Earth's internal heat budget (Earth 🌍)

Earth's internal heat budget is fundamental to the thermal history of the Earth. The flow of heat from Earth's interior to the surface is estimated at 47±2 terawatts and comes from two main sources in roughly equal amounts: the radiogenic heat produced by the radioactive decay of isotopes in the mantl...

https://en.wikipedia.org/wiki/Earth's_internal_heat_budget

#EarthSInternalHeatBudget #Earth #Geodynamics #HeatTransfer #PlateTectonics #GeothermalEnergy

🍥 Nanofluids and turbulators have potential to boost renewable energy and slash dependence on fossil fuels

https://techxplore.com/news/2025-01-nanofluids-turbulators-potential-boost-renewable.html

#energy #engineering #heattransfer #technology #efficiency #materials

How Cooling Towers Work

Power plants (and other industrial settings) often need to cool water to control plant temperatures. This usually requires cooling towers like the iconic curved towers seen at nuclear power plants. Towers like these use little to no moving parts — instead relying cleverly on heat transfer, buoyancy, and thermodynamics — to move and cool massive amounts of water. Grady breaks them down in terms of operation, structural engineering, and fluid/thermal dynamics in this Practical Engineering video. Grady’s videos are always great, but I especially love how this one tackles a highly visible piece of infrastructure from multiple engineering perspectives. (Video and image credit: Practical Engineering)

#buoyancy #civilEngineering #convection #engineering #evaporation #fluidDynamics #heatTransfer #infrastructure #physics #science #thermodynamics

Eğer bir su borusuna ísí yalıtımí yapmak isterseniz, belli bir kalınlığa ulaşana kadar arttırdığınız yalıtım kalınlığı ısı transferini arttırır. Misal 1 cm kalınlığında bir kaplama yapmak istiyorsunuz ama kalınlığı 0.25 olarak arttirabiliyorsuniz diyelim. 0.25 den0.50ye, 0.50den 0.75 e gelince ısı yalıtımı ters etki yapıp ısı transferini arttırıyor, taki 1 cm değerini geçene kadar. Düşününce akla mantığa ters geliyor değil mi?
#heat #heattransfer #engineering #mechanical #energy

This book aims to equip readers with the mathematical physics skills necessary to solve problems in mechanics, heat conduction, and electromagnetism. It covers a wide range of topics, from basic to advanced, and is intended for both students and researchers. The book provides hints for solving problems and includes detailed solutions to selected ones. Readers should have a solid background in applied mathematics to fully benefit from the book, but most problems in the earlier chapters are accessible to those with a basic understanding of mathematical physics methods.

Translated from the Russian by Richard A. Silverman.

Get the book here.

Contents

PART 1

CONTENTS

PROBLEMS, Page 1

DERIVATION OF EQUATIONS AND FORMULATION OF PROBLEMS, Page 3

1. Mechanics, 3
2. Heat Conduction, 9
3. Electricity and Magnetism, 11

SOME SPECIAL METHODS FOR SOLVING HYPERBOLIC AND ELLIPTIC EQUATIONS, Page 19

1. Hyperbolic Equations, 19
2. Elliptic Equations: The Green’s Function Method, 27
3. Elliptic Equations: The Method of Conformal Mapping, 33

STEADY-STATE HARMONIC OSCILLATIONS, Page 42

1. Elastic Bodies: Free Oscillations, 43
2. Elastic Bodies: Forced Oscillations, 46
3. Electromagnetic Oscillations, 49

THE FOURIER METHOD, Page 55

1. Mechanics: Vibrating Systems, Acoustics, 60
2. Mechanics: Statics of Deformable Media, Fluid Dynamics, 73
3. Heat Conduction: Nonstationary Problems, 77
4. Heat Conduction: Stationary Problems, 83
5. Electricity and Magnetism, 91

THE EIGENFUNCTION METHOD FOR SOLVING INHOMOGENEOUS PROBLEMS, Page 103

1. Mechanics: Vibrating Systems, 107
2. Mechanics: Statics of Deformable Media, 114
3. Heat Conduction: Nonstationary Problems, 119
4. Heat Conduction: Stationary Problems, 124
5. Electricity and Magnetism, 131

INTEGRAL TRANSFORMS, Page 143

1. The Fourier Transform, 146
2. The Hankel Transform, 160
3. The Laplace Transform, 169
4. The Mellin Transform, 189
5. Integral Transforms Involving Cylinder Functions of Imaginary Order, 194

CURVILINEAR COORDINATES, Page 203

1. Elliptic Coordinates, 204
2. Parabolic Coordinates, 210
3. Two-Dimensional Bipolar Coordinates, 212
4. Spheroidal Coordinates, 219
5. Paraboloidal Coordinates, 231
6. Toroidal Coordinates, 233
7. Three-Dimensional Bipolar Coordinates, 242
8. Some General Problems on Separation of Variables, 247

INTEGRAL EQUATIONS, Page 253

1. Diffraction Theory, 254
2. Electrostatics, 259

PART 2 SOLUTIONS, Page 273

MATHEMATICAL APPENDIX, Page 381

1. Special Functions Appearing in the Text, 381
2. Expansions in Series of Orthogonal Functions, 384
3. Some Definite Integrals Frequently Encountered in the Applications, 386
4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates, 388

Supplement: VARIATIONAL AND RELATED METHODS, Page 391

1. Variational Methods, 392
   1.1 Formulation of Variational Problems, 392
   1.2 The Ritz Method, 396
   1.3 Kantorovich’s Method, 401
2. Related Methods, 404
   2.1 Galerkin’s Method, 404
   2.2 Collocation, 407
   2.3 Least Squares, 411

References, 412

BIBLIOGRAPHY, Page 415

NAME INDEX, Page 423

SUBJECT INDEX, Page 427

https://mirtitles.org/2024/10/09/worked-problems-in-applied-mathematics-by-n-n-lebedev-i-p-skalskaya-y-s-uflyand/

#curvilinearCoordinates #eigenfunctionMethod #ellipticEquations #FluidDynamics #fourierMethod #harmonicOscillations #heatTransfer #hyperbolicEquations #integralEquations #mathematicalPhysics #mathematics #mechanics #physics #problemsAndSolutions #variationalMethods

🧨 Sette capestri per sette sorelle
by @enrico_dassereto

#artedigitale #illustrazione #cardboard #heattransfer #adesivi #graphicstudio #disegnodigitale #artedigitale #illustrazionedigitale #creativit