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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
Mechanisms of Heat Transfer II01:20

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...
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Heat transfer between the human body and its environment occurs through four main mechanisms: conduction, convection, radiation, and evaporation.
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Heat Flow and Specific Heat01:12

Heat Flow and Specific Heat

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 the kilocalorie...
Mechanisms of Heat Transfer I01:14

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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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Isothermal Processes

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.
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Near-Infrared Temperature Measurement Technique for Water Surrounding an Induction-heated Small Magnetic Sphere
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Published on: April 30, 2018

Hydrothermal convection in moderately thin spherical shells.

Zhifeng Dai1, Keke Zhang, Xinhao Liao

  • 1Department of Mathematical Sciences, University of Exeter, EX4 4QE, United Kingdom.

Physical Review Letters
|September 4, 2008
PubMed
Summary

This study investigates hydrothermal convection in spherical shells, finding that nonlinear effects resolve mathematical degeneracy in convective instabilities. Analytical and numerical simulations show good agreement for pore water flow.

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Last Updated: Jul 2, 2026

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Area of Science:

  • Geophysics
  • Fluid Dynamics
  • Geochemistry

Background:

  • Hydrothermal convection is crucial for heat and mass transport in Earth's crust and mantle.
  • Pore water viscosity changes with temperature, significantly impacting fluid flow dynamics.
  • Spherical shell geometries are relevant for modeling planetary interiors.

Purpose of the Study:

  • To investigate hydrothermal convection in a permeable, internally heated, thin spherical shell with temperature-dependent viscosity.
  • To analyze the role of nonlinear effects in resolving mathematical degeneracy in convective instabilities.
  • To compare analytical solutions with direct numerical simulations.

Main Methods:

  • Perturbation analysis to study convective instabilities.
  • Direct numerical simulation of nonlinear convection.
  • Derivation of four 3D analytical solutions by removing degeneracy.

Main Results:

  • Convective instabilities in thin spherical shells are characterized by spherical harmonic degree l=6.
  • Mathematical degeneracy (13-fold) is resolved through nonlinear effects.
  • Four distinct 3D analytical solutions for convection were obtained.
  • Numerical simulations demonstrated satisfactory agreement with analytical solutions.

Conclusions:

  • Nonlinear effects are essential for understanding complex hydrothermal convection patterns.
  • The study provides validated analytical models for convective instabilities in spherical shells.
  • Findings contribute to the understanding of fluid dynamics in geological systems.