Showing papers in "Numerical Heat Transfer Part A-applications in 1983"
TL;DR: In this paper, a general numerical method for two-dimensional incompressible flow and heat transfer in irregular-shaped domains is presented, where the calculation domain is first divided into six-node macroelements, and each macroelement is divided into four three-node triangular subelements.
Abstract: The formulation of a general numerical method for two-dimensional incompressible flow and heat transfer in irregular-shaped domains is presented. The calculation domain is first divided into six-node macroelements. Then each macroelement is divided into four three-node triangular subelements. Polygonal control volumes are associated with the nodes of these elements. All dependent variables other than pressure are stored at the nodes of the subelements, and they are interpolated by functions that respond appropriately to an element Peclet number and the direction of an element-averaged velocity vector. The pressure is stored only at the vertices of the macroelements and is interpolated linearly in these elements. The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes. An iterative procedure akin to SIMPLER is used to solve the discretization equations.
313 citations
TL;DR: In this paper, a solution methodology has been employed that enables the fully developed regime in a duct of periodically varying cross section to be determined without dealing with the entrance region of the duct.
Abstract: A solution methodology has been employed that enables the fully developed regime in a duct of periodically varying cross section to be determined without dealing with the entrance region. ...
72 citations
TL;DR: In this article, a numerical method involving finite elements is presented for the solution of multidimensional problems of heat transfer with phase transformation, where both the media and the energy equation on the change of phase interface are regarded as independent governing equations, when solved through the use of a finite-element formulation, yield the temperature distribution in the media as well as the continuous displacement of the interface.
Abstract: A numerical method involving finite elements is presented for the solution of multidimensional problems of heat transfer with phase transformation. Specific to the method is that both the energy equation in the media and the energy equation on the change of phase interface are regarded as independent governing equations which, when solved through the use of a finite-element formulation, yield the temperature distribution in the media as well as the continuous displacement of the interface. Specific examples illustrate the ability of the method to handle problems with arbitrary boundary conditions which result in irregular two-dimensional shapes of the change of phase interface.
66 citations
TL;DR: In this paper, the simulation of the in-package pasteurization process for fluids contained in bottles or cans is considered, and a variable step implicit time integration technique coupled with a quasi-Newton nonlinear equation solver is employed.
Abstract: The problem considered in this paper is the simulation of the in-package pasteurization process for fluids contained in bottles or cans. In a typical pasteurization operation, the product enters the pasteurizer at a temperature of about 36°F and passes through several progressively hotter zones, which raise its temperature to approximately 140°F. This temperature of 140°F is maintained in the holding zone. The product then passes through several progressively cooler zones, which lower the temperature to 70-80°F This process was simulated by using a penalty Galerkin finite-element procedure. A variable step implicit time integration technique coupled with a quasi-Newton nonlinear equation solver was employed. The numerical results are in excellent agreement with experimental results.
55 citations
TL;DR: In this paper, a numerical method is presented for predicting the laminar and turbulent flow of a binary gas mixture along a plane vaporizing liquid film, including the shear layer flow including the heat and mass transfer at the gas-liquid interface.
Abstract: A numerical method is presented for predicting the laminar and turbulent flow of a binary gas mixture along a plane vaporizing liquid film. The shear layer flow including the heat and mass transfer at the gas-liquid interface is described by a system of boundary-layer equations. Each of the parabolic equations is numerically solved using an implicit finite-difference method of Hermitiah type. However, the overall solution procedure handles the coupled differential equations together with the boundary conditions in an explicit manner. Polynomials in terms of temperature are used to approximate the physical properties of the gas components at 1 atm pressure. Turbulence is accounted for by the algebraic eddy viscosity approach of Cebeci and Smith. The accuracy and efficiency of the numerical procedure developed is demonstrated for various temperatures of the external flow. A comparison of the numerical results with measurements in terms of flow profiles and Stanton numbers indicates good agreement.
48 citations
TL;DR: The results of a numerical simulation of natural convection in a vertical rectangular porous enclosure subjected to a horizontal temperature differential are presented in this paper, which provides a clear physical picture of the development process as R is increased toward asymptotically high values (R →).
Abstract: The results of a numerical simulation of natural convection in a vertical rectangular porous enclosure subjected to a horizontal temperature differential are presented. By use of the stable exponential differencing computation scheme, values of the Darcy-Rayleigh number R have been obtained which are substantially larger than those in previous numerical studies. The present results provide a clear physical picture of the development process as R is increased toward asymptotically high values (R →). Correlations for the heat transfer rate are presented for four different aspect ratios and are compared with earlier experimental and theoretical results.
46 citations
TL;DR: In this paper, the capabilities of a new control volume finite element method (CVFEM) are demonstrated by its application to four different example problems, and the results are compared with exact solutions or with the results of independent numerical and experimental investigations available in the literature.
Abstract: The capabilities of a new control volume finite-element method (CVFEM) are demonstrated by its application to four different example problems. Whenever possible, the results are compared with exact solutions or with the results of independent numerical and experimental investigations available in the literature. These comparisons indicate that the proposed CVFEM can successfully solve two-dimensional elliptic fluid flow and heat transfer problems in regular- and irregular-shaped domains.
46 citations
TL;DR: In this paper, the authors considered natural convection flows induced in vertical channels by heat sources situated at the channel inlet, where a channel plume is created by a horizontal line source, while a chimney-like flow is induced by a uniformly distributed source.
Abstract: Natural convection flows induced in vertical channels by heat sources situated at the channel inlet are considered. A channel plume is created by a horizontal line source, while a chimneylike flow is induced by a uniformly distributed source. Numerical solutions were carried out for both problems. Supplementary results were obtained from a fully developed model, which was further specialized for the case in which buoyancy effects dominate the frictional effects. Results were also adapted from available solutions for the classical free plume. For short, wide channels, the uniformly distributed source induces a larger mass flow than does a line source of the same strength, while for tall, narrow channels, the induced flows are equal. On the other hand, the bulk temperature rise associated with the uniform source is smaller than (or, in the limit, equal to) that associated with an equal-strength line source. Furthermore, for short, wide channels, the mass flow and bulk temperature results for the ch...
40 citations
TL;DR: In this article, a new simple stable approach to the numerical solution of problems in fluid flow and heat transfer has been developed, which avoids the stability problems of the skew upwind difference scheme while reducing the inaccuracies of numerical diffusion associated with upwind differencing.
Abstract: A new simple stable approach to the numerical solution of problems in fluid flow and heat transfer has been developed. The new approach avoids the stability problems of the skew upwind difference scheme while reducing the inaccuracies of numerical diffusion associated with upwind differencing. The origin of the instability is examined. Skew upwind differencing is compared with the proposed scheme for some idealized numerical results. The numerical computations presented show the superiority of the new scheme with respect to the shortcoming noted for the skew upwind scheme.
29 citations
TL;DR: In this article, a finite-difference numerical procedure was used to determine the interactions between the fin and cylinder boundary layers through the elliptic nature of the solution technique, and heat transfer correlations were developed to predict local and total heat transfer rates for both the fin as a function of the three governing dimensionless parameters: Rayleigh number, Prandtl number, and fin conduction parameter.
Abstract: Conjugate heat transfer by steady laminar natural convection from an isothermal circular cylinder with one infinitely long vertical plate fin has been studied by a finite-difference numerical procedure. Interactions between the fin and cylinder boundary layers are determined through the elliptic nature of the solution technique. Heat transfer from both the fin and the cylinder is less than predicted, disregarding the complex interactions. A fin of low conductance reduces the total heat transfer below the free-cylinder value. Fins of large conductance enhance the total heat transfer by a few percent. Heat transfer correlations have been developed to predict local and total heat transfer rates for both the fin and the cylinder as a function of the three governing dimensionless parameters: Rayleigh number, Prandtl number, and fin conduction parameter.
29 citations
TL;DR: In this paper, the eigenvalue method is applied to problems in heat conduction and its formulation is decribed in terms of an examination of transient heat convection in a square slab, taking advantage of the availability of the exact solution.
Abstract: The eigenvalue method, which has been used by researchers in structure mechanics, is applied to problems in heat conduction. Its formulation is decribed in terms of an examination of transient heat conduction in a square slab. Taking advantage of the availability of the exact solution, we compare the accuracy and other numerical properties of the eigenvalue method with those of existing numerical schemes. The comparsion shows that, overall, the eigenvalue method appears to be fairly attractive. Furthermore, only a few dominant eigenvalues and their corresponding eigenvectors need to be computed and retained to yield reasonably high accuracy. Greater savings are attained in the computation time for a transient problem with long time duration and a large computational domain.
TL;DR: In this article, a method for numerically solving two-dimensional radiative and conductive problems was developed for the first time, which bypasses the unnecessary use of the integrodifferential energy transport equation and accounts for the two dimensionality of radiative fluxes.
Abstract: A method has been developed for numerically solving two-dimensional radiative and conductive problems. Unlike conventional approaches in which the radiative fluxes are assumed to be one-dimensional, the proposed method bypasses the unnecessary use of the integrodifferential energy transport equation and accounts for the two-dimensionality of the radiative fluxes. Energy conservation is directly taken within a circular control volume. In addition, nodal intensities in four directions are introduced as unknowns. The system of nonlinear algebraic equations is closed with the aid of the equation of transfer in the discretized form. With such a formulation, it is possible to derive, for any grid point j, a set of generalized equations that are readily applicable to other grid points simply by changing the indices; the radiation that arrives at the control volume from remote areas does not explicitly appear in the algebraic equations, but is implicitly accounted for.
TL;DR: In this paper, a finite difference method for the solution of the transient equation of transfer in a plane parallel medium is developed, which is based on the adding/doubling method.
Abstract: A finite-difference method for the solution of the transient equation of transfer in a plane parallel medium is developed. In this method the adding/doubling method is used by solving a form of the equation of transfer at discrete values of the transient variable. A number of initializations for the adding/doubling method are available. The accuracy of each is dependent on the size of the initial layer used. Once an initialization is chosen, reflection and transmission matrices are built, and both upward and downward radiance are calculated at interior points for all discrete values of the transient variable. The advantages of the method are that (1) calculations of all the transient intensity distributions may be found throughout the layer for specified layer thicknesses, (2) solutions may be obtained for a variety of boundary conditions, and (3) exact solutions are approached as the initial layer size and step size approach zero. Numerous distributions are plotted and compared for two different...
TL;DR: In this article, a finite-difference solution for the entrance region laminar fluid flow and heat transfer in square ducts is presented, which uses two-dimensional computer storage and a marching technique to save computation costs.
Abstract: A finite-difference solution is presented for the entrance region laminar fluid flow and heat transfer in square ducts. The solution procedure uses two-dimensional computer storage and a marching technique to save computation costs. The results presented are in excellent agreement with other published axial velocity measurements. The lateral velocities do not exhibit the previously reported oscillatory behavior found near a diagonal. Temperature profiles and Nussdt number data in the thermal entrance region for Pr = 6.0 are presented.
TL;DR: In this article, an improved k-e numerical procedure is presented for the calculation of two-dimensional turbulent recirculating flows in which the reattachment point is not predetermined, the procedure involves a two-stage calculation consisting of two computational passes.
Abstract: An improved k-e numerical procedure is presented for the calculation of two-dimensional turbulent recirculating flows. For flows in which the reattachment point is not predetermined, the procedure involves a two-stage calculation consisting of two computational passes. The k-e model is also modified by developing generalized expressions for Cμand Prt through incorporation of algebraic approximations for the Reynolds stress and scalar flux equations. As a result of these modifications, the turbulence model is sensitized to account for the effects of streamline curvature and pressure-strain (scalar) interaction, including wall damping. The merits of the improved procedure are assessed by comparison with experimental results.
TL;DR: In this article, vertical laminar buoyancy-induced flows were determined in a porous medium, such as coarse sand, saturated with cold water, and two regions of multiple solutions were found over a range of bounding temperature conditions in terms of a generalized temperature-ratio parameter R.
Abstract: Vertical laminar buoyancy-induced flows were determined in a porous medium, such as coarse sand, saturated with cold water. Two regions of multiple solutions were found over a range of bounding temperature conditions in terms of a generalized temperature-ratio parameter R. In the range 0 < R < ½, buoyancy force reversals occur across the thermal transport region. This results in flow reversals for some values of R. Further, there is a gap in R where numerical solutions were not found. It can also be shown mathematically that no solutions exist over a subrange of R, consistent with the numerical results. The ranges of R in which multiple solutions do exist are a narrow region below the lower edge of the gap and a wide region above it. In the lower region of multiple solutions, for each value of R, the several solutions found are rather similar. However, in the upper region, the pairs of solutions at the same values of R can be drastically different. One of the two upper-region solutions is largely...
TL;DR: In this paper, the accuracy of six numerical approximations of the convection terms in the conservation equations is examined for a steady, recirculating flow, and Quadratic upwind, central, nine-point, third-order, and power-law approximates are tested as alternatives to the widely used upwind I central hybrid method.
Abstract: The accuracy of six numerical approximations of the convection terms in the conservation equations is examined for a steady, recirculating flow Quadratic upwind, central, nine-point, third-order, and power-law approximations are tested as alternatives to the widely used upwind I central hybrid method Forced flow in a heated cavity is chosen as a reasonably severe test problem An exact analytical solution is used to evaluate truncation errors and solution errors Expressions for the leading truncated terms, including velocity derivatives, provide insight into why errors in the convection terms dominate errors in the diffusion terms for high grid Peclet numbers If an average solution error of less than 10% is desired, higher order methods are clearly superior to the first-order upwind/hybrid method One must have at least one finite domain within a wall gradient layer to reduce flux errors to 10% with the second-order central-difference method, whereas one must have at least two finite domains
TL;DR: In this paper, an extension of the classical MAC (marker and cell) method to curvilinear quadralateral cells is presented, which uses the contravariant velocity components to calculate the mass flux across the cells.
Abstract: An explicit finite-difference method has been developed for solving the equations of unsteady laminar natural convection in an arbitrarily shaped cavity. The method developed is an extension of the classical MAC (marker and cell) method to curvilinear quadralateral cells. These cells permit great geometric versatility. The boundary-fitted curvilinear coordinate system is used to generate a coordinate surface coincident with the boundary contours in the physical plane. The conservative form of the momentum equations in primitive variables are transformed to the rectangular computational plane. The MAC technique, formulated in the boundary-fitted coordinates, uses the contravariant velocity components to calculate the mass flux across the cells. A first-order forward difference approximation is used for the time derivative and second-order central difference approximation is used for the space derivatives. The finite-difference form of the continuity equation is satisfied for each cell, which is al...
TL;DR: In this article, a numerical model is constructed to analyze the simultaneous development of the dynamic and thermal regimes of an incompressible viscous ducted flow under the influence of sinusoidal pulsations.
Abstract: A numerical model is constructed to analyze the simultaneous development of the dynamic and thermal regimes of an incompressible viscous ducted flow under the influence of sinusoidal pulsations. The Navier-Stokes and energy equations are solved by a finite-difference method and by using asymptotic developments for the different dynamic and thermal functions. The model is validated by obtaining the Poiseuille regime for steady mean flow and by verifying Uchida's solutions for the unsteady dynamic components in fully developed flow. The model allows the description of Richardson's effect and depicts the existence of an annular effect for the pulsed temperature term.
TL;DR: In this article, a cylinder with external longitudinal fins rotates within a stationary shroud and a recirculating flow in the cavity between two adjacent fins and a throughflow in the clearance space between the fin tips and the shroud is computed.
Abstract: Laminar flow and the associated heat transfer are computed for the situation in which a cylinder with external longitudinal fins rotates within a stationary shroud. The situation is commonly encountered in electrical motors and generators. The cylinder rotation creates a recirculating flow in the cavity between two adjacent fins and a throughflow in the clearance space between the fin tips and the shroud. Results for shear force on the shroud and heat transfer rate are presented for a range of values of the Reynolds number and geometric parameters such as the fin spacing and the fin height. Streamline and isotherm patterns are shown to provide details of the convection process.
TL;DR: In this article, the authors demonstrate the feasibility of a numerical technique to provide generalized solutions to one-dimensional phase change problems by using finite differences for a finite region undergoing one or more phase changes.
Abstract: An attempt is made to demonstrate the feasibility of a numerical technique to provide generalized solutions to one-dimensional phase change problems. In this simple and effective numerical method finite differences are used for a finite region undergoing one or more phase changes. The nonlinearity of the problem is isolated by a technique that accurately tracks the interfaces for all times. The temperatures away from the interfaces are obtained by using simple recurrence equations, thereby avoiding costly nodal iterations.
TL;DR: In this paper, a simple multiple grid (MG) technique has been used to solve the linear system of equations arising from the finite-difference discretization of the Neumann problem for elliptic Poisson equations formulated in nonorthogonal curvilinear coordinate systems.
Abstract: A simple multiple grid (MG) technique has been used to solve the linear system of equations arising from the finite-difference discretization of the Neumann problem for elliptic Poisson equations formulated in nonorthogonal curvilinear coordinate systems. Fast, flexible, and simple solution methods for such problems are mandatory when they should act as, for example, pressure solvers in hydrodynamic codes for incompressible fluid flow. The robustness of the solution method chosen can be derived from the fact that only strong nonorthogonal grids have some influence on the asymptotic convergence rate. Problems including patched coordinate systems-for example, with interfaces describing material discontinuities-can also be handled without loss of efficiency.
TL;DR: In this paper, the authors analyzed the transient heat transport by solving the general hydro-dynamic equations of superfluid helium and showed that, according to the heat pulse duration or amplitude, one of these two effects can be accentuated.
Abstract: Transient heat transport is analyzed theoretically by solving the general hydro-dynamic equations of superfluid helium. The system that completely describes the heat transport process consists of two coupled equations, whose unknown quantities are the temperature T and the normal fluid velocity VN, under assumptions that are precisely noted. The transport process is both propagative and diffusive: the temperature front, due to a heat flux disturbance, propagates at the second sound velocity but decreases along the helium channel by a diffusion phenomenon. These two effects exist simultaneously, but it shown that, according to the pulse duration or amplitude, one of these phenomena can be accentuated. In particular, the higher the heat pulse amplitude, the more pronounced the diffusion.
TL;DR: In this article, a finite-difference model is used to predict the temperature distribution in a solid under a moving heat source, and a coordinate system centered on the heat source is adopted so that the temperature field relative to the source is taken to be fully developed and static.
Abstract: A method is presented in which a finite-difference model is used to predict the temperature distribution in a solid under a moving heat source. A coordinate system centered on the heat source is adopted so that the temperature field relative to the source is taken to be fully developed and static. As the method uses a nonuniform grid and allows for the variation of thermophysical properties to be specified, solutions can be determined for actual processes. Two processes are considered here: plasma arc heating in a hot machining process (where heating of the metal is carried out upstream of the cutting operation) and internal heating during chip formation in the machining.
TL;DR: In this article, a finite-element method for natural convection in a horizontally confined, infinite layer of fluid, heated from below and cooled from above, was computed by a finite element method.
Abstract: Natural convection in a horizontally confined, infinite layer of fluid, heated from below and cooled from above, was computed by a finite-element method. The behavior was modeled in terms of a two-dimensional roll cell with a square cross section. Triangular elements of three different sizes were tested for Pr = 10 and a range of Rayleigh numbers from the critical value up to 3000. The Nusselt numbers obtained by extrapolation to zero element size agree well with the experimental values of Silveston. The critical Rayleigh numbers computed for the three element sizes extrapolated similarly to close agreement with the theoretical value of 1708. Contrary to some prior claims, these extrapolations indicate that the truncation error for finite-element computations is significant. Hence computations for two or more element sizes, followed by extrapolation to zero element size, are essential.
TL;DR: In this paper, a fictitious finite-element layer method was developed to analyze transient thermal contact problems and applied to the two-dimensional thermal contact problem associated with transient forced-convection heat transfer in a channel.
Abstract: A fictitious finite-element layer method developed to analyze transient thermal contact problems is examined. The method obviates the early response errors and inaccuracies at the interface associated with conventional computational schemes. A comparison is made between the analytical and conventional computational solutions to the one-dimensional thermal contact problem; the results point to the need for an alternative computational approach. The fictitious finite-element layer method is introduced and applied to the one-dimensional thermal contact problem. It is shown to be superior to the approach with no fictitious layer without compromising computational economy. Finally, the method is successfully extended to the two-dimensional thermal contact problem associated with transient forced-convection heat transfer in a channel
TL;DR: In this paper, a numerical analysis has been performed on the three-dimensional natural convecrive heat transfer characteristics of a porous medium enclosed by a vertical concentric curved annulus heated from the inner surface and cooled from the outer surface with relation to the thermal insulation layer in the high-temperature ducting system of a high temperature gas-cooled reactor.
Abstract: A numerical analysis has been performed on the three-dimensional natural convecrive heat transfer characteristics of a porous medium enclosed by a vertical concentric curved annulus heated from the inner surface and cooled from the outer surface with relation to the thermal insulation layer in the high-temperature ducting system of a high-temperature gas-cooled reactor. Darcy's law and the Boussinesq approximation are assumed to be applicable. The governing equations are transformed into finite-difference equations, which are numerically solved by a successive over-relaxation procedure for a range of RaDa (a product of the Rayleigh number and the Darcy number) from 100 to 800. Two typical vertical arrangements (case A, in which a 90° bend is attached at the upper part of a vertical straight tube, and case B, in which it is attached at the lower part) were analyzed and compared with each other. The numerical results show that the flow field and the temperature profile have characteristics of those...
TL;DR: In this article, partial spectral expansions are applied to an example of natural convection in spherical annulus enclosures, and the computational effort required to arrive at a viable solution is discussed.
Abstract: The relatively new approximate method known as partial spectral expansions is applied to an example of natural convection in spherical annulus enclosures. The implementation of the method, as applied to the example, and the computational effort required to arrive at a viable solution are discussed. Results for the test case are compared to experimental results. It is found that the effort to arrive at an accurate solution increases nearly as the cube of the number of terms retained in the series and that a relatively few terms (usually less than eight) are required. The comparison with experimental data is favorable.
TL;DR: In this paper, a variable mass-lumping numerical model (nodal domain integration) of three-dimensional heat conduction in an inhomogeneous continuum is developed where the domain is discretized by tetrahedron-shaped elements and the state variable is approximated by linear trial functions.
Abstract: A variable mass-lumping numerical model (nodal domain integration) of three-dimensional heat conduction in an inhomogeneous continuum is developed The domain is discretized by tetrahedron-shaped elements and the state variable is approximated by linear trial functions. The resulting model represents the Galerkin finite-element, subdomain intergration, and integrated finite-difference methods as special cases and accommodates both Dirichlet and Neumann boundary conditions similar to a Galerkin finite-element model Consequently, a unified domain numerical model is developed that readily represents each of the abovementioned domain numerical methods and an infinity of finite-element mass-lumping schemes by the specification of a single constant model parameter. Application of the nodal domain integration model to linear heat conduction problems indicates that the degree of model mass lumping must vary to minimize the approximation error.