Showing papers in "Numerical Heat Transfer Part A-applications in 1982"

The numerical treatment of advection: a performance comparison of current methods

Abstract: A new “test problem ” for evaluating numerical models of advection is introduced, which exhibits many of the features encountered in practical advection-diffusion problems such as streamline curvature and steep variations in the advected variable. The problem was devised for the Third Meeting of the International Association for Hydraulic Research Working Group on Refined Modeling of Flow. At the meeting solutions of the problem generated by more than 20 different methods were reported. These methods are presented here and their relative performances compared and analyzed. No single method emerges as best, although some clearly perform better than others. It seems that advection modeling remains the art of compromise between diffusive and oscillatory errors.

Numerical calculation of two-dimensional natural convection in isothermal open cavities

Abstract: Numerical computations of free convection flow inside an isothermal open square cavity are presented The effects of Grashof number and inclination of cavity are examined Unsteady solutions are observed for Grashof number larger than 105 and cavity aperture facing upward

Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem

Abstract: The nonlinear inverse heat conduction problem is the calculation of surface heat fluxes and temperatures by utilizing measured interior temperatures in opaque solids possessing temperature-variable thermal properties. The most widely used numerical method for this problem was developed by Beck. The new sequential procedure presented here reduces the number of computer calculations by a factor of 3 or 4. The general heat conduction model used permits treatment of various one-dimensional geometries (plates, cylinders, and spheres), energy sources, and fin effects. The numerical procedure is illustrated for finite differences, but the basic concepts are also applicable to the finite-element method. Detailed descriptions of the computational algorithms are given and a nonlinear example is provided.

Hyperbolic heat transfer with reflection

Abstract: The non-Fourier model for heat transfer leads to a hyperbolic evolution problem describing the temperature solution. A one-dimensional case is considered for such a propagating heat wave reflected at a boundary. A primary goal is investigation of the effectiveness of numerical solution techniques for the case of a propagating heat front and the influence of different boundary conditions. Finite elements are employed in space and alternative time integration schemes are studied, including ordinary differential equation system integrators. The effect of solution “roughness” on the error and oscillations before and after reflection is examined and rates of convergence are numerically determined.

Heat transfer by free convection between two parallel flat plates

Abstract: A few numerical analyses of the free convection between two heated parallel plates have been carried out without using the boundary-layer approximation. In this paper, an approach that can determine the flow rate with consideration of the pressure drop is proposed. As an example of the calculation, the method is applied to Kettleborough's model. In addition, a comparison is made with Kettleborough's and Aihara's results.

Finite-element solution of the incompressible navier-stokes equations

Abstract: A finite-element procedure is presented for the calculation of two-dimensional, viscous, incompressible flows of a recirculating nature. As in finite-difference procedures, velocity and pressure are uncoupled and the equations are solved one after the other. Velocity fields are determined by first calculating intermediate velocity values based on an estimated pressure distribution and then obtaining appropriate corrections to satisfy the continuity equation. Illustrative examples involving flow in the entrance region between parallel plates, lid-driven cavity flow, and flow around an obstacle demonstrate the accuracy and capabilities of the proposed technique.

Natural and Mixed Convection Heat Transfer Around a Horizontal Cylinder within Confining Walls

Abstract: Laminar natural and mixed convection around a heated cylinder placed within confining walls is investigated numerically. The numerical scheme involves the use of a cylindrical network of nodes in the vicinity of the cylinder with a Cartesian mesh covering the remainder of the flow domain. Results are obtained for the streamlines, isotherms, and heat transfer coefficients. Effects of varying the ratio of width across the walls to cylinder diameter are also investigated. The results obtained are of direct use, for instance, in the design of certain thermal energy storage devices and ocean thermal energy conversion units under investigation.

Laminar natural convection along vertical square ducts

Abstract: Laminar natural convection of air along a vertical square duct open at both ends has been investigated for constant temperature and constant heat flux boundary conditions on the duct walls. The velocity of entering air at the bottom of the duct is assumed uniform at atmospheric pressure or the acceleration head of the entering fluid. The three-dimensional differential equations for momentum and energy have been solved numerically by a strongly implicit finite-difference procedure. The axial development of flow and heat transfer rates are presented, A curve fit for the mean heat transfer coefficient in the Rayleigh number range of 10 to 1000 results in the following relations: Constant wall temperature: Num = 0.512Ra0.285 Constant heat flux: Num = 0.53 Ra0.3 Comparison of the computed heat transfer rates with the measurements of W. Elen-bass for constant wall temperature square ducts show very good agreement over the entire Rayleigh number range of investigation.

A literature survey on numerical heat transfer

Abstract: (1982). A LITERATURE SURVEY ON NUMERICAL HEAT TRANSFER. Numerical Heat Transfer: Vol. 5, No. 4, pp. 369-420.

The calculation of turbulent flow in wide-angle\diffusers

Abstract: A method of calculating the properties of axisymmetric swirling and nonswirling turbulent recirculating flows in wide-angle diffusers is described and appraised. It is based on the numerical soluti...

A Numerical Study of the Effect of a Vertical Temperature Difference Imposed on a Horizontal Enclosure

Abstract: Results are presented for a numerical investigation of the flow and heat transfer in an enclosure subjected to comparable horizontal and vertical temperature differences. This problem is an extension of the unidirectional heat flow case and also has applications in the area of design. The regime characterized by dominant horizontal heat flow as well as that of dominant vertical heat flow are delineated. A stabilizing vertical temperature difference is found to decrease the vertical velocities next to the hot wall, but actually to increase the horizontal heat transfer. An interesting result is that for a destabilizing temperature difference, horizontal heat transfer can effectively occur from the cold wall to the hot wall if the vertical heat flux is high enough. Finally, actual heat transfer data are presented for a square enclosure and a Prandtl number of 0.71. A qualitative comparison with earlier experiments is made.

Heat Transfer Rates in Natural Convection at High Rayleigh Numbers in Rectangular Enclosures: a Numerical Study

Abstract: Numerical approximations to heat transfer rates for steady-state laminar free convection in rectangular cavities for Rayleigh numbers up to 107, angle of inclination varying up to ±90° with respect to the vertical direction, and aspect ratios 1, 5, and 10 are reported. These have been obtained with a penalty function finite-element algorithm using primitive fluid variables. The thermal structure and velocity fields of the flow are also presented for some of the most representative cases.

Stability of Mixed Time Integration Schemes for Transient Thermal Analysis

Abstract: A current research topic in coupled-field problems is the development of effective transient algorithms that permit different time integration methods with different time steps to be used simultaneously in various regions of the problems. The implicit-explicit approach seems to be very successful in structural, fluid, and fluid-structure problems. This paper summarizes this research direction. A family of mixed time integration schemes, with the capabilities mentioned above, is also introduced for transient thermal analysis. A stability analysis and the computer implementation of this technique are also presented. In particular, it is shown that the mixed time implicit-explicit methods provide a natural framework for the further development of efficient, clean, modularized computer codes.

Laminar Free Convection from a Vertical Plate with Nonuniform Surface Conditions

Abstract: A procedure is described for the calculation of the rates of momentum and heal transfer due to free convective flow along a vertical plate with either an arbitrarily prescribed surface temperature

Analysis of Natural Convection in the Space Between Concentric Vertical Cylinders of Different Height and Diameter

Abstract: Numerical finite-difference solutions were carried out for natural convection in the enclosed space between two concentric vertical cylinders, with each cylinder being maintained at a different uni...

Buoyancy-driven fluid flow and heat transfer in a pair of interacting vertical parallel channels

Abstract: Consideration is given to a system consisting of two parallel vertical channels that share a common wall across which heat is transferred from one channel to the other. The other walls of the system are characterized by prescribed surface temperatures that exceed the ambient temperature, and this induces a buoyancy-driven upflow in the channels. To cope with the strong interaction between the channels, a solution scheme was employed in which each channel was visited successively and iteratively. The single-channel solutions that were performed at each visitation were also iterative in character, with the computations carried out with a parabolic finite-difference method. Three parameters were varied during the course of the computations. These Included the dimensionless channel height, a dimensionless temperature difference, and the dimensionless position of the common wall between the channels. Results are presented for the surface-integrated heat transfer at each channel wall, the total system ...

Natural convection from a horizontal cylinder at small grashof numbers

Abstract: Numerical solutions for steady two-dimensional free convection from a horizontal circular cylinder are obtained for small Grashof numbers by the method of series truncation. The temperature distribution and flow variables are expanded as cosine and sine Fourier series, respectively, with variable coefficients. The governing partial differential equations are reduced to three coupled sets of nonlinear ordinary differential equations of second order. Detailed calculations are performed for Grashof numbers in the range I0−5 to 10 and a Prandtl number of 0.7. The flow patterns, isotherms, and heat transfer results thus obtained are compared with those from experimental and theoretical studies under similar conditions.

Comparison of Three Numerical Methods for Evaluation of Radiant Energy Transfer in Scattering and Heat Generating Media

Abstract: A plane-symmetric, gray model of coal particle suspensions is developed to test the accuracy of the low-order discrete ordinates and flux methods and of the differential approximation for calculating the radiant energy transport in multiply scattering and heat generating media bounded by diffusely reflecting surfaces. Results obtained by these three approximate techniques are compared with those computed by a high-order discrete ordinates method. In this study, the internal heat generation function is represented by a constant model and a diffusion-limited Arrhenius model; however, the solution method presented is applicable to arbitrary nonlinear and temperature-dependent heat production rates, ft is shown that the accuracy of flux methods decreases while the accuracy of the differential approximation increases with increasing optical thickness of the suspension. The approximate methods are found to yield more accurate results for temperature profiles than for profiles of the radiation intensity. With th...

Self-adaptive closed constrained solution algorithms for nonlinear conduction

Abstract: Self-adaptive solution algorithms are developed for nonlinear heat conduction problems encountered in analyzing materials for use in high temperature or cryogenic conditions. The nonlinear effects are noted to occur due to convection and radiation effects, as well as temperature-dependent properties of the materials. Incremental successive substitution (ISS) and Newton-Raphson (NR) procedures are treated as extrapolation schemes which have solution projections bounded by a hyperline with an externally applied thermal load vector arising from internal heat generation and boundary conditions. Closed constraints are formulated which improve the efficiency and stability of the procedures by employing closed ellipsoidal surfaces to control the size of successive iterations. Governing equations are defined for nonlinear finite element models, and comparisons are made of results using the the new method and the ISS and NR schemes for epoxy, PVC, and CuGe.

Thermal Instability of Mixed Convection Flow Over Inclined Surfaces

Abstract: The vortex instability of laminar mixed convection flow over isothermal, inclined flat plates is investigated by the linear stability theory. Critical Grashof and Reynolds numbers that predict the first occurrence of vortex rolls are obtained for fluids having a Prandtl number of 0.7 under various buoyancy force intensities and over a range of angles of inclination. It is found that at a given angle of inclination the flow becomes more susceptible to the vortex mode of instability as the buoyancy force increases. However, for a given bouyancy force intensity, the susceptibility of the flow to the vortex mode of instability decreases as the plate is tilted from the horizontal toward the vertical orientation, finally attaining the absolutely stable condition when the plate is vertical. The results are also compared with analytical results for the wave mode of instability.

Polynomial Approximation Solution of Heat Transfer by Conduction and Radiation in a One-Dimensional Absorbing, Emitting, and Scattering Medium

Abstract: A polynomial approximation method for the solution of heat transfer by conduction and radiation in an absorbing, emitting, and isotropically scattering medium has been developed. Consideration is given to a one-dimensional system bounded by two parallel gray, diffuse, isothermal walls. A function f(t) representing the relation between incident radiation and temperature is defined and approximated by a polynomial equation over the entire optical thickness. The integrodifferential equation is transformed, by introducing radiation operators, into simple expressions, which are then solved iteratively. The method of solution is shown to be relatively simple and converges very quickly to the exact solutions.

a Physical Approach to the Finite-Difference Solution of the Conduction Equation in Generalized Coordinates

Abstract: A finite-difference formulation is presented for modeling conduction heat transfer in a generalized nonorthogonal curvilinear coordinate system. A control volume energy balance approach is taken in this work, and this leads to a formulation that permits direct physical interpretation. The inclusion of a convective boundary condition is demonstrated by example, and it is shown that this condition can be used to implement convective, Neumann, adiabatic, and Dirichlet boundary constraints. Three examples are examined to demonstrate the application of the generalized nonorthogonal formulation. For the three examples examined, the results agree well with previous solutions, where they are available. The examples are also used to provide the first application of the modified strongly implicit procedure for solving the algebraic equation system of a nonorthogonal coordinate formulation. The procedure is observed to perform well on all three test problems.

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

Abstract: The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Some New Finite-Difference Schemes for Parabolic Differential Equations

Abstract: Finite-difference schemes for parabolic differential equations are considered. It is well known that the Crank-Nicolson scheme can lead to considerable inaccuracy if the time step is large or the initial-value function is unfavorable. Methods that overcome these defects are known but, computationally, are considerably more expensive. Two families of schemes are presented here which also overcome these deficiencies in the Crank-Nicolson scheme but which involve no extra amount of computation.

Numerical Solution of the Contact Interface Temperature with Internal Thermal Radiation and Conduction Effects

Abstract: The transient temperature distribution of two semi-infinite media at different temperatures that are suddenly brought into contact is investigated. The effect of thermal radiation in the hot medium is considered. Solutions are obtained by a hybrid technique, using an explicit fourth-order Runge-Kutta method for the time variable and the finite-difference method for the space variable. A variable grid spacing system utilizing hyperbolic sine functions is incorporated to extend the computational boundary as well as to minimize the computation time and the number of nodal points. The technique is shown to be relatively simple and accurate, and illustrative solutions are presented for the transient contact temperature after sudden contact of molten uranium with molten sodium.

Instant nonsimilarity solutions of unsteady laminar boundary-layer heat transfer

Abstract: An instant nonsimilarity method is proposed for the analysis of unsteady thermal boundary layers. The method is an improvement on the instant similarity method, which assumes that similarity solutions are obtained instantly by deleting time derivative terms that cause nonsimilarity in the boundary-layer energy equation. A basic feature of the nonsimilarity solution is that the nonsimilar terms in the conservation equations are retained without approximation, while those in derived auxiliary equations are selectively neglected. Therefore, more accurate results are obtained. The method is illustrated by analyzing the problems of unsteady laminar forced convection heat transfer from a rotating disk and at the two- and three-dimensional stagnation points due to a step change in surface temperature. The flow is steady and incompressible and has constant physical properties. Numerical results are compared with data from the literature. Excellent agreement is obtained at both short and long times.

Further results on the heat transfer to low-prandtl-number fluids in pipes

Abstract: Numerical predictions have been made of heat transfer to low-Prandtl-number fluids in pipes with constant wall heat flux. The turbulence model employed is of the two-equation (k-)c kind in the core and the one-equation (k) kind in the near-wall region. Fluids with Prandtl numbers in the range 0.007-0.045 have been examined, in the Reynolds range from 7600 to 106. Temperature profiles and Nusselt numbers are in fairly good agreement with experiments on fully developed flow. Nusselt numbers for the thermal entrance region are found to be in reasonable agreement with the experimental results, which, however, display a large scatter.

Numerical and approximate numerical solutions to a three-dimensional mixed convection boundary-layer flow

Abstract: The three-dimensional laminar mixed convection boundary layer on a vertical heated surface exposed to a horizontal cross flow was investigated by using a full three-dimensional finite-difference code, local similarity, and a first-order perturbation solution The full three-dimensional equations were solved by a modified version of the box scheme of Keller and Cebeci The results indicate that natural convection dominates near the lower leading edge of the surface and at large values of the horizontal coordinate, whereas forced convection dominates near the vertical leading edge and at large values of the vertical coordinate In comparing the approximate methods of local similarity and first-order perturbation, where the perturbation parameter was taken to be α = gc β ΔTK/w2 ∞,, it was found that local similarity yielded more accurate results and required less computer time and programming effort

A note on approximation of one-dimensional heat transfer with and without phase change.

Abstract: A numerical model is developed for the one-dimensional heat transfer equation with and without phase change. The numerical model is based on the nodal dimain integration method, which can represent...