Eigensolutions for Coupled Thermoelastic Vibrations of Timoshenko Beams

1979 ◽  
Vol 46 (1) ◽  
pp. 169-174 ◽  
Author(s):  
R. C. Shieh
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Solution Procedure ◽  
Surface Heat ◽  
Timoshenko Beams ◽  
Thermal Boundary Conditions ◽  
Linear Thermoelasticity ◽  
Special Case

A general solution procedure, together with two special case solutions, for the free-vibration boundary-value problem of a circular or rectangular cross-section Timoshenko beam under general mechanical boundary conditions and the thermal boundary conditions that follow the Newton surface heat transfer law is presented within the context of coupled linear thermoelasticity.

Flow and Heat Transfer in Ducts of Arbitrary Shape With Arbitrary Thermal Boundary Conditions

1966 ◽  
Vol 88 (4) ◽  
pp. 351-357 ◽  
Author(s):  
E. M. Sparrow ◽  
A. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Space Technology ◽  
Closed Form Solutions ◽  
Thermal Boundary Conditions ◽  
Flow And Heat Transfer ◽  
Temperature Distributions ◽  
Circular Segment

A computation-oriented method of analysis is presented for determining closed-form solutions for fully developed laminar flow and heat transfer in ducts of arbitrary cross section. The analytical method can accommodate both uniform and circumferentially varying thermal boundary conditions. The solutions provide information for local quantities such as the velocity and the temperature distributions as well as for overall quantities such as the friction factor and the Nusselt number. As an application of the method, solutions are presented for flow and for heat transfer in ducts of circular-segment cross section, a configuration that is of current interest in space technology.

Steady Thermochromic Liquid Crystal Technique for Study of Conjugate Heat Transfer Problems

2003 ◽  
Author(s):  
C. J. Douglass ◽  
J. S. Kapat ◽  
E. Divo ◽  
A. J. Kassab ◽  
J. Tapley ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Liquid Crystal ◽  
Boundary Conditions ◽  
Surface Heat Flux ◽  
Conjugate Heat Transfer ◽  
Surface Heat ◽  
Test Block ◽  
Thermochromic Liquid Crystal ◽  
Thermal Boundary Conditions

This paper presents a steady measurement technique based on thermochromic liquid crystals (TLC) that can be used for study of conjugate heat transfer. In contrast to the more commonly used transient thermochromic liquid crystal technique, this technique requires steady-state experiments, and eliminates some of the limitations of the transient version at the cost of measurements or knowledge of thermal conditions all surfaces and increased computations for data reduction. This technique requires that thermal boundary conditions be known or measured on all internal or external surfaces of the test block. All surfaces that are exposed to external air flow are coated with a broad-bandwidth TLC. The thermal boundary conditions are then sent to a steady conduction solver that involves the boundary element method (BEM) and an inverse problem approach (BEM/IP). This combined BEM/IP approach minimizes the effects of random experimental error in measured data and calculates surface heat flux, from which the intended convective heat flux coefficients can then be calculated. The technique is applied to a prismatic stainless steel block exposed to warm air flows on three sides — an arrangement that has been used often to simulate flow through a blade tip gap. It is found that an in-situ pixel-by-pixel calibration of TLC hue vs temperature is needed in order to obtain reasonable accuracy. A calibration-curve-fit uncertainty of better than 0.4°C (at 95% confidence level) was obtained in this process. In the actual experiments, conjugate heat transfer was set up by passing cold water through three cooling channels that span the test block. Once the experiments are completed and the TLC colors are converted to surface temperature distributions, the BEM/IP approach is used to obtain surface heat flux distributions, and then distribution of heat transfer coefficients.

Thermoelastic Vibration and Damping for Circular Timoshenko Beams

1975 ◽  
Vol 42 (2) ◽  
pp. 405-410 ◽  
Author(s):  
R.-C. Shieh
Keyword(s):  
Boundary Conditions ◽  
Circular Cross Section ◽  
Timoshenko Beams ◽  
Thermoelastic Damping ◽  
Governing Equations ◽  
Damping Coefficients ◽  
Thermal Boundary Conditions ◽  
Transverse Vibrations ◽  
Thermoelastic Vibration ◽  
Linear Thermoelasticity

Within the framework of the theories of coupled linear thermoelasticity and Timoshenko beams, the vibration and thermoelastic damping (with emphasis on the transverse ones) of circular cross-section beams are studied. The governing equations are derived for the case of general mechanical boundary conditions and special thermal boundary conditions that follow the Newton surface heat transfer law. A variational principle governing the eigenfunctions associated with an eigenvalue is formulated. An exact solution, together with the thermoelastic damping coefficient, is obtained for the case of transverse vibrations of a simply supported beam with lateral surfaces thermally insulated and end surfaces kept at constant temperature. Numerical results, together with the discussion for the first two eigenvalues and the thermoelastic damping coefficients, are also presented.

scholarly journals The Role of the Impingement Plate in Array Heat Transfer

1996 ◽  
Author(s):  
Kenneth W. Van Treuren ◽  
Zoulan Wang ◽  
Peter Ireland ◽  
Terry V. Jones ◽  
S. T. Kohler
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Boundary Conditions ◽  
Temperature Difference ◽  
Target Surface ◽  
Surface Heat ◽  
Plate Temperature ◽  
Thermal Boundary Conditions ◽  
Impingement Plate ◽  
The Heat Transfer Coefficient

Most research involving arrays of impinging jets was conducted using steady state techniques which allow the impingement plate (through which the gas flows) to achieve an equilibrium (adiabatic) temperature during the test. Invariably, the impingement plate temperature was not reported for these tests as the floating temperature condition was taken to be representative of conditions in the application being modeled. Thermal analysis of gas turbine conditions showed the present authors that conditions in the engine could often be significantly different from this floating plate temperature state. Such conditions include engine operating point transients and situations in which the plate is fixed to the aerofoil in such a way to achieve good thermal contact. Furthermore, the capacity of the impingement plate to contribute to enhanced heat transfer by paying attention to the thermal boundary conditions at its support has not been realized. The influence of the impingement plate temperature on local target surface heat transfer was fully quantified by Van Treuren et al. (1993, 1994 and 1996), using a transient liquid crystal heat transfer technique. Superposition was used to show that the target surface heat flux can be written as the summation af two separate heat transfer coefficients. These temperature difference products quantify the contributions of the impingement plate and the target surface thermal boundary conditions. In other words:(1)q=hjTw-Tj+hpTw-TpVan Treuren et al.’s experiments showed the heat transfer coefficient for target surface heat flux and impingement plate to target surface temperature difference, hp, can be up to 40% of the heat transfer coefficient for plenum to target surface temperature difference, hj, in crossflow areas away from the jet stagnation zone. The present report covers steady state experiments conducted at three average jet Reynolds numbers (10,000, 14,000, and 18,000) and two impingement to target plate spacings (1 and 4) for an inline array of jets. The purpose of the experiments was to determine the adiabatic impingement plate temperature expressed as a non-dimensional temperature difference, θ. The data allow the difference in thermal boundary conditions between the steady state experiments and the transient heat transfer experiments to be accounted for.

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