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Thermal expansion and Thermal stress: Problem Solving

Thermal expansion and Thermal stress: Problem Solving

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 °C.

Heating and Cooling Curves

Heating and Cooling Curves

When a substance—isolated from its environment—is subjected to heat changes, corresponding changes in temperature and phase of the substance is observed; this is graphically represented by heating and cooling curves.
For instance, the addition of heat raises the temperature of a solid; the amount of heat absorbed depends on the heat capacity of the solid (q = mcsolidΔT). According to thermochemistry, the relation between the amount of heat absorbed or released by a substance, q, and its...

Mechanism of heat transfer

Mechanism of heat transfer

Understanding heat transfer mechanisms is essential for understanding how our bodies maintain balance in different environmental conditions. When the environment is thermoneutral, the body is in a state of balance, neither using nor releasing energy to maintain its core temperature. However, when the environment is not thermoneutral, the body employs four heat transfer mechanisms to maintain homeostasis: conduction, convection, evaporation, and radiation. These mechanisms facilitate heat...

Mechanisms of Heat Transfer II

Mechanisms of Heat Transfer II

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...

Mechanisms of Heat Transfer

Mechanisms of Heat Transfer

Heat transfer between the human body and its environment occurs through four main mechanisms: conduction, convection, radiation, and evaporation.
Conduction, accounting for approximately 3% of body heat loss at rest, is the process of exchanging heat between molecules of two materials in direct contact. This can result in both heat loss and gain. For instance, when the body is submerged in water, which conducts heat 20 times more effectively than air, it can either lose or gain significant heat.

Mechanisms of Heat Transfer I

Mechanisms of Heat Transfer I

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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Related Experiment Video

Updated: May 18, 2026

Design, Instrumentation and Usage Protocols for Distributed In Situ Thermal Hot Spots Monitoring in Electric Coils using FBG Sensor Multiplexing

Design, Instrumentation and Usage Protocols for Distributed In Situ Thermal Hot Spots Monitoring in Electric Coils using FBG Sensor Multiplexing

Published on: March 8, 2020

Minimum maximum temperature gradient coil design.

Peter T While¹, Michael S Poole, Larry K Forbes

¹School of Mathematics and Physics, Faculty of Science, Engineering and Technology, University of Tasmania, Hobart, Tasmania, Australia. peter.while@imtek.unifreiburg.de

Magnetic Resonance in Medicine

|October 9, 2012

Summary

This summary is machine-generated.

Gradient coil redesign minimizes peak temperature using minimaxT optimization, improving thermal performance in MRI systems without compromising field quality. This method enhances operational efficiency and safety.

Keywords:

gradient coil design heating minimax optimization temperature thermal performance

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Comparative Study of Simulation of Temperature Rise in Ring Main Unit

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Published on: July 5, 2024

Area of Science:

Magnetic Resonance Imaging (MRI) Engineering
Applied Electromagnetics
Thermal Management in Scientific Instruments

Background:

Ohmic heating is a significant challenge in gradient coil operation, potentially impacting performance and safety.
Existing methods for gradient coil design do not adequately address thermal management, leading to suboptimal operating temperatures.

Purpose of the Study:

To develop and validate a novel method for redesigning cylindrical gradient coils to minimize peak operating temperature.
To maintain or improve field homogeneity and overall coil performance while reducing thermal load.

Main Methods:

Integration of an analytic spatial temperature distribution simulation for single-layer gradient coils.
Application of a minimax optimization routine utilizing sequential quadratic programming (SQP) to generate optimized coil windings (minimaxT).
Experimental validation using small-scale prototype coils.

Main Results:

Simulations demonstrated considerable reductions in maximum temperature for both symmetric and asymmetric gradient coils compared to existing methods.
The resulting minimaxT coil winding patterns exhibited unique 'fish-eye' spreading in dense regions, influenced by thermal material properties.
Experimental validation confirmed significant thermal performance improvements with negligible impact on field error or standard figures of merit.

Conclusions:

The minimaxT coil redesign method effectively reduces peak operating temperatures in gradient coils.
This approach offers a practical solution for enhancing thermal management in MRI systems, improving reliability and performance.
Accurate estimation of thermal material properties is crucial for successful implementation of the minimaxT design.