Two Dimensional Analysis of Transient Heat Conduction in a Sector of a Hollow Circular Cylinder
Report Number: ASD TDR 63-642
Author(s): Torian, J. G. , Bennett, G. K.
Corporate Author(s): Martin Company Aerosciences Research Laboratory
Laboratory: AF Flight Dynamics Laboratory
Date of Publication: 1963-11
Pages: 138
Contract: AF 33(657)-10315
DoD Project: 1467
DoD Task: 146702
Identifier: AD0429077
Abstract:
This study was undertaken to develop an exact mathematical formulation of transient heat conduction to reduce the amount of idealization required by currently employed finite difference techniques. A two-dimensional analysis is developed beginning with the differential equations for conduction of heat in a segment of a hollow cylinder in polar coordinates. An exact solution with constant thermal diffusivity and conditions of prescribed surface temperature, convection, and direct heat input is written in an infinite series of Bessel and trigonometric functions. Provisions are made for incorporating a coordinate varying, arbitrary, initial temperature distribution as well as coordinate and time varying arbitrary surface conditiions. A solution that incorporates the effect of temperature dependent thermophysical properties is developed by combining the exact solution with a finite difference approach. The solution has been programmed for an IBM 7090 or 7094 digital computer.The geometry of the problem is indicative of wing leading edges such as found on the ASSET vehicle. It is anticipated that this geometry will remain applicable to many future vehicles.
Provenance: Lockheed Martin Missiles & Fire Control
Author(s): Torian, J. G. , Bennett, G. K.
Corporate Author(s): Martin Company Aerosciences Research Laboratory
Laboratory: AF Flight Dynamics Laboratory
Date of Publication: 1963-11
Pages: 138
Contract: AF 33(657)-10315
DoD Project: 1467
DoD Task: 146702
Identifier: AD0429077
Abstract:
This study was undertaken to develop an exact mathematical formulation of transient heat conduction to reduce the amount of idealization required by currently employed finite difference techniques. A two-dimensional analysis is developed beginning with the differential equations for conduction of heat in a segment of a hollow cylinder in polar coordinates. An exact solution with constant thermal diffusivity and conditions of prescribed surface temperature, convection, and direct heat input is written in an infinite series of Bessel and trigonometric functions. Provisions are made for incorporating a coordinate varying, arbitrary, initial temperature distribution as well as coordinate and time varying arbitrary surface conditiions. A solution that incorporates the effect of temperature dependent thermophysical properties is developed by combining the exact solution with a finite difference approach. The solution has been programmed for an IBM 7090 or 7094 digital computer.The geometry of the problem is indicative of wing leading edges such as found on the ASSET vehicle. It is anticipated that this geometry will remain applicable to many future vehicles.
Provenance: Lockheed Martin Missiles & Fire Control