M. Manzan

Natural convection from a horizontal cylinder in a rectangular cavity

Abstract A numerical and experimental analysis is performed for natural convection heat transfer from a horizontal cylinder enclosed in a rectangular cavity. The temperature distribution in the air and the heat transfer coefficients are measured by a holographic interferometer and compared with numerical predictions obtained by a finite-element procedure based on the streamfunction-vorticity formulation of the momentum equations. The influence of the Rayleigh number and the geometry of the cavity on the heat transfer are investigated.

CFD simulation of refrigerated display cabinets

Abstract The finite element method is employed for the analysis of velocity and temperature distributions in refrigerated open display cabinets. The CFD code is based on the streamfunction-vorticity formulation, and incorporates a LES turbulence model. As an example of application, a vertical multi-deck cabinet is investigated under different operating conditions. The numerical results have been validated by comparison with experimental tests performed in accordance with the EN441 Standard. The influence of various design parameters has been investigated.

A general procedure for deriving stabilized space–time finite element methods for advective–diffusive problems

A procedure to derive stabilized space-time finite element methods for advective-diffusive problems is presented. The starting point is the stabilized balance equation for the transient case derived by Onate using a finite increment calculus approach. A description of the new stabilization method and a procedure for computing the stabilization parameter of the space-time solution is given. The efficiency of the stabilization approach is shown in the solution of some transient advective-diffusive problems, including the non-linear Burgers equation

Numerical analysis of heat and mass transfer in a passive building component cooled by water evaporation

Abstract In this paper, the behaviour of a special roofing system is investigated. It is a passive building component that consists of a ventilated roof with a maintained wet lower surface of the cavity over which flows the external air. The authors have carried out numerical simulations of the thermal field, flow field and water vapour concentration of air within the duct for thermal performance evaluation purposes. In order to obtain an estimate of the thermal cooling flux on the wet surface, suitable procedures were coded and linked to a commercial program for computational fluid dynamics (CFX 4.4). An original approach to solve a coupled heat and mass transfer problem is presented. Results of numerical simulations of the temperature field and the values of the mean specific heat and mass fluxes of the wet lower surface are shown. Numerical problems that have been dealt with, due to particular physical phenomena such as boundary coupled fields and radiation between cavity surfaces, are highlighted.

A STREAMFUNCTION-VORTICITY-BASED FINITE-ELEMENT FORMULATION FOR LAMINAR-CONVECTION PROBLEMS

Abstract The finite-element method is used to solve mixed-, farced-, and natural-convection problems in two-dimensional incompressible laminar flows. The streamfunction-vorticity equations are uncoupled and solved in sequence with the energy equation. The wall vorticity is evaluated in the framework of the streamfunction equation, and particular care is taken to specify inflow and outflow boundary conditions properly. The resulting scheme achieves convergence without the traditional need for upwinding, even for very high values of the Reynolds and the Rayleigh numbers. Stability and accuracy of the approach are demonstrated by the solution of three well-known test problems concerning mixed and forced convection downstream of a backward-facing step, and natural convection in a heated square cavity.

OPEN BOUNDARY CONDITIONS FOR THE STREAMFUNCTION -VORTICITY FORMULATION OF UNSTEADY LAMINAR CONVECTION

Abstract The streamfunction-vorticity formulation is used to analyze unsteady laminar-convection problems in two-dimensional incompressible flows. The Bubnov-Galerkin finite-element method and a sequential procedure are employed to discretize and solve the governing differential equations. Very accurate results are obtained by employing “advective derivative conditions” at the outflow for all the variables involved. The boundary conditions for the streamfUnction at internal walls are imposed during the assembly process, and the vorticity at inflow and wall boundaries is evaluated in the framework of the stream/unction equation. The accuracy of the approach is demonstrated by the solution of two well-known benchmark problems concerning forced convection over a circular cylinder in cross flow and mixed convection in a plane channel heated from below.

A PHYSICAL APPROACH TO FINITE-ELEMENT MODELING OF COUPLED CONDUCTION AND CONVECTION

Abstract Finite-element formulations for coupled conduction and convection problems are obtained by a direct approach based on energy balances, at both element and node levels. This way, clear physical interpretations are provided for all the essential steps of conventional finite-element procedures of the Galerkin type. In the examples, the finite-element formulation is validated first by comparison with the analytical solution of a typical benchmark problem. Then the capabilities of the finite-element method are demonstrated by the analysis of coupled conduction and convection problems of practical interest

Natural convection in rectangular open cavities

In this paper, we use a finite element discretization and a streamfunctionvorticity formulation to investigate natural convection in rectangular open cavities with the one vertical side heated and the two horizontal sides adiabatic. The numerical results concern streamfunction and temperature contours, and Nusselt number distributions for Pr = 1, several values of the Rayleigh number and two different aspect ratios. For the well documented square cavity problem, the average Nusselt numbers and the volumetric flow rates are compared with literature results.

A streamfunction–vorticity formulation of spatially periodic flows

We implement the spatially periodic boundary conditions in finite element solutions of the Navier-Stokes equations based on the streamfunction-vorticity formulation. Periodic boundary conditions are enforced at both inflow/outflow and lower/upper boundaries. As an example of application we consider the fluid flow, at two different Reynolds numbers, through an array of pin fins

Numerical And Experimental Analysis Of Heat Transfer From Two Horizontal Cylinders In A Cavity

In this paper, natural convection heat transfer from two horizontal heated cylinders in a rectangular cavity is analysed, both by computational and experimental method. The two horizontal cylinders are located one above the other in the vertical symmetry plane of the cavity. A finite-element procedure based on the streamfunction-vorticity formulation of the momentum and energy equations is employed for the numerical solution of the flow and thermal field. Computed results include plots of the flow and thermal field patterns, and plots of the distribution of the local Nusselt number on the cylinder surfaces. The experimental apparatus consists of a test cell, made by a rectangular enclosure filled with air, and of a holographic interferometer. The temperature distribution in the air is measured by real-time and double-exposure holographic interferometry. A comparison between computational and experimental results is carried out, revealing good agreement. Transactions on Engineering Sciences vol 18,