SEMI-ANALYTICAL SOLUTIONS FOR SINGLE-PHASE THERMAL CONDUCTION AND STRESS PROBLEMS OF FINITE-DOMAIN SLAB AND CYLINDER WITH A GROWING OR RECEDING BOUNDARY
Restricted (Penn State Only)
- Author:
- Kumar, Pavan
- Graduate Program:
- Engineering Science and Mechanics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 22, 2024
- Committee Members:
- Albert Segall, Program Head/Chair
Corina Drapaca, Co-Chair & Dissertation Advisor
Christopher Kube, Major Field Member
Albert Segall, Co-Chair & Dissertation Advisor
Alok Sinha, Outside Unit & Field Member - Keywords:
- Moving Boundary Problem
Thermal Conduction
Semi-Analytical Solution
Finite Element Analysis
Laplace Transform
Inverse Problems
Additive Manufacturing - Abstract:
- Thermal conduction and thermoelastic stress considerations of a solid media with moving boundaries are of great interest in many research areas. Unfortunately, it is very difficult to find analytical or semi-analytical solutions for the single-phase thermal conduction equation in real time with a growing or receding boundary. While analytical solutions for infinite and semi-infinite domains are available, these cannot accurately model many common situations met in industry. To overcome this shortcoming, a semi-analytical solution for the heat equation for a single phase, homogeneous, and finite-slab with a growing or receding boundary under unit loading was derived using the Laplace transform method and the Zakian series representation of the inverse Laplace transform. Conformal mapping was then used to solve a similar problem for a finite hollow cylinder with a receding or growing inner radius. A methodology based on Duhamel’s and Laplace convolution theorems was derived to solve the unsteady heat conduction problems on the above-mentioned finite domains under time dependent arbitrary thermal loading. The resulting semi-analytical solutions were then used to determine the transient thermoelastic stresses. Lastly, a straightforward approach was developed that solves the inverse heat transfer problems on finite domains with moving boundaries. All solutions allow for convection on the fixed boundary. The semi-analytical predictions were in good agreement with finite-element solutions obtained in COMSOL Multiphysics. An important application of this model with an increasing thickness could be used in the prediction and/or verification of numerical and/or experimental studies of the temperature and thermal stresses in real time during solid state additive manufacturing as seen with cold-spray methods. Moreover, similar calculations could be employed to assess temperature, thermal stresses, and/or recession rates during machining and/or eroding surfaces. Indeed, the resulting solutions might be utilized to remotely assess surface temperature and/or erosion/wear and/or oxidation/growth rates in severe conditions where direct measurements are not feasible.