Showing papers in "Numerical Heat Transfer Part A-applications in 1980"

A new finite-element formulation for convection-diffusion problems

Abstract: A general numerical method for convection-diffusion problems is presented The method is formulated for two-dimensional problems, but its key Ideas can be extended to three-dimensional problems The calculation domain is first divided into three-node triangular elements, and then polygonal control volumes are constructed by joining the centroids of the elements to the midpoints of the corresponding sides In each element, the dependent variable is interpolated exponentially in the direction of the element-average velocity vector and linearly in the direction normal to it These interpolation functions respond to an element Peclet number and become linear when it approaches zero The discretization equations are obtained by deriving algebraic approximations to integral conservation equations applied to the polygonal control volumes The proposed method has the conservative property, can handle problems in the whole range of Peclet numbers, and avoids the false-diffusion difficulties that commonly afflict o

On the calculation of turbulent heat transport downstream from an abrupt pipe expansion

Abstract: A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion Computations employed an adaptation of the TEACH-2E computer program with the standard model of turbulence Emphasis is given to the simulation, from both a physical and numerical viewpoint, of the region in the immediate vicinity of the wall where turbulent transport gives way to molecular conduction and diffusion Wall resistance laws or wall functions used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall Predictions of expermental data for a diameter ratio of 054 show generally encouraging agreement with experiment At a diameter of 043 different trends are discernible between measurement and calculation though this appears to be due to effects unconnected with the wall region studied

A semi-implicit calculation procedure for flows described in boundary-fitted coordinate systems

Abstract: A semi-implicit numerical procedure is described for solving the Navier-Stokes equations in boundary-fitted coordinate systems. The procedure solves the steady-state equations directly without marching in time, and in the current study it is applied to flows with a predominant flow direction. Two illustrative flow situations have been analyzed and are reported. The required computing times are modest, and are less than those for fully explicit schemes, when the steady-state behavior is of prime concern.

Natural convection in a vertical channel: i. interacting convection and radiation. ii. the vertical plate with and without shrouding

Abstract: Numerical finite-difference solutions enabled the determination of heat transfer rates for pure natural convection and for Interacting natural convection and radiation in a vertical parallel plate channel of finite height. Attention was focused on the effect of the thermal boundary conditions and on the role of radiation as an enhancement mechanism. The results also enabled comparisons of the heat transfer from a single isothermal vertical plate with that for a plate that is shrouded by an adiabatic wall situated parallel to the plate. For pure convection and at intermediate and large Grashof numbers, the rate of heat transfer for a channel with two Isothermal equt-temperature walls exceeds by more than a factor of 2 that for a channel with one isothermal wall and one adiabatic wall (note that the ratio of active heat transfer areas for the two cases Is equal to 2). At lower Grashof numbers, the heat transfer rates differ only slightly. Radiation effects were explored for the case of a channel having one ...

Numerical solution for free convection between concentric spheres at moderate grashof numbers

Abstract: Steady axisymmetric natural convection between two isothermal concentric spheres is Investigated by the method of series truncation. The flow variables and temperature distribution are expressed as series of orthogonal Gegenbauer functions and Legendre polynomials, respectively, with variable coefficients. Thus, the governing equations are reduced to three coupled sets of nonlinear ordinary differential equations of the second order with two-point boundary conditions. Numerical solutions are obtained by truncating the series at a certain stage and by using step-by-step methods. Detailed calculations are carried out for Grashof numbers in the range 1000-20,000 and for Prandtl numbers equal to 0.02, 0.7, and 6. Flow patterns, velocity components, and heat transfer results obtained are compared with published results.

Numerical solutions to the partially parabolized navier-stokes equations for developing flow in a channel

Abstract: The partially parabolized Navier-Stokes equations are a set of approximate governing equations that are applicable to flows possessing a predominant flow direction and are obtained when terms representing viscous diffusion of momentum in the main flow direction are dropped from the full Navier-Stokes equations. These reduced equations differ from Prandtl's boundary-layer equations in that no further simplifying assumptions have been made regarding the transverse pressure gradients and transverse momentum equations. Hence, transmission of influences through pressure can be significant even against the main flow direction. The present study was motivated by an interest in evaluating the merits of this reduced flow model for conditions where the boundary-layer equations are known to be inadequate. The principle features of a numerical scheme used to solve the partially parabolized Navier-Stokes equations are described. Results for the flow in the inlet region of a channel are compared with solutions to the f...

Natural convection between two concentric spheres: transition toward a multicellular flow

Abstract: A moderate temperature difference maintained between two concentric spherical surfaces induces, in steady state, unicellular toroidal movements in the enclosed fluid. Beyond a critical temperature difference, the flow becomes unstable and the convective phenomena rearrange into counter-rotating toroidal cells. A two-dimensional axisymmetric numerical model confirms the existence of a unicellular regime and shows that, beyond the critical conditions and for the same set of parameters, two convergent solutions can be obtained. One is unicellular and the other is bicellular; in the latter, the additional cell appears at the top of the layer. The initial conditions determine which one of these two will be established. This transition is investigated as a function of several parameters and the results are compared with the experimental results in the literature.

Quasi-three-dimensional modeling of flow in mhd channels

Abstract: A set of two-dimensional turbulent boundary-layer equations that describe the three-dimensional fluid flow in a magnetohydrodynamic channel is outlined. The equations are solved by an implicit finite-difference scheme: a method of calculating the pressure gradient is used that avoids the need to iterate over the coefficients of the difference equations. The numerical method is tested by applying it to low- and high-speed flows over a flat plate. It is shown that the governing equations fully satisfy the three-dimensional conservation laws. The importance of accounting for three-dimensional effects is assessed, and an advanced technique for bringing out better the interaction between the boundary layers on sidewalls and electrode walls is discussed.

Analysis of Nusselt-type condensation on a vertical fluted surface

Abstract: This analysis considers isothermal flow and gravity-controlled condensation on a vertical fluted surface. In the initial part of the analysis, isothermal flow (drainage), which mainly occurs in the trough region of the flute, is considered, and velocity profiles, parametric dependences, etc. are studied. The simplified form of the equation of motion is solved by using the orthogonal collocation technique, which is particularly suitable for this kind of problem. In the second part, the condensation of a vapor on the fluted surface is studied with the basic assumptions required in Nusselt's analysis. The average Nusselt number for a given length of the tube is computed by solving the surface tension-governed equation of motion, while the Reynolds number is calculated by the method mentioned earlier. As a result, the Nusselt number as a function of Reynolds number can be computed for a given set of other parameters.

Buoyancy effects on heat and mass transfer in boundary layer on a continuous, moving horizontal plate

Abstract: The combined effects of buoyancy forces from thermal and mass diffusion in laminar boundary layer adjacent to a continuous, horizontal flat plate moving through an otherwise quiescent fluid are studied analytically by the local nonsimilarity method of solution. In the analysis, the diffusion-thermo and thermo-diffusion effects as well as the interfacial velocities due to mass diffusion are neglected. Numerical results are presented for a Prandtl number of 0.7, with Schmidt numbers of 0.6 and 2.0, for thermal buoyancy parameter Grx/Rex s/2 ranging from 0 to 1.0 and relative buoyancy parameter N = Grx,c/Grx from —0.5 to 2.0. In general, it has been found that the wall shear stress and the surface heat and mass transfer rates increase with increasing thermal buoyancy force. These quantities are further increased when the buoyancy force from mass diffusion assists the thermal buoyancy force, but are decreased when it opposes the thermal buoyancy force. While a Schmidt number of 0.6 is found to yield higher wa...

Natural convection heat transfer performance evaluations for discrete-(in-line or staggered) and continuous-plate arrays

Abstract: Basic heat transfer results for natural convection in an array of vertical in-line plate segments were obtained by numerical finite-difference solutions and are tabulated along with previously computed results for staggered and continuous-plate arrays. These results were employed as the basis of three performance comparisons Involving alt three types of arrays, with the continuous-plate array serving as a baseline case. In the first of these comparisons, it was found that the discrete-plate arrays can enhance the heat transfer rate by as much as 80-90% for fixed values of the wall-to-ambient temperature difference and heat transfer surface area. Furthermore, the use of discrete plates affords the possibility of reducing the wall-to-bulk temperature differences by as much as 35-40% at a fixed heat load and surface area. Reductions in the height of the array of up to 50% can also be achieved for conditions of fixed heat load and fixed wall-to-bulk temperature difference. The attainment of enhanced heat tran...

Spline collocation solution of combined radiation-convection in thermally developing flows with scattering

Abstract: A collocation method employing piece-wise cubic splines as approximating functions and Gaussian quadrature points as the collocation points provides a very convenient technique for the solution of thermally developing combined radiation-convection problems with and without radiation scattering. It is demonstrated that this method provides an alternative noniterative technique that with a small number of equations can produce a more accurate solution than the existing iterative methods. For the solution of these problems by the collocation method, one needs only the standard software available at any computing laboratory, thus considerably reducing the preparation time for successfully setting up the problem on the computer. It is shown that the existing solution for the case of thermally developing slug flow with radiation scattering suffers from inaccuracies.

Buoyancy effects on heat and mass transfer in boundary layers adjacent to inclined, continuous, moving sheets

Abstract: The combined buoyancy effects of thermal and mass diffusion on the heat and mass transfer characteristics of a laminar boundary layer adjacent to a continuous plate moving in a vertical or inclined direction through a quiescent ambient fluid are studied analytically. The surface of the plate is either maintained at a uniform temperature/concentration or subjected to a uniform surface heat/mass flux. The governing equations describing the nonsimilar boundary layers are reduced to a dimensionless form and then solved by a finite-difference method. Numerical results for the local friction factor and the local and average Nusselt/Sherwood numbers are presented for a Prandtl number of 0.7 with Schmidt numbers of 0.6 and 2.0. It is found that for the thermal buoyancy assisting condition, the wall shear stress and the surface heat/mass transfer rates are further increased when the buoyancy force from mass diffusion assists the thermal buoyancy force, but are reduced when the two buoyancy forces oppose each other...

Steady Periodic Heat Transfer in Fins of Arbitrary Profile

Abstract: An analysis is presented for steady periodic heat transfer In convecting fins of arbitrary profile. Both the eases of periodic variation of base temperature and periodic variation of environment temperature are considered. A method of complex combination is used to reduce the problem to two coupled linear boundary-value problems, which are subsequently solved by a noniterative numerical scheme. Numerical results are presented for rectangular, triangular, and convex parabolic fin geometries. Effects of amplitude and frequency of periodic disturbance on spatial temperature, base heat flux, and time-average fin efficiency are discussed

Forced-convection heat transfer in a duct having spanwise-periodic rectangular protuberances

Abstract: Laminar fully developed flow and heat transfer have been analyzed for a duct in which there ore cross-sectional nonuniformities. The nonuniformity consists of a spanwise-periodic array of rectangul...

Evaluation of finite-element formulations for transient conduction forced-convection analysis

Abstract: Numerical studies clarifying the advantages and disavantages of conventional versus upwind convective finite elements are presented along with lumped versus consistent formulations for practical conduction forced-convection analysis. A finite-element procedure for treatment of negligible capacitance fluid nodes is presented. The procedure is based on procedures used in finite-element structural dynamics to treat nodes with negligible structural mass. Two finite-element programs and a finite-difference lumped-parameter program used in the studies are discussed. Evaluation studies utilizing three convection and two combined conduction-convection problems are then presented and discussed. Additionally, the computational time saving offered by the finite element procedure is considered for a practical combined conduction-convection problem.

Effects of variable properties and internal heat generation on natural convection at a heated vertical plate in air

Abstract: Numerical results are presented for the transient and steady-state velocity field, temperature field, and heat transfer characteristics. These results were obtained by solving the partial differential equations describing the conservation of mass, momentum, and energy by an explicit finite-difference method in time-dependent form. Two cases were studied, namely the variable fluid property (VFP) case and the constant fluid property (CFP) case. Values of the velocity components u, v (absolute) and the temperature 8 in the VFP case are larger away from the plate and smaller near the plate than those in the CFP case. Further, the velocity and temperature fields are more prominent in the presence of heat sources than in their absence. Numerical results indicate that the wall heat transfer coefficient in the VFP case is about 30% higher than in the CFP case. This warrants further analyses of the effect of variable fluid properties on the flow and heat transfer characteristics. Another useful result is that the ...

Calculation of variable property heat transfer in ducts of annular cross section

Abstract: A calculation procedure for flow and heat transfer in ducts of annular cross section is described. This procedure is applied to study heat transfer in the laminar flow of water and ethylene glycol in vertical ducts. When only one wall is heated the effect of buoyancy is to cause a flow reversal, the onset of which is well predicted by the calculation method. An improved correlation parameter for this flow regime is identified. Results are also presented for a turbulent flow using a turbulence model that utilizes the turbulence kinetic energy as a parameter.

Finite-element analysis of nonlinear conduction problems subject to moving fields

Abstract: Through the use of a space-time warp, specialized moving finite elements are developed that can be employed to generate a nonlinear heat conduction model for situations involving traveling boundary and heat generation fields superposed on an initial state. To facilitate the solution of the resulting nonlinear finite-element formulation, a multilevel heuristic iterative solution strategy is developed. In order to demonstrate the versatility and accuracy of the moving elements and their associated nonlinear solution strategy, the results of several numerical experiments are presented.

Temperature distribution in generalized von karman rotating-disk flows

Abstract: The title problem is solved subject to the boundary conditions T(r,0) = σN n = 0 Tn · rn(ω/ν)IV2on the disk z = 0, and limz→∞,T = T∞ a constant. The similar velocity field leads to viscous heating proportional to r2 as well as r0. The nonsimilar temperature is found by superimposing N + 1 similar profiles Qn(z*) scaled by rn. It Is concluded that Q0(z*) exists only when the fluid at infinity corotates with the disk and at a lower rate. Specifically, (1) the temperature profile due to viscous heating of generalized von Karman disk flows is obtained, (2) the effects of Prandtl number, ambient fluid rotation, and degree of inhomogeneity N are discussed in detail, and (3) the limitations of the thermal boundary-layer approximation are delineated.

Spline-collocation solution of integral equations occurring in radiative transfer and laminar boundary-layer problems

Abstract: A collocation method for the solution of linear and nonlinear integral equations occurring in such physical applications as radiation heat transfer, radiative transfer in atmospheres, laminar boundary layers, and many others is described. The method employs piecewise Hermite splines as approximating functions and the Gaussian quadrature points as the collocation points. It is demonstrated that the method is considerably superior to the finite-element method both computationally and in accuracy. The collocation method is expected to be computationally faster than the finite-element method in view of the fact that the latter method requires double quadratures, in contrast to single quadratures for the collocation method. By virtue of being a high-order method, it requires only a small number of equations to produce the desired accuracy at a very small computational cost.

Modified partial-cell method for free-surface incompressible flow simulations

Abstract: A modified partial-cell method, SAMPAC, is presented to numerically calculate the time-dependent, viscous, incompressible flow of a fluid with a free surface. Lagrangian marker particles and partial cells are used to delineate the free surface, refine the surface velocity calculation, and enforce rigorous mass conservation in fluid. The axisymmetric Navier-Stokes equations are solved by a time-average, central-space differencing scheme that gives second-order accuracy to the computation, while the pressure field is found through direct matrix inversion. The versatility and accuracy of the method are illustrated in three sample calculations, which demonstrate satisfactory agreement with experimental and analytical results.

Finite-difference solution of boundary-layer equations

Abstract: In this article nonlinear third-order ordinary differential equations representing boundary-layer flows are reduced to integrodifferential equations, approximated by finite differences, and solved by a perturbed iterative scheme (PIS). PIS has a quadratic rate of convergence and is generally independent of initial guesses for the root.

An efficient algorithm for the numerical solution of the transient diffusion equation with an implicit formulation

Abstract: A new algorithm is developed for the numerical solution of the multidimensional transient diffusion equation with an implicit formulation. This algorithm can be considered as a generalization of the tridiagonal algorithm commonly used for the one-dimensional transient diffusion problem. It is demonstrated to be accurate, efficient, and reduce substantially the computation time and storage requirement generally associated with implicit numerical solutions to this class of problems. A simple problem of transient conduction in a two-dimensional rectangular solid is solved as an illustration. For an M x N node finite-difference grid, an implicit numerical solution with a direct matrix inversion will involve the inversion of an MN x MN matrix. The present algorithm, however, requires only the inversion of N matrices of dimension M x M. For even moderate values of M and N, the present algorithm represents a significant reduction in computational complexity.

Estimation of Transient Responses by Spectral Analysis of Simulated Stochastic Vapor Fraction Fluctuations in Boiling Flow

Abstract: Simulation of stochastic vapor fraction fluctuations in a flow-boiling channel is carried out using the drift-flux model by a method similar in principle to the Langevin technique. Vapor fraction fluctuations are studied at several channel axial locations. Deterministic information such as the propagation speed of vapor fraction perturba-tations is calculated by cross-covariance and cross-spectral analysis. Estimation of other types of transient responses is also possible.

Analysis of Natural Convection Due to Localized Heating in a Shallow Water Layer

Abstract: Natural convection due to localized heating from an array of horizontal cylinders in a shallow water layer has been simulated numerically by approximating the symmetrical region between cylinders as an enclosure with localized heating from a side. Calculations performed for a Rayleigh number range between 103 and 3 X 105 reveal a unicellular vortex motion characterized by three thermal boundary-layer regions (two vertical boundary layers at the sides of the enclosure and a horizontal boundary layer at the air-water interface) In the core region between the boundary layers, the temperature is approximately uniform along horizontal lines but increases slightly along vertical lines to provide a stratified condition. Heat transfer increases with increasing Rayleigh number and decreasing aspect ratio, slightly exceeding that associated with uniform heating from below.

Computational Considerations in Free-Molecule Conical Pore Diffusion

Abstract: (1980). COMPUTATIONAL CONSIDERATIONS IN FREE-MOLECULE CONICAL PORE DIFFUSION. Numerical Heat Transfer: Vol. 3, No. 4, pp. 499-503.