Analytical solution of heat conduction of a multilayered annular disk and associated thermal deflection and thermal stresses

2020 ◽  
Vol 43 (5) ◽  
pp. 563-578 ◽  
Author(s):  
V. R. Manthena ◽  
V. B. Srinivas ◽  
G. D. Kedar
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Thermal Stresses ◽  
Annular Disk ◽  
Thermal Deflection

Thermal stress analysis of a thermosensitive functionally graded rectangular plate due to thermally induced resultant moments

2018 ◽  
Vol 14 (5) ◽  
pp. 857-873 ◽  
Author(s):  
V.R. Manthena ◽  
G.D. Kedar ◽  
K.C. Deshmukh
Keyword(s):  
Heat Conduction ◽  
Rectangular Plate ◽  
Material Properties ◽  
Heat Conduction Equation ◽  
Thermal Stresses ◽  
Functionally Graded ◽  
Conduction Equation ◽  
Content Type ◽  
Thin Rectangular Plate ◽  
Thermal Deflection

PurposeThe purpose of this paper is to determine the temperature distribution of a thin rectangular plate made of thermosensitive functionally graded (FG) material. By finding out thermal deflection and stress resultants, the thermal stresses have been obtained and analyzed.Design/methodology/approachInitially, the rectangular plate is kept at the surrounding temperature. The upper, lower and two parallel sides (y=0,bandz=0, c) are thermally insulated, while other parallel sides (x=0,a) are given convective-type heating, that is, the rate of change of the temperature of the rectangular plate is proportional to the difference between its own temperature and the surrounding temperature. The non-linear heat conduction equation has been converted to linear form by introducing Kirchhoff’s variable transformation and the resultant heat conduction equation is solved by integral transform technique with hyperbolic varying point heat source.FindingsA mathematical model is prepared for FG ceramic–metal-based material, in which alumina is selected as the ceramic and nickel as the metal. The thermal deflection and thermal stresses have been obtained for the homogeneous and nonhomogeneous materials. The results are illustrated numerically and depicted graphically for comparison. During this study, one observed that variations are seen in the stresses, due to the variation in the inhomogeneity parameters.Research limitations/implicationsThe paper is constructed purely on theoretical mathematical modeling by considering various parameters and functions.Practical implicationsThis type of theoretical analysis may be useful in high-temperature environments like nuclear components, spacecraft structural members, thermal barrier coatings, etc., as the effect of temperature and evaluation of temperature-dependent and nonhomogeneous material properties plays a vital role for accurate and reliable structural analysis.Originality/valueIn this paper, the authors have used thermal deflection and resultant stresses to determine the thermal stresses of a thin rectangular plate with temperature- and spatial variable-dependent material properties which is a new and novel contribution to the field.

Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Solution ◽  
Least Squares ◽  
Series Solution ◽  
Point Matching ◽  
State Heat ◽  
Temperature Heat ◽  
Steady State Heat ◽  
Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

Effects of Thermo-Physically Initial Properties on Inverse Heat Conduction Problem

2013 ◽  
Vol 284-287 ◽  
pp. 733-737
Author(s):  
Sung Deok Hong ◽  
Mi Gyung Cho ◽  
Chan Soo Kim ◽  
Cheol Ho Bai ◽  
Sung Yull Hong ◽  
...  
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Conduction Problem ◽  
Damping Ratio ◽  
Initial Guess ◽  
Convergence Time ◽  
Theoretical Equation ◽  
Inverse Heat Conduction ◽  
Marquardt Algorithm ◽  
Infinite Slab

The Levenberg-Marguardt algorithm is used to study effects on convergence for inverse heat conduction in the unsteady state. In this model, the finite volume method is usedto obtain anestimated temperature, which is necessary for minimizing inverse error. To validate the model, constant thermal conductivity (k) and heat capacity (ρCpC) are identified from a semi-infinite slab subjected to constant heat flux. These properties are inserted into the theoretical equation for a semi-infinite slab, and an analytical solution is obtained by solving the theoretical equation including the two identified properties. The analytical solution and the identified resultare in very good agreement. Three simulations were performed to investigate the sensitivity of computation time and conversion to initial thermo-physical values by changing three different damping ratios of the Levenberg-Marquardt algorithm. Our results show that agood initial guessallowsgood convergence, but convergence time decreases as the value of damping ratio decreases.A poor initial guess results in more convergence time, and causes divergence when a small damping ratio is used. Once the simulation converges, our model shows that results areobtained within an error of 0.01%.

Transient Thermal Stress Analysis of the Typical Structures in Turbine Rotor Based on Thermomechanical Analysis

2014 ◽  
Author(s):  
Ning Xu ◽  
Zhansheng Liu ◽  
He Peng
Keyword(s):  
Finite Element ◽  
Heat Conduction ◽  
Thermal Stress ◽  
Thermal Stresses ◽  
Transition Process ◽  
Transient Heat Conduction ◽  
Work Conditions ◽  
Turbine Rotor ◽  
Design Stage ◽  
Turbine Rotors

Thermal stress is one of the most important monitoring parameters in turbine rotors during the transition of work conditions. It has significant influence on the safety and life of turbine rotors. In order to obtain the thermal stress in turbine rotors during the transition process conveniently, the transient heat conduction process in typical structures of turbine rotors is analyzed based on heat conduction equation and finite element simulation. According to thermomechanical principle, thermal stress distributions in the typical structures of turbine rotor are investigated. The solutions of thermal stress in a solid cylinder are derived. A corner formed by shaft and disc is modeled and analyzed by finite element method, and the influences of structure parameters on thermal stresses are studied. The results on thermal stresses in cylinder and corner structures could provide a continent method to estimate thermal stress of turbine rotor on early design stage.

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