Green’s Function Approach to Nonlinear Conduction and Surface Radiation Problems

2009 ◽  
Author(s):  
Matthew R. Jones ◽  
Vladimir P. Solovjov
Keyword(s):  
Steady State ◽  
Green’S Function ◽  
Green's Function ◽  
Transient Analysis ◽  
Radiative Heat ◽  
Surface Radiation ◽  
Temporal Response ◽  
Nonlinear Conduction ◽  
Insight Into ◽  
Transient And Steady State

An analytical approach for solving both transient and steady state conduction and surface radiation problems is presented. The method is based on the use of a Green’s function, and the temperature field is obtained by solving an integral equation. This is in contrast to the approach presented in radiative heat transfer texts in which temperature profiles are obtained from the simultaneous solution of coupled integral and differential equations. The analysis presented in this paper provides insight into the solution of this important class of problems. The method is illustrated by solving two representative problems. The first problem considered is the steady state analysis of radiating fins, which are frequently incorporated in the design of spacecraft. The second problem considered is the transient analysis of a radiating target, which is used to determine the temporal response of radiation thermometers.

Green’s Function Approach to Nonlinear Conduction and Surface Radiation Problems

2009 ◽  
Vol 132 (2) ◽  
Author(s):  
Matthew R. Jones ◽  
Vladimir P. Solovjov
Keyword(s):  
Steady State ◽  
Green’S Function ◽  
Green's Function ◽  
Transient Analysis ◽  
Radiative Heat ◽  
Surface Radiation ◽  
Temporal Response ◽  
Nonlinear Conduction ◽  
Insight Into ◽  
Transient And Steady State

An exact approach for solving both transient and steady state conduction and surface radiation problems is presented. The method is based on the use of Green’s function, and the temperature field is obtained by solving an integral equation. This is in contrast to the approach presented in radiative heat transfer texts in which temperature profiles are obtained from the simultaneous solution of coupled integral and differential equations. The analysis presented in this paper provides insight into the solution of this important class of problems. The method is illustrated by solving two representative problems. The first problem considered is the steady state analysis of a radiating fin. The second problem considered is the transient analysis of a radiating target, which is used to determine the temporal response of radiation thermometers.

Support Flexibility and Natural Frequencies of Pipe Mounted Thermowells

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
David S. Bartran
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Natural Frequencies ◽  
Pipe Wall ◽  
Simplified Model ◽  
Load Model ◽  
Distributed Load ◽  
Pipe Fittings ◽  
Insight Into ◽  
Design And Application

A simplified model of a pipe mounted thermowell provides a measure of insight into the design and application of intrusive pipe fittings. A combination of Fourier and Green’s function methods together with a distributed load model of the thermowell/pipe wall interface are used to calculate the support compliance and subsequently the natural frequencies of the thermowell. These are compared with limited though independent calculations. This comparison confirms a profound reduction in natural frequencies for commonly encountered thermowell installations, reductions that should not be ignored where the risk of flow-induced resonance is high.

scholarly journals Creating Nodes at Selected Locations in a Harmonically Excited Structure Using Feedback Control and Green’s Function

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Bassam A. Albassam
Keyword(s):  
Steady State ◽  
Feedback Control ◽  
Green’S Function ◽  
Green's Function ◽  
Nodal Point ◽  
Control Force ◽  
Velocity Measurements ◽  
Numerical Examples ◽  
Control Forces

The paper deals with designing a control force to create nodal point(s) having zero displacements and/or zero slopes at selected locations in a harmonically excited vibrating structure. It is shown that the steady-state vibrations at desired points can be eliminated using feedback control forces. These control forces are constructed from displacement and/or velocity measurements using sensors located either at the control force position or at some other locations. Dynamic Green’s function is exploited to derive a simple and exact closed from expression for the control force. Under a certain condition, this control force can be generated using passive elements such as springs and dampers. Numerical examples demonstrate the applicability of the method in various cases.

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