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01:14Mechanisms 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.
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.
01:20Mechanisms 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...
01:27Thermal 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.
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.
01:14Mechanisms 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.
01:19Mechanism 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...
02:44Heating 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...
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...
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Published on: May 2, 2016
Effects of optimal control over thermoconvective patterns.
1Departamento de Matemáticas, Facultad de Ciencias Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain.
Summary
Optimal control methods prevent pattern formation in Rayleigh-Bénard convection with horizontal temperature gradients. This research introduces controlled states that avoid thermoconvective instability, enhancing stability in fluid dynamics.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Heat Transfer
Background:
- Rayleigh-Bénard convection is a fundamental model for pattern formation in fluids.
- Horizontal temperature gradients introduce complexities and can lead to various instabilities.
- Controlling fluid behavior is crucial for many engineering applications.
Purpose of the Study:
- To investigate the application of optimal control techniques to suppress pattern formation.
- To determine if specific thermal boundary conditions can prevent thermoconvective instability.
- To achieve controlled basic states with reduced pattern formation.
Main Methods:
- Utilizing optimal control theory to derive boundary conditions.
- Analyzing the Rayleigh-Bénard problem with a horizontal temperature gradient.
- Numerical or analytical methods to verify the suppression of instability and pattern formation.
Main Results:
- Demonstrated that optimal control can effectively avoid pattern formation.
- Identified specific thermal boundary conditions that lead to stable, controlled states.
- Achieved reduced pattern formation and avoided thermoconvective instability.
Conclusions:
- Optimal control is a viable strategy for stabilizing fluid systems prone to pattern formation.
- Tailored boundary conditions can significantly alter convective instabilities.
- This approach offers a method for designing more stable fluid systems.