DOCSLIB.ORG

Joule Heating Effects in Electroosmotically Driven Microchannel Flows

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Joule Heating Effects in Electroosmotically Driven Microchannel Flows International Journal of Heat and Mass Transfer 47 (2004) 3085–3095 www.elsevier.com/locate/ijhmt Joule heating effects in electroosmotically driven microchannel flows Keisuke Horiuchi, Prashanta Dutta * Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920, USA Received 26 September 2003; received in revised form 23 February 2004 Abstract Analytical solutions for temperature distributions, heat transfer coefficients, and Nusselt numbers of steady elec- troosmotic flows are obtained for two-dimensional straight microchannels. This analysis is based on an infinitesimal electric double layer in which flow velocity becomes ‘‘plug-like’’, except very close to the wall. Both constant surface temperature and constant surface heat flux conditions are considered in this study. Separation of variables technique is applied to obtain analytical solutions of temperature distributions from the energy equation of electroosmotically driven flows. The thermal analysis considers interaction among inertial, diffusive and Joule heating terms in order to obtain thermally developing behavior of electroosmotic flows. Heat transfer characteristics are presented for low Reynolds number microflows where the viscous and electric field terms are very dominant. For the parameter range studied here (Re 6 0:7), the Nusselt number is independent of the thermal Peclet number, except in the thermally developing region. Analytical results for cases with and without Joule heating are also compared with the existing heat transfer results, and an excellent agreement is obtained between them. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Microfluidics; Electroosmotic flow; Joule heating 1. Introduction electro-mechanical systems (MEMS) have made a breakthrough progress toward utilizing electroosmotic Electroosmosis, one of the main electrokinetic effects, flows in complex microfluidic networks for ‘‘lab-on-a- is the process by which an ionized liquid moves with chip’’ applications. Lately, scientists at Sandia National respect to a stationary charged surface under the action Lab [3] and Stanford University [4,5] have successfully of an external electric field. The electroosmotic phe- developed electrokinetic micropumps capable of creat- nomenon was first observed by Ruess in 1809 from an ing in excess of 20 atm by packing micron sized non- experimental study on clay diaphragms [1]. In the mid- porous silica particles in a 500–900 lm diameter fused 19th century, Wiedemann repeated the experiment and silica capillary. Due to the ability of pumping a wide formally introduced the mathematical theory behind it range of working fluid, this non-mechanical pumping [2]. Though the electroosmotic phenomenon has been has become an attractive fluid handling method in the known for more than a century, the application of emerging ‘‘lab-on-a-chip’’ microfluidic devices for sam- electroosmotic flow was only limited in the field of ple loading, mixing, flushing and reagent transporting analytical chemistry to transport samples in capillaries. [6,7]. So far, most of the studies have been focused only But, recent developments in microelectronics and micro- on the fluid flow behavior where the velocity distribution is plug like in most of the channel [8–12], and not much attention has been paid on the thermal behavior. * Corresponding author. Tel.: +1-509-335-7989; fax: +1-509- One of the main objectives of electroosmotic action is 335-4662. to generate pressure head for pumping liquid in micro- E-mail address: [email protected] (P. Dutta). fluidic devices for bioanalytical applications. Here the 0017-9310/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2004.02.020 3086 K. Horiuchi, P. Dutta / International Journal of Heat and Mass Transfer 47 (2004) 3085–3095 Nomenclature 2 AC cross-sectional area of a microchannel [m ] b0 Fourier coefficient cp specific heat at constant pressure [J/(kg K)] bn Fourier coefficient D half channel height [m] d99 effective Debye layer thickness [m] DH hydraulic diameter [m] e permittivity of the medium [C/(V m)] ~E applied electric field [V/m] U viscous dissipation function Ex electric field component in the streamwise cn exponentialpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi decay parameter, 2 direction [V/m] ð PeT þ 4kn À PeTÞ=2 e electron charge [C] g non-dimensional cross-stream distance, G non-dimensional generation term y=D h local heat transfer coefficient [W/(m2 K)] k Debye length [m] k thermal conductivity [W/(m K)] kn eigenvalues 2 kB Boltzmann constant [J/K] l dynamic viscosity coefficient [N s/m ] L channel length [m] h non-dimensional temperature m_ mass-flow rate [kg/s] ha auxiliary temperature field n0 average number of positive/negative ions in hp particular type of function the buffer [1/m3] Dh non-dimensional temperature difference Nu Nusselt number, Dh=k hs À h 3 PeT thermal Peclet number, Re Á Pr qf fluid density [kg/m ] 3 Pr Prandtl number, m=a qe electric charge density [C/m ] 00 2 qs surface heat flux [W/m ] r electrical conductivity of the buffer fluid Re Reynolds number, umD=m [S/m] 2 Rev ratio of Joule heating to viscous dissipation t kinetic viscosity [m /s] T temperature [K] n non-dimensional streamwise distance u velocity component in the streamwise x=D direction [m/s] w electrokinetic potential [V] uHS Helmholtz–Smoluchowski velocity [m/s] f zeta potential [V] V~ velocity field [m/s] Subscripts v velocity component in the cross-stream c centerline direction [m/s] h homogenous W channel width [m] i inlet z valence m mean Greek symbols o non-homogenous 2 a thermal diffusivity, k=ðqcpÞ [m /s] s surface an Fourier coefficient pumping action can be achieved by applying a very high little attention, especially for electroosmotic microflows. external electric field along the channel. This high However, there are several analytical and experimental external electric field creates both conduction and con- works that appeared in literature describing the effect of vection current in the liquid, where convection current Joule heating in capillary electrophoresis for identical contributes to net flow in the system and conduction electric field and ion concentration [14,15]. Those works current generates volumetric Joule heating in the system identified thermal band broadening due to Joule heating. [8]. This Joule heating effect is very significant for high Explicit analytical solutions have been reported in electric field strength and/or highly conductive buffer. the past for both developing and fully developed thermal Since Joule heating is a volumetric phenomenon, its transport problems with or without volumetric heat magnitude is directly related to the channel volume. In generation. In a seminal work, Sparrow and co-workers typical electroosmotic flows with a fluid of 10À3 S/m [16] studied the effect of an arbitrary generation term in electrical conductivity and an applied electric field of 10 pressure driven thermally developing flows, and they V/mm, the Joule heating term contributes 105 W/m3. obtained analytical solutions for heat transfer charac- Depending on the surface (thermal) conditions, this teristics. Their framework is very similar to this study, thermal energy may elevate the system enthalpy signifi- but in our case the hydraulically fully developed elec- cantly [13]. The thermal energy generation and the troosmotic (plug like) velocity is used instead of pressure associated dissipation mechanisms have received very driven parabolic velocity profiles. In literature there also K. Horiuchi, P. Dutta / International Journal of Heat and Mass Transfer 47 (2004) 3085–3095 3087 exist numerous heat transfer studies in the slug flows by the anode. This results in the net movement of ion- both in parallel plates and in circular channels [17,18], ized fluid in the direction of the electric field. where they have not considered any Joule heating or generation terms. Recently, Maynes and Webb have 2.1. Governing equations presented thermal analysis of electroosmotic flows for circular tubes and parallel plates under Debye Huckel The steady electroosmotic flow is governed by the linearization [19]. However, that study is limited only to modified Navier–Stokes equations as [20] the fully developed thermal region. q ðV~ rÞV~ À lr2V~ þrP À q ~E ¼ 0 ð1Þ In this article, we obtain analytical solutions for f e temperature distributions and heat transfer characteris- ~ where qf is the fluid density, l is the dynamic viscosity, E tics for thermally developing steady electroosmotic flow is the applied electric field, and V~ ¼ðu; vÞ is the velocity in two-dimensional straight microchannels. Our analysis field. The incompressibility condition requires a diver- takes care of the interaction among convection, viscous, gence free velocity field (rV~ ¼ 0), subjected to no slip and Joule heating terms to obtain the temperature dis- and no penetration boundary conditions at the surface. tribution of the fluid in microchannels. This analysis The first and second terms of Eq. (1) indicate the inertia identifies the effects of Joule heating during electroos- and viscous forces, respectively. While the third term motic pumping in designing electroosmotically driven ~ shows the pressure force, and the final term, qeE, rep- micropumps, valves, and mixers where surface can be resents the electrokinetic body force due to the forma- maintained either at constant temperature or at constant tion of the EDL next to the surface. Here qe is the heat flux with the surrounding. electric charge density, and for a symmetric univalent dilute electrolyte it can be found as [20] 2. Theory ezw qe ¼2n0ez sinh ð2Þ kBT The formation of electroosmotic flow in a straight microchannel is shown in Fig. 1. Here the channel walls where w is the electrokinetic potential, n0 is the average attain net negative charges due to ionization, ion number of positive or negative ions in the buffer, e is the absorption, or ion adsorption from the polar liquid next electron charge, z is the valence, kB is the Boltzmann to the solid surface. These trapped surface charges sig- constant, and T is the absolute temperature.
Load more

Recommended publications
  • 3-D Electromagnetic Radiative Non-Newtonian Nanofluid Flow With
    www.nature.com/scientificreports OPEN 3‑D electromagnetic radiative non‑Newtonian nanofuid fow with Joule heating and higher‑order reactions in porous materials Amel A. Alaidrous1* & Mohamed R. Eid2,3* The aim of this work is to discuss the efect of mth‑order reactions on the magnetic fow of hyperbolic tangent nanofuid through extending surface in a porous material with thermal radiation, several slips, Joule heating, and viscous dissipation. In order to convert non‑linear partial diferential governing equations into ordinary ones, a technique of similarity transformations has been implemented and then solved using the OHAM (optimal homotopy analytical method). The outcomes of novel efective parameters on the non‑dimensional interesting physical quantities are established utilizing the tabular and pictorial outlines. After a comparison with previous literature studies, the results were fnely compliant. The study explores that the reduced Nusselt number is diminished for the escalating values of radiation, porosity, and source (sink) parameters. It is found that the order of the chemical reaction m = 2 is dominant in concentration as well as mass transfer in both destructive and generative reactions. When m reinforces for a destructive reaction, mass transfer is reduced with 34.7% and is stabled after η = 3. In the being of the destructive reaction and Joule heating, the nanofuid’s temperature is enhanced. Abbreviations a, b Constants (–) B0 Magnetic parameter C Concentration (mol/m3) cp Specifc heat C Free stream concentration (mol/m3)
    [Show full text]
  • Electric Permittivity of Carbon Fiber
    Carbon 143 (2019) 475e480 Contents lists available at ScienceDirect Carbon journal homepage: www.elsevier.com/locate/carbon Electric permittivity of carbon fiber * Asma A. Eddib, D.D.L. Chung Composite Materials Research Laboratory, Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, Buffalo, NY, 14260-4400, USA article info abstract Article history: The electric permittivity is a fundamental material property that affects electrical, electromagnetic and Received 19 July 2018 electrochemical applications. This work provides the first determination of the permittivity of contin- Received in revised form uous carbon fibers. The measurement is conducted along the fiber axis by capacitance measurement at 25 October 2018 2 kHz using an LCR meter, with a dielectric film between specimen and electrode (necessary because an Accepted 11 November 2018 LCR meter is not designed to measure the capacitance of an electrical conductor), and with decoupling of Available online 19 November 2018 the contributions of the specimen volume and specimen-electrode interface to the measured capaci- tance. The relative permittivity is 4960 ± 662 and 3960 ± 450 for Thornel P-100 (more graphitic) and Thornel P-25 fibers (less graphitic), respectively. These values are high compared to those of discon- tinuous carbons, such as reduced graphite oxide (relative permittivity 1130), but are low compared to those of steels, which are more conductive than carbon fibers. The high permittivity of carbon fibers compared to discontinuous carbons is attributed to the continuity of the fibers and the consequent substantial distance that the electrons can move during polarization. The P-100/P-25 permittivity ratio is 1.3, whereas the P-100/P-25 conductivity ratio is 67.
    [Show full text]
  • Joule Heating of the South Polar Terrain on Enceladus K
    JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, E04010, doi:10.1029/2010JE003776, 2011 Joule heating of the south polar terrain on Enceladus K. P. Hand,1 K. K. Khurana,2 and C. F. Chyba3 Received 12 November 2010; revised 1 February 2011; accepted 13 February 2011; published 27 April 2011. [1] We report that Joule heating in Enceladus, resulting from the interaction of Enceladus with Saturn’s magnetic field, may account for 150 kW to 52 MW of power through Enceladus. Electric currents passing through subsurface channels of low salinity and just a few kilometers in depth could supply a source of power to the south polar terrain, providing a small but previously unaccounted for contribution to the observed heat flux and plume activity. Studies of the electrical heating of Jupiter’s moon Europa have concluded that electricity is a negligible heating source since no connection between the conductive subsurface and Alfvén currents has been observed. Here we show that, contrary to results for the Jupiter system, electrical heating may be a source of internal energy for Enceladus, contributing to localized heating, production of water vapor, and the persistence of the “tiger stripes.” This contribution is of order 0.001–0.25% of the total observed heat flux, and thus, Joule heating cannot explain the total south polar terrain heat anomaly. The exclusion of salt ions during refreezing serves to enhance volumetric Joule heating and could extend the lifetime of liquid water fractures in the south polar terrain. Citation: Hand, K. P., K. K. Khurana, and C. F. Chyba (2011), Joule heating of the south polar terrain on Enceladus, J.
    [Show full text]
  • Joule Heating-Induced Particle Manipulation on a Microfluidic Chip
    Joule Heating-Induced Particle Manipulation on a Microfluidic Chip Golak Kunti,a) Jayabrata Dhar,b) Anandaroop Bhattacharyaa) and Suman Chakrabortya)* a)Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal - 721302, India b)Universite de Rennes 1, CNRS, Geosciences Rennes UMR6118, Rennes, France *E-mail address of corresponding author: [email protected] We develop an electrokinetic technique that continuously manipulates colloidal particles to concentrate into patterned particulate groups in an energy efficient way, by exclusive harnessing of the intrinsic Joule heating effects. Our technique exploits the alternating current electrothermal flow phenomenon which is generated due to the interaction between non-uniform electric and thermal fields. Highly non-uniform electric field generates sharp temperature gradients by generating spatially-varying Joule heat that varies along radial direction from a concentrated point hotspot. Sharp temperature gradients induce local variation in electric properties which, in turn, generate strong electrothermal vortex. The imposed fluid flow brings the colloidal particles at the centre of the hotspot and enables particle aggregation. Further, manoeuvering structures of the Joule heating spots, different patterns of particle clustering may be formed in a low power budget, thus, opening up a new realm of on-chip particle manipulation process without necessitating highly focused laser beam which is much complicated and demands higher power budget. This technique can find its use in Lab-on-a-chip devices to manipulate particle groups, including biological cells. INTRODUCTION Manipulation and assembly of colloidal particles including biological cells are essential in colloidal crystals, biological assays, bioengineered tissues, and engineered Laboratory-on- a-chip (LOC) devices.1–6 Concentrating, sorting, patterning and transporting of microparticles possess several challenges in these devices/systems.
    [Show full text]
  • Lecture 1: Basic Terms and Rules in Mathematics
    Lecture 5: electricity Content: - introduction - electric charge, potential, field, current, flux - electric dipole - resistance, conductance, Ohm‘s law - resistivity, conductivity - Kirchhoff's circuit laws - dielectric materials, permittivity - capacitor, capacitance - alternating current - skin effect, dispersion - Gaussian law in electrics fundamentals of electric field Electricity is the set of physical phenomena associated with the presence and flow of electric charge. Electric charge has a positive and negative sign. Electricity gives a wide variety of well-known effects, such as lightning, static electricity, electromagnetic induction and electric current (naturally originated). In addition, electricity permits the creation and reception of electromagnetic radiation such as radio waves. fundamentals of electric field Charge carriers: - in metals, the charge carriers are electrons (they are able to move about freely within the crystal structure of the metal). (a cloud of free electrons is called as a Fermi gas). - in electrolytes (such as salt water) the charge carriers are ions, atoms or molecules that have gained or lost electrons so they are electrically charged (anions, cations). This is valid also in melted ionic solids. - in a plasma, an electrically charged gas which is found in electric arcs through air, the electrons and cations of ionized gas act as charge carriers. - in a vacuum, free electrons can act as charge carriers. - in semiconductors (used in electronics), in addition to electrons, the travelling vacancies in the valence-band electron population (called "holes"), act as mobile positive charges and are treated as charge carriers. interesting trials with plasma lamp: https://www.youtube.com/watch?v=2gttW4F86Sg fundamentals of electric field Basic quantities: - electric charge: a property of some subatomic particles, which determines their electromagnetic interactions.
    [Show full text]
  • The Effects of Joule Heating on Electric-Driven Microfluidic Flow Alexander P
    Research Article from the SC Junior Academy of Science The Effects of Joule Heating on Electric-Driven Microfluidic Flow Alexander P. Spitzer South Carolina Governor’s School for Science and Mathematics This study sought out to more clearly understand the relationship between Joule heating and fluid flow in microfluidic environments, and more specifically, under what circumstances would the fluid flow in the device possibly hinder an experiment being run on it. It had been previous theorised that an electric field may produce turbulence and even vortices within the fluid, which this study attempted to reproduce. Several variables were tested, namely insulating and conducting fluids, higher and lower AC voltages, Newtonian vs. non- Newtonian fluids, and higher and lower DC voltages. A correlation between these variables and turbulent flow was found, with more conductive fluids, higher AC voltages, non-Newtonian fluids, and higher DC voltages more prone to fluid turbulence. Introduction Lab-on-a-chip devices are widely used in research to perform microfluidic chemical and biomedical analysis. However, some of these chips are driven using an electric field, which can cause potentially catastrophic side-effects, one of which is joule heating. Joule heating is an effect where heat is produced in a medium through which an electric current is passed. This can be an issue in microfluidic devices, especially in those with designs that contain constrictions in their channels. Due to the fact that electrical resistance increases with decreasing cross-sectional area and more heat is produce when resistance increases, temperature gradients can form in the fluid. This creates chaotic flow that may disrupt any experiment being performed on the chip.
    [Show full text]
  • Joule Heating in Nanowires
    Accepted for publication in Physical Review B (6 May 2011) Joule heating in nanowires Hans Fangohr,1, ∗ Dmitri S. Chernyshenko,1 Matteo Franchin,1 Thomas Fischbacher,1 and Guido Meier2 1School of Engineering Sciences, University of Southampton, SO17 1BJ, Southampton, United Kingdom 2Institut f¨urAngewandte Physik und Zentrum f¨urMikrostrukturforschung, Universit¨atHamburg, Jungiusstrasse 11, 20355 Hamburg, Germany We study the effect of Joule heating from electric currents flowing through ferromagnetic nanowires on the temperature of the nanowires and on the temperature of the substrate on which the nanowires are grown. The spatial current density distribution, the associated heat generation, and diffusion of heat is simulated within the nanowire and the substrate. We study several different nanowire and constriction geometries as well as different substrates: (thin) silicon nitride membranes, (thick) silicon wafers, and (thick) diamond wafers. The spatially resolved increase in temperature as a function of time is computed. For effectively three-dimensional substrates (where the substrate thickness greatly exceeds the nanowire length), we identify three different regimes of heat propagation through the substrate: regime (i), where the nanowire temperature increases approximately logarithmically as a function of time. In this regime, the nanowire temperature is well-described analytically by You et al. [APL89, 222513 (2006)]. We provide an analytical expression for the time tc that marks the upper applicability limit of the You model. After tc, the heat flow enters regime (ii), where the nanowire temperature stays constant while a hemispherical heat front carries the heat away from the wire and into the substrate. As the heat front reaches the boundary of the substrate, regime (iii) is entered where the nanowire and substrate temperature start to increase rapidly.
    [Show full text]
  • Experimental Evidence in Support of Joule Heating Associated with Geomagnetic Activity
    SA TECHNICAL NOTE LOAN COPY AFWL ( KIRTLAND EXPERIMENTAL EVIDENCE IN SUPPORT OF JOULE HEATING ASSOCIATED WITH GEOMAGNETIC ACTIVITY b by Leonard L. DeVries George C. Marshall Spuce Flight Center Marshall Space Flight Center, Ala 35812 NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. NOVEMBER 1971 I TECH LIBRARY KAFB, NM 1. Report No. 2. Government Accession No. .LLKL.. I I 4. Title and Subtitle 1 5. Report Date I November 1971 Experimental Evidence in Support of Joule Heating 6. Performing Organization Code Associated with Geomagnetic Activity I I 7. Author(s) I El. Performing Organization Report No. MI75 Leonard L. DeVries I 10. Work.Unit No. I 9. Performing Organization Name and Address I 976-30-00 George C. Marshall Space Flight Center 11. Contract or Grant No. Marshall Space Flight Center, Alabama 35812 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration Washington, D.C. 20546 15. Supplementary Notes Prepared by Aero-Astrodynamics Laboratory, Science and Engineering I 16. Abstract High resolution acccleromctcr measurements in the altitude region 140 to 300 km from a satellite in a near-polar orbit during a period of extremely high geomagnetic activity indicate that Joule heating is tlie primary source of energy for atmospheric heating associated with geomagnetic activity. This concl~isionis supported by the following observational evidence: (I) There is an atmospheric rcsponsc in tlie auroral zone which is nearly simultaneous with the onset of geomagnetic activity, with no significant response in the equatorial region until several hours later; (2) the maximum heating occurs at geographic locations near the maximum current of the auroral electrojet; and (3) there is evidence of atmospheric waves originating near the auroral zone at altitudes where Joule heating would be expected to occur.
    [Show full text]
  • Preview of Period 13: Electrical Resistance and Joule Heating
    Preview of Period 13: Electrical Resistance and Joule Heating 13.1 Electrical Resistance of a Wire What does the resistance of a wire depend upon? 13.2 Resistance and Joule Heating What effect does resistance have on current flow? What is joule heating? 13.3 Temperature and Resistance How does the temperature of a wire affect its resistance? 13-1 Measuring Resistance with a Multimeter 1. Turn the dial to the ohm symbol (Ω). 2. Check that the wire leads are attached to the outlets on the lower right of the meter. 3. To measure resistance, touch the ends of the leads to each end of the resistor wire. Ω V Ω COM 13-2 Act. 13.1: Measuring Resistance Measuring the resistance of the 30 cm wire. Ω 1. Do not connect the battery tray to the green board with resistance wires. 2. Set the multimeter to “ Ω ” to measure resistance. 3. Touch the ends of the multimeter leads across the thin 30 cm wire to measure its resistance. Then move the multimeter leads to the ends of the 15 cm wire to measure its resistance. 13-3 Act.13.1: Resistance of a Wire Resistance of a wire = Resistivity x Length Area ρ L R = A R = resistance (in ohms) ρ = resistivity (in ohm meters) L = length of resistor (in meters) A = cross-sectional area (in meters2) A Wire Resistor of Length L and Cross-Sectional Area A A L 13-4 Joule Heating in Wires ♦ Current flowing through wires encounters resistance, and some electrical energy is transformed into thermal energy.
    [Show full text]
  • Chapter 20: Electric Current, Resistance & Ohm's
    Chapter 20: Electric Current, Resistance & Ohm’s Law Brent Royuk Phys-112 Concordia University The “Minds of Our Own” Challenge • Light a bulb with a battery and a wire. Could you do it? 2 Introduction • Batteries supply charge to produce a current – How? Electrochemistry stuff: oxy/redux • cathode and anode • dry cell vs. battery – Electric current = moving charges • dc vs. ac • How does this relate to electrostatics? – Electroscope and D-cell? – Voltage of charge strips 3 Electric Current • Current Flow – Consider a simple circuit diagram • What direction does the current flow? – Electron flow vs. conventional current • Curse you Ben Franklin! 4 Electric Current ΔQ • Definition: I = Δt • Unit: The ampere (A) – “amps” • 1 A =€ 6.25 x 1018 electrons/s 5 The Water Pump Analogy 6 Drift Velocity • Even without a potential, electrons are in constant motion • Electric field --> force --> drift velocity – How many conduction electrons are in a wire? • So drift velocities are often very slow, like walking speeds. • So why don’t we have to wait for the light when we hit the switch? – What moves fast? – “Marbles in a tube” analogy 7 Ohm’s Law • Two laws for resistive circuits: – I α ΔV – I α 1/R • Put them together and you get V = IR – Ohm’s Law 8 Ohm’s Law • Definition of resistance: R = V/I – Resistance Unit: The ohm (Ω) • Ohm’s Law doesn’t apply to all materials – E.g. semi-conductors, lightbulb filaments – (Known as Ohmic & Non-Ohmic materials) 9 Resistivity • Resistivity is a measure of how well a material conducts electricity.
    [Show full text]
  • Joule's Experiment: an Historico-Critical Approach
    Joule's experiment: An historico-critical approach Author: Marcos Pou Gallo Advisor: Enric P´erezCanals Facultat de F´ısica, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Spain. Abstract: We present the result of the historical analysis of Joule's paper \The mechanical equivalent of heat" (1849). We give a brief but close examination of his measurements of the mechanical value of a calorie, as well as their influence in the birth of thermodynamics. I. INTRODUCTION know it today wasn't even born. Heat, temperature and energy belong to different The study of heat and temperature yielded a great scales, such as the motion of microscopic particles and number of contradictions to resolve. Concepts like the thermal state a certain body. In the 19th century \heat" or \temperature" were confused and usually these concepts were widely discussed. The discoveries misunderstood. In the eighteenth century these ideas and the experiments of those years changed physics had been widely discussed, but we want to emphasize and its way of explaining reality. Among the involved the work by Joseph Black. The fact that heat had a scientists, James Prescott Joule stands out with his kind of capacity to increment an object's temperature famous measurement of the mechanical equivalent of by contact made him think that fire (for instance) had heat. \something" that passed to other objects [3]. Other experiments suggested to Black that heat was not Joule's experiment had a big influence and was one created or destroyed; it simply changed \location". The of the most relevant results around the emergence of temperature that a body gain when heated would be the principle of conservation of energy.
    [Show full text]
  • Entangled Dynamos and Joule Heating in the Earth's Ionosphere
    Ann. Geophys., 38, 1019–1030, 2020 https://doi.org/10.5194/angeo-38-1019-2020 © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. Entangled dynamos and Joule heating in the Earth’s ionosphere Stephan C. Buchert Swedish Institute of Space Physics, Uppsala, Sweden Correspondence: Stephan C. Buchert ([email protected]) Received: 9 May 2019 – Discussion started: 21 May 2019 Revised: 2 June 2020 – Accepted: 5 August 2020 – Published: 24 September 2020 Abstract. The Earth’s neutral atmosphere is the driver of the cently by Yamazaki and Maute(2017). Sq is driven by a well-known solar quiet (Sq) and other magnetic variations neutral dynamo. Vasyliunas¯ (2012) has summarized the fun- observed for more than 100 years. Yet the understanding of damental equations for a neutral dynamo and his critical view how the neutral wind can accomplish a dynamo effect has of the understanding within the community. The conceptual been incomplete. A new viable model is presented where a difficulty of the author’s interpretation of the neutral dynamo dynamo effect is obtained only in the case of winds perpen- can be phrased less mathematically as follows: in the frame dicular to the magnetic field B that do not map along B. of the neutral gas the product j · E∗, j the electric current, Winds where u × B is constant have no effect. We identify and E∗ the electric field is in the steady state zero or pos- Sq as being driven by wind differences at magnetically con- itive, because of the well-known Ohm’s law for the iono- jugate points and not by a neutral wind per se.
    [Show full text]