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Thermal expansion and Thermal stress: Problem Solving01:27

Thermal expansion and Thermal stress: Problem Solving

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San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55...
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Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
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A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to maintain thermal equilibrium. Processes involving phase changes like water evaporation into steam or freezing water into ice at a constant temperature are examples of Isothermal Processes.
An ideal gas can also undergo isothermal expansion or compression.
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If the temperature of an object is changed while it is prevented from expanding or contracting, the object is subjected to stress. The stress is compressive if the object expands in the absence of constraint and tensile if it contracts. This stress resulting from temperature change is known as thermal stress. It can be quite large and can cause damage. To avoid this stress, engineers may design components so they can expand and contract freely. For instance, on highways, gaps are deliberately...
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In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...
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Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature difference, heat transfer occurs. It may occur rapidly, such as through a cooking pan, or slowly, such as through the walls of a picnic ice box. So many processes involve heat transfer that it is hard to imagine a situation where no heat transfer occurs. Yet, every heat transfer takes place by only three methods: conduction, convection, and radiation.
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Thermoelastic Processes by a Continuous Heat Source Line in an Infinite Solid via Moore-Gibson-Thompson

Ahmed E Abouelregal1,2, Ibrahim-Elkhalil Ahmed1,3, Mohamed E Nasr1,4

  • 1Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 77423, Saudi Arabia.

Materials (Basel, Switzerland)
|October 14, 2020
PubMed
Summary

This study introduces a new thermoelasticity model based on the Moore-Gibson-Thompson equation to analyze heat transfer and wave propagation. The novel model overcomes limitations of previous theories and provides validated numerical results for physical fields.

Keywords:
Moore–Gibson–Thompson heat equationheat sourcethermoelasticityunbounded solid

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Area of Science:

  • Solid Mechanics
  • Thermodynamics
  • Continuum Mechanics

Background:

  • Classical heat transfer models, such as Fourier's law, have limitations.
  • Existing thermoelastic models sometimes fail to maintain positivity, necessitating improved approaches.

Purpose of the Study:

  • To introduce and investigate a novel thermoelasticity model based on the Moore-Gibson-Thompson equation.
  • To analyze wave propagation in an infinite isotropic body under a continuous thermal line source using the new model.
  • To address limitations in positivity found in some existing thermoelastic models.

Main Methods:

  • Development of a thermomechanical model combining hyperbolic and parabolic partial differential equations.
  • Application of Laplace and Hankel transform methods, along with a potential function approach.
  • Utilizing Laplace and Hankel inverse transformations for space-time domain solutions.

Main Results:

  • The model successfully investigates wave propagation under a continuous thermal line source.
  • Numerical calculations validate the physical fields derived from the model.
  • Theoretical and numerical results are compared with those from other thermoelastic models.

Conclusions:

  • The proposed Moore-Gibson-Thompson-based thermoelasticity model offers a robust framework for analyzing thermomechanical phenomena.
  • The model provides accurate predictions for wave propagation and thermal fields.
  • This work contributes to the advancement of thermoelasticity theories and their applications.