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Conduction, Convection and Radiation: Problem Solving01:20

Conduction, Convection and Radiation: Problem Solving

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There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting characteristics, but all three have two things in common: they transfer heat solely because of a temperature difference; and the greater the temperature difference, the faster the heat transfer.
In order to solve a problem related to heat transfer, first of all, the situation needs to be examined to determine the type of heat transfer involved. This could...
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Mechanisms of Heat Transfer II01:20

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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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Mechanisms of Heat Transfer I01:14

Mechanisms of Heat Transfer I

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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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Heat Flow and Specific Heat01:12

Heat Flow and Specific Heat

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Heat is a type of energy transfer that is caused by a temperature difference, and it can change the temperature of an object. Since heat is a form of energy, its SI unit is the joule (J). Another common unit of energy often used for heat is the calorie (cal), which is defined as the energy needed to change the temperature of 1 g of water by 1 °C, specifically between 14.5 °C and 15.5 °C, since the energy needed shows a slight temperature dependence. Another commonly used unit is...
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Mechanisms of Heat Transfer01:14

Mechanisms of Heat Transfer

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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...
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Specific Heat01:16

Specific Heat

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The specific heat capacity of a substance refers to the energy required to increase the temperature of one gram of that substance by one degree Celcius. Specific heat capacity is often represented in calories (cal), grams (g), and degrees Celsius (oC), but can also be expressed in joules (J), kilograms (kg), and Kelvin (K), among other units.
For example, increasing the temperature of one gram of water by 1°C requires one calorie of heat energy and can be written as 1 cal/g-°C, or...
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Related Experiment Video

Updated: Jan 13, 2026

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
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Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment

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Heat Conduction Model Based on the Explicit Euler Method for Non-Stationary Cases.

Attila Érchegyi1,2, Ervin Rácz3

  • 1Doctoral School of Applied Informatics and Applied Mathematics, Obuda University, 1034 Budapest, Hungary.

Entropy (Basel, Switzerland)
|October 28, 2025
PubMed
Summary
This summary is machine-generated.

This study optimizes the explicit Euler method for heat conduction by introducing a No-Sway Threshold to prevent temperature oscillations. Variable grid spacing and this new threshold improve simulation accuracy and stability.

Keywords:
FlexblueNo-Sway Thresholdexplicit Euler schemefinite difference methodmesh optimizationsmall modular reactorthermal diffusiontransient heat conduction

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Characterization of Thermal Transport in One-dimensional Solid Materials
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Area of Science:

  • Computational Heat Transfer
  • Numerical Methods in Engineering
  • Thermal Engineering

Background:

  • The explicit Euler method is prone to oscillations in transient heat conduction simulations.
  • The classical Courant-Friedrichs-Lewy (CFL) condition is insufficient for monotonic temperature approximations.
  • Oscillations in intermediate states can lead to inaccurate thermal modeling.

Purpose of the Study:

  • To optimize the explicit Euler method for heat conduction models.
  • To eliminate oscillations in transient temperature simulations.
  • To develop a more stable and accurate numerical approach for thermal analysis.

Main Methods:

  • Introduced a No-Sway Threshold for the Fourier number (K), stricter than CFL.
  • Determined optimal time (Δt) and spatial (Δx) steps using the Method of Equating Coefficients.
  • Constructed variable grid spacing (M2) using an inequality system and specified element thickness (Δξ).

Main Results:

  • The No-Sway Threshold ensures monotonic temperature-time evolution.
  • Variable grid spacing (M2) combined with the No-Sway Threshold enhances simulation accuracy.
  • Application to a Flexblue® SMR shutdown scenario showed improved temperature gradient prediction in M2 compared to uniform grid (M1).

Conclusions:

  • The optimized explicit Euler method with a No-Sway Threshold and variable grid spacing provides superior accuracy for heat conduction.
  • This approach effectively mitigates oscillations and improves the stability of transient thermal simulations.
  • The findings are validated by a realistic emergency shutdown scenario, demonstrating practical applicability.