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Lecture

Transient Heat Diffusion: Lumped Capacitance Model

In course

ME-341: Heat and mass transfer

This course covers fundamentals of heat transfer and applications to practical problems. Emphasis will be on developing a physical and analytical understanding of conductive, convective, and radiative heat transfer. ...

Description

This lecture covers the transient heat diffusion phenomenon, introducing the lumped capacitance model and its application in solving transient heat conduction under convective cooling. The instructor explains the Biot number, spatial effects, and provides a generalized solution for planar, radial, and spherical geometries. The lecture also discusses the assumptions behind the model, such as high thermal conductivity ensuring uniform temperature in the solid and the impact of liquid volume on temperature stability. An electrical analogy is presented to aid in understanding the cooling process, emphasizing the importance of the Biot number in determining heat transfer characteristics. Practical examples, like using a thermocouple for temperature measurement in a gas stream, are used to illustrate the concepts.

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Instructor

Giulia Tagliabue

Dr. Giulia Tagliabue is an Assistant Professor at the Institute of Mechanical Engineering (IGM). She obtained her B.S. and M.S degrees cum laude in Mechanical Engineering from the University of Udine in Italy. Concurrently she also obtained the diploma from the Scuola Normale Superiore of Udine. In 2015 she obtained her PhD in Mechanical Engineering from ETH Zurich with a thesis on nanophotonic design for light-to-heat and light-to-charge conversion devices. In 2015 Dr. Tagliabue was awarded the Early Mobility Fellowship from the Swiss National Science Foundation and moved to Caltech as a PostDoctoral fellow. In 2017, thanks to the award of an Advanced Mobility Fellowship, she prolonged her stay at Caltech. Here, in collaboration with the Joint Center for Artificial Photosynthesis (JCAP) she investigated coupled light, heat and charge transfer processes in nanophotonic structures and low-dimensional materials for photoelectrochemical and photovoltaic sustainable energy conversion.

Official source

Ontological neighbourhood

Physics

Physical quantities: Topics in physical quantities

Related concepts (32)

Thermal conduction

Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its thermal conductivity, and is denoted k. Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body). For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it.

Biot number

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot (1774–1862). The Biot number is the ratio of the thermal resistance for conduction inside a body to the resistance for convection at the surface of the body. This ratio indicates whether the temperature inside a body varies significantly in space when the body is heated or cooled over time by a heat flux at its surface.

Thermal resistance

Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the reciprocal of thermal conductance. (Absolute) thermal resistance R in kelvins per watt (K/W) is a property of a particular component. For example, a characteristic of a heat sink. Specific thermal resistance or thermal resistivity Rλ in kelvin–metres per watt (K⋅m/W), is a material constant.

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer.

Heat

In thermodynamics, heat is the thermal energy transferred between systems due to a temperature difference. In colloquial use, heat sometimes refers to thermal energy itself. An example of formal vs. informal usage may be obtained from the right-hand photo, in which the metal bar is "conducting heat" from its hot end to its cold end, but if the metal bar is considered a thermodynamic system, then the energy flowing within the metal bar is called internal energy, not heat.

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