Speed of energy propagation for parabolic equations.
Analysis of system described by heat equation where disturbance propagates with infinite speed as function of time
PROPAGATION VELOCITY↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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An implicit-iterative solution of the heat conduction equation with a radiation boundary condition
For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.
Williams, S. D.↗
Asynchronous and corrected-asynchronous numerical solutions of parabolic PDES on MIMD multiprocessors
A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent process. Removing the synchronization constraint has the potential of speeding up the computation. The authors present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although the discussion concentrates on the Euler scheme for the solution of the heat equation, it has the potential for being extended to other schemes and other parabolic partial differential equations (PDEs). These schemes are analyzed and implemented on the shared memory multi-user Sequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that the synchronization penalty can be about 50 percent of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time level, and with the problem dimension. The efficiency of the AS may reach 90 percent and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient, but provides more accurate results for intermediate (non steady-state) values.
Amitai, Dganit↗
On associated radial heat expansions
Procedure for obtaining series representation avoiding use of complex expansion in solution of radial heat equation
HEAT EQUATION↗
Dual Functions and Heat Expansions
Radial heat polynomial transformations in series expansions of heat equation
HEAT EQUATION↗
Series representation of generalized temperature functions.
Maclaurin series expansion representation of generalized heat equation
HEAT EQUATION↗
Solutions of the heat conduction equation in multilayers for photothermal deflection experiments
Analytical expressions for temperature and laser beam deflection in multilayer medium is derived using Green function techniques. The approach is based on calculation of the normal component of heat fluxes across the boundaries, from which either the beam deflections or the temperature anywhere in space can be found. A general expression for the measured signals for the case of four-quadrant detection is also presented and compared with previous calculations of detector response for finite probe beams.
Mcgahan, William A.↗
Mathematical equations for heat conduction in the fins of air-cooled engines
The problem considered in this report is that of reducing actual geometrical area of fin-cooling surface, which is, of course, not uniform in temperature, to equivalent cooling area at one definite temperature, namely, that prevailing on the cylinder wall at the point of attachment of the fin. This makes it possible to treat all the cooling surface as if it were part of the cylinder wall and 100 per cent effective. The quantities involved in the equations are the geometrical dimensions of the fin, thermal conductivity of the material composing it, and the coefficient of surface heat dissipation between the fin and the air streams.
Harper, R R↗
Implementation of ADI: Schemes on MIMD parallel computers
In order to simulate the effects of the impingement of hot exhaust jets of High Performance Aircraft on landing surfaces a multi-disciplinary computation coupling flow dynamics to heat conduction in the runway needs to be carried out. Such simulations, which are essentially unsteady, require very large computational power in order to be completed within a reasonable time frame of the order of an hour. Such power can be furnished by the latest generation of massively parallel computers. These remove the bottleneck of ever more congested data paths to one or a few highly specialized central processing units (CPU's) by having many off-the-shelf CPU's work independently on their own data, and exchange information only when needed. During the past year the first phase of this project was completed, in which the optimal strategy for mapping an ADI-algorithm for the three dimensional unsteady heat equation to a MIMD parallel computer was identified. This was done by implementing and comparing three different domain decomposition techniques that define the tasks for the CPU's in the parallel machine. These implementations were done for a Cartesian grid and Dirichlet boundary conditions. The most promising technique was then used to implement the heat equation solver on a general curvilinear grid with a suite of nontrivial boundary conditions. Finally, this technique was also used to implement the Scalar Penta-diagonal (SP) benchmark, which was taken from the NAS Parallel Benchmarks report. All implementations were done in the programming language C on the Intel iPSC/860 computer.
Vanderwijngaart, Rob F.↗
The radial heat polynomials and related functions.
Generalized heat equation solution expansion in terms of radial heat polynomials, Appel transforms and Laguerre polynomials
RADIAL DISTRIBUTION↗
Computer integration of hydrodynamics equations for heat pipes
Program has five operational modes that provide user flexibility in answering crucial heat-pipe design questions. User specifies heat input and rejection distribution.
Edwards, D. K.↗
Oscillations and stability of numerical solutions of the heat conduction equation
The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.
Kozdoba, L. A.↗
Analysis, approximation, and computation of a coupled solid/fluid temperature control problem
An optimization problem is formulated motivated by the desire to remove temperature peaks, i.e., 'hot spots', along the bounding surfaces of containers of fluid flows. The heat equation of the solid container is coupled to the energy equations for the fluid. Heat sources can be located in the solid body, the fluid, or both. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. Both mathematical analyses and computational experiments are given.
Gunzburger, Max D.↗
A Second-Order Closure Turbulence Model: New Heat Flux Equations and No Critical Richardson Number
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Y. Cheng↗
Temperature
The problems in human comfort in heat stress are emphasized, with less emphasis placed upon cold exposure problems. Physiological parameters related to human thermal interactions are discussed, as well as data concerning thermal protective clothing. The energy balance equation, heat transfer equation, thermal comfort, heat stress, and cold stress are also considered. A two node model of human temperature regulation in FORTRAN is appended.
Berenson, P. J.↗
An engineering aerodynamic heating method for hypersonic flow
A capability to calculate surface heating rates has been incorporated in an approximate three-dimensional inviscid technique. Surface streamlines are calculated from the inviscid solution, and the axisymmetric analog is then used along with a set of approximate convective-heating equations to compute the surface heat transfer. The method is applied to blunted axisymmetric and three-dimensional ellipsoidal cones at angle of attack for the laminar flow of a perfect gas. The method is also applicable to turbulent and equilibrium-air conditions. The present technique predicts surface heating rates that compare favorably with experimental (ground-test and flight) data and numerical solutions of the Navier-Stokes (NS) and viscous shock-layer (VSL) equations. The new technique represents a significant improvement over current engineering aerothermal methods with only a modest increase in computational effort.
Riley, Christopher J.↗
An Engineering Aerodynamic Heating Method for Hypersonic Flow
A capability to calculate surface heating rates has been incorporated in an approximate three-dimensional inviscid technique. Surface streamlines are calculated from the inviscid solution, and the axisymmetric analog is then used along with a set of approximate convective-heating equations to compute the surface heat transfer. The method is applied to blunted axisymmetric and three-dimensional ellipsoidal cones at angle of attack for the laminar flow of a perfect gas. The method is also applicable to turbulent and equilibrium-air conditions. The present technique predicts surface heating rates that compare favorably with experimental (ground-test and flight) data and numerical solutions of the Navier-Stokes (NS) and viscous shock-layer (VSL) equations. The new technique represents a significant improvement over current engineering aerothermal methods with only a modest increase in computational effort.
Riley, Christopher J.↗
An axisymmetric analog two-layer convective heating procedure with application to the evaluation of Space Shuttle Orbiter wing leading edge and windward surface heating
A numerical procedure for predicting the convective heating rate of hypersonic reentry vehicles is described. The procedure, which is based on the axisymmetric analog, consists of obtaining the three-dimensional inviscid flowfield solution; then the surface streamlines and metrics are calculated using the inviscid velocity components on the surface; finally, an axisymmetric boundary layer code or approximate convective heating equations are used to evaluate heating rates. This approach yields heating predictions to general three-dimensional body shapes. The procedure has been applied to the prediction of the wing leading edge heating to the Space Shuttle Orbiter. The numerical results are compared with the results of heat transfer testing (OH66) of an 0.025 scale model of the Space Shuttle Orbiter configuration in the Calspan Hypersonic Shock Tunnel (HST) at Mach 10 and angles of attack of 30 and 40 degrees. Comparisons with STS-5 flight data at Mach 9.15 and angle of attack of 37.4 degrees and STS-2 flight data at Mach 12.86 and angle of attack of 39.7 degrees are also given.
Wang, K. C.↗