogen particles are measured to increase at much slower rates than in subcooled LN₂, which is due to the latent heat of fusion of solid nitrogen. Even after the solid nitrogen particles surrounding the heater are apparently depleted, the average heat transfer coefficients for SlN₂ are still found to be greater than those for LN₂ with the improvement in heat transfer being larger for lower Grashof number regime. Our analysis also indicates that solid nitrogen particles in close proximity to heated surface do not discourage local convection due to the porous nature of SlN₂, making the heat transfer in SlN₂ more effective than in the case of solid–liquid phase change of nitrogen involving melting and conduction processes.     

Transient natural convection in a liquid during cooling

An experimental study was made for an analysis of cooling of a liquid under conditions of natural convection.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 1, pp. 5–12, July, 1979.     

Heat transfer in turbulent free convection around a horizontal nonisothermal cylinder

The heat transfer of a horizontal cylinder in turbulent free convection and for a quadratic law of temperature variation on its surface is investigated numerically: 10⁹Ra 10¹³, Pr=0.71.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 1, pp. 28–34, July, 1985.     

Mixed convection around a horizontal circular cylinder immersed in a Darcy flow

The forced and free mixed convection problem around a horizontal circular cylinder in a fluid-saturated porous medium is investigated at small Peclet number with Gr/Re = O(1). The Darcy flow model is used for the velocity field. The method of matched asymptotic expansions is used to obtain asymptotic solutions for small Peclet number. It is shown that, up to the present order of approximation, natural convection has no effects on the temperature field, and the effects of the parameter Gr/Re on the velocity field are examined in detail.     

Panel flutter optimization—a refined finite element approach

This paper presents the results of an aeroelastic optimization study. In this study the weight of a large aspect ratio panel immersed in high Mach number supersonic flow is minimized subject to the requirement that a critical aeroelastic parameter for flutter be held within specified limits. A refined finite element technique is used to model the panel flutter equilibrium equations, equations which act as constraints on the design search. The optimization mechanism itself is studied and discussed to provide qualitative results which may be useful to the solution of other aeroelastic optimization problems. The numerical results of this investigation are compared to converged numerical results to illustrate finite element accuracy. The results of the study show that the weight savings and material distribution found with an effective finite element model are comparable to those found by more complicated numerical methods.     

The scaled boundary finite element method—alias consistent infinitesimal finite element cell method—for diffusion

The scaled boundary finite element method, alias the consistent infinitesimal finite element cell method, is developed starting from the diffusion equation. Only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals need to be evaluated. Essential and natural boundary conditions on surfaces and conditions on interfaces between different materials are enforced exactly without any discretization. The solution of the function in the radial direction is analytical. This method is thus exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions. The semi‐analytical solution inside the domain leads to an efficient procedure to calculate singularities accurately without discretization in the vicinity of the singular point. For a bounded medium symmetric steady‐state stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption. Copyright © 1999 John Wiley & Sons, Ltd.