How Properties that Distinguish Solids from Fluids and Constraints of Spherical Geometry Suppress Lower Mantle Convection

Hofmeister, Anne M.; Criss, Everett M.

doi:10.1007/s12583-017-0819-4

Cited by 18 publications

(3 citation statements)

References 91 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Rigidity permits a solid to remain motionless, except for the small, cyclical excursions of its vibrating atoms, while sustaining temperatures up to melting. In contrast, fluids flow under any stress, whereas some minimum stress (the elastic limit) must be exceeded for a solid to permanently deform below its melting temperature, e.g., [ 9 ].…”

Section: Theoretical Description Of Solids Conducting Heat In Steady ...mentioning

confidence: 99%

“…Constructs for heat storage in gas and solids must each account for differences in the types of energy stored, plus restrictions on converting energy between the different reservoirs. Crucially, for solids, heat transfer is independent of mass diffusion, as shown by Hofmeister and Criss [ 9 ]. Heat may be stored in the cyclical and microscopically localized vibrations of interatomic bonds in solids, but its transport across the solid does not involve net displacement of the atoms or deformation of their structural arrangement.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow

Hofmeister

Criss

2022

Materials

Self Cite

View full text Add to dashboard Cite

Available data on insulating, semiconducting, and metallic solids verify our new model that incorporates steady-state heat flow into a macroscopic, thermodynamic description of solids, with agreement being best for isotropic examples. Our model is based on: (1) mass and energy conservation; (2) Fourier’s law; (3) Stefan–Boltzmann’s law; and (4) rigidity, which is a large, yet heretofore neglected, energy reservoir with no counterpart in gases. To account for rigidity while neglecting dissipation, we consider the ideal, limiting case of a perfectly frictionless elastic solid (PFES) which does not generate heat from stress. Its equation-of-state is independent of the energetics, as in the historic model. We show that pressure-volume work (P𝜕V) in a PFES arises from internal interatomic forces, which are linked to Young’s modulus (Ξ) and a constant (n) accounting for cation coordination. Steady-state conditions are adiabatic since heat content (Q) is constant. Because average temperature is also constant and the thermal gradient is fixed in space, conditions are simultaneously isothermal: Under these dual restrictions, thermal transport properties do not enter into our analysis. We find that adiabatic and isothermal bulk moduli (B) are equal. Moreover, Q/V depends on temperature only. Distinguishing deformation from volume changes elucidates how solids thermally expand. These findings lead to simple descriptions of the two specific heats in solids: 𝜕ln(cP)/𝜕P = −1/B; cP = nΞ times thermal expansivity divided by density; cP = cVnΞ/B. Implications of our validated formulae are briefly covered.

show abstract

Section: Theoretical Description Of Solids Conducting Heat In Steady ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow

Hofmeister

Criss

2022

Materials

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since the Rayleigh numbers strongly depend on the thickness of the system, d, through a power relationship with exponent three or five according to the thermal source, intrinsic stratification greatly affects thermal stability of the mantle. At last, further objections could be added to the effective meaning of the Rayleigh number in a system such as Earth's mantle (e.g., [138]). More realistic calculations of the Rayleigh numbers give ∼ 10 3 [91].…”

Section: Mantle Motionsmentioning

confidence: 99%

Earth’s gradients as the engine of plate tectonics and earthquakes

Zaccagnino

Doglioni

2022

Riv. Nuovo Cim.

View full text Add to dashboard Cite

The processes occurring on the Earth are controlled by several gradients. The surface of the Planet is featured by complex geological patterns produced by both endogenous and exogenous phenomena. The lack of direct investigations still makes Earth interior poorly understood and prevents complete clarification of the mechanisms ruling geodynamics and tectonics. Nowadays, slab-pull is considered the force with the greatest impact on plate motions, but also ridge-push, trench suction and physico-chemical heterogeneities are thought to play an important role. However, several counterarguments suggest that these mechanisms are insufficient to explain plate tectonics. While large part of the scientific community agreed that either bottom-up or top-down driven mantle convection is the cause of lithospheric displacements, geodetic observations and geodynamic models also support an astronomical contribution to plate motions. Moreover, several evidences indicate that tectonic plates follow a mainstream and how the lithosphere has a roughly westerly drift with respect to the asthenospheric mantle. An even more wide-open debate rises for the occurrence of earthquakes, which should be framed within the different tectonic setting, which affects the spatial and temporal properties of seismicity. In extensional regions, the dominant source of energy is given by gravitational potential, whereas in strike-slip faults and thrusts, earthquakes mainly dissipate elastic potential energy indeed. In the present article, a review is given of the most significant results of the last years in the field of geodynamics and earthquake geology following the common thread of gradients, which ultimately shape our planet.

show abstract

Investigation of the effect of geometric configurations on natural convection heat transfer in external flow

Güler

2024

Heat Trans

View full text Add to dashboard Cite

The complexities of natural convection heat transfer are investigated through experimentation, focusing on the influence of geometric configurations such as spheres, cylinders, and cubes in external flows. The study aims to understand how different geometries affect heat transfer coefficients, providing insights for architectural and engineering applications. Experimental results revealed significant variations in heat transfer efficiency among geometric models, with cubic configurations exhibiting the lowest heat transfer rates compared with spherical and cylindrical counterparts. This underscores the critical impact of geometric configuration on thermal performance and heat dissipation characteristics. The findings highlight the necessity of considering geometric factors in design processes to optimize thermal management strategies. The study contributes to a deeper understanding of convective heat transfer mechanisms, emphasizing the importance of precise geometric modeling in enhancing energy efficiency and sustainability in built environments

show abstract

How Properties that Distinguish Solids from Fluids and Constraints of Spherical Geometry Suppress Lower Mantle Convection

Cited by 18 publications

References 91 publications

Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow

Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow

Earth’s gradients as the engine of plate tectonics and earthquakes

Investigation of the effect of geometric configurations on natural convection heat transfer in external flow

Contact Info

Product

Resources

About