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Microwave Heating of Fluid/Solid Layers : a Study of Hydrodynamic Stability

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Microwave Heating of Fluid/Solid Layers : a Study of Hydrodynamic Stability Copyright Warning & Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be “used for any purpose other than private study, scholarship, or research.” If a, user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of “fair use” that user may be liable for copyright infringement, This institution reserves the right to refuse to accept a copying order if, in its judgment, fulfillment of the order would involve violation of copyright law. Please Note: The author retains the copyright while the New Jersey Institute of Technology reserves the right to distribute this thesis or dissertation Printing note: If you do not wish to print this page, then select “Pages from: first page # to: last page #” on the print dialog screen The Van Houten library has removed some of the personal information and all signatures from the approval page and biographical sketches of theses and dissertations in order to protect the identity of NJIT graduates and faculty. ASAC MICOWAE EAIG O UI/SOI AYES A SUY O YOYAMIC SAIIY A MEIG O OAGAIO y o Gicis In this work we study the effects of externally induced heating on the dynamics of fluid layers, and materials composed of two phases separated by a thermally driven moving front. One novel aspect of our study, is in the nature of the external source which is provided by the action of microwaves acting on dielectric materials. The main challenge is to model and solve systems of differential equations which couple fluid dynamical motions (the Navier-Stokes equations for non-isothermal flows) and electromagnetic wave propagation (governed by Maxwell's equations). When an electromagnetic wave impinges on a material, energy is generated within the material due to dipolar and ohmic heating. The electrical and thermal properties of the material dictate the dynamics of the heating process, as well as steady-state temperature profiles. Such forms of heating have received little attention in studies of hydrodynamic instabilities of non-isothermal flows, such as the classical Benard problem, for instance. The novel feature, which allows possibilities for fluid management and control, is the non-local coupling between the electro- magnetic field and the temperature distribution within the fluid. In the first part of the thesis, we consider hydrodynamic instabilities of such systems with particular emphasis on conditions for onset of convection. This is achieved by solving the linear stability equations in order to identify parameter values which produce instability. The analysis and subsequent numerical solutions are carried out both for materials with constant dielectric attributes (in such cases the electric field equations decouple and they can be solved in closed form), and materials with temperature dependent MICOWAE EAIG O UI/SOI AYES A SUY O YOYAMIC SAIIY A MEIG O OAGAIO y o Gicis A isseaio Sumie o e acuy o ew esey Isiue o ecoogy i aia uime o e equiemes o e egee o oco o iosoy eame o Maemaics Augus 199 AOA AGE MICOWAE EAIG O UI/SOI AYES A SUY O YOYAMIC SAIIY A MEIG O OAGAIO o Gicis Gregory X. Kriiegsmann, Ph.D.", Dissertation Advisor Date Distinguished Professor, Department of Mathematics, New Jersey Institute of Technology, Newark NJ Price Papageorgiou, Ph.D., Dissertation Advisor Date Associate Professor, Department of Mathematics, New Jersey Institute of Technology, Newark NJ Jo9an H. C. Luke, Ph.D., Committee Member Date Associate Professor, Department of Mathematics, New Jersey Institute of Technology, Newark NJ Yuriko Renardy, Ph.D., Committee Member Date Professor, Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg VA Burt S. Tilley, Ph.D., Commyhe Member Date Assistant Professor, Department of Mathematics, New Jersey Institute of Technology, Newark NJ IOGAICA SKEC Auo o Gicis egee oco o iosoy ae Augus 199 Uegauae a Gauae Eucaio • oco o iosoy i Aie Maemaics ew esey Isiue o ecoogy ewak 199 • Mase o Sciece i Aie Maemaics ew esey Isiue o ecoogy ewak 1991 • aceo o Sciece i Comue Sciece uges Uiesiy (Cook Coege ew uswick 19 Mao Aie Maemaics uicaios o Gicis Gegoy A Kiegsma emeius aageogiou "Saiiy o A Micowae eae ui aye" 1MA oua o Aie Maemaics auay 199 o Gicis C Musae S aa oicks uac "Moeig o i iames o oymeic iqui Cysas" Caemo Coeges Maemaics Moeig Wokso oceeigs Caemo CA ue 199 i o my aes v ACKOWE GME I i a oaiiy ee wou ae usue a ocoa egee wiou e isiaio a ecouageme o wo ey secia eoe oesso emeius aageogiou a oesso Gegoy A Kiegsma wo saw i me aes a aiiies a I i see i myse I wou ike o ak oesso oaa uke oesso Yuiko eay a oesso u S iey wo wee aways ee o oe me gui 4.1 ce i my eseac ei wos wee aways wos o ecouageme a ese wos oie me wi e seg o eue e oug imes I wou ike o ak my amiy wo oee ei cosa suo a ecouageme aks o my ies wo ee me o maiai a oe aace ewee wok a ay ey ee me o maiai my saiy uig ese yeas o iese wok i AE O COES Cae age 1 IOUCIO 1 11 yoyamic Saiiy 1 1 Aicaios o Micowaes i e Meig o Maeias 4 YOYAMIC SAIIY O A UI AYE COSA IEECIC EMIIIY CASE 6 1 e Moe 6 2.2 asic Saes 1 1 A imiig Case k —÷ (ow equecy 11 3 iea Saiiy 13 2.4 umeica Souios 1 1 A imiig Case (ow Wae ume euaie Moes 1 2.4.2 A imiig Case (Saiiy o Moes o age Ciica owe ees 17 5 esus 19 2.6 iscussio 26 3 YOYAMIC SAIIY O A UI AYE EMEAUE EEE COME EMIIIY 28 31 e Moe 28 3 asic Saes 31 31 ema uaway 3 33 iea Saiiy eoy 39 3 umeica Souios 42 31 A iie ieece Aoac 42 35 esus 5 3 iscussio 5 ii Cae age A MOE O MEIG O SOIS USIG MICOWAES 5 1 A ysica Oeiew (e Sea Coiio 5 e Maemaica Moe 5 3 e Case o Cosa ieecic emiiiy 57 31 Seay-Sae Souios 57 3 Asymoic imi o age Sea ume e Case o emeaue eee ieecic Aiues 1 Seay-Sae Souios 5 A ie o Meo o ackig e Moig ouay 51 umeica Imemeaio 9 5 e Case o Cosa ieecic oeies (Geea Sea ume 7 53 e Case o emeaue eee ieecic oeies (Geea Sea ume 7 iscussio 77 AEI A E MEO O MUIE SCAES 7 AEI EIAIO O EQUAIOS GOEIG "COME EECIC IE" 1 AEI C WK AAYSIS 3 EEECES 5 iii IS O IGUES igue age 1 e geomey o e yoyamic oem 7 yica uisue emeaue oies; e ysica aamees ae [3 =1; Er = 5 ; 6 = 5 1 3 Gow ae cues igi-igi case; )3 = 1; k = 1; Er = 5; Pr = 17; =. 5 15 Eigeucios TV(z) (o a e(z) (oom; = 1; k = 1; Er = 5; Pr = 17; e = 5 17 5 Asymoic eigeucios a age Rx, 3 = 1; k 1 ; Er = 5; e = 5 19 eua saiiy cues i e Rx-a ae; k = 1; Er = 5; ; e = 5 1 7 eua cues igi-igi case (3 = 1; Er = 5; 6 = 5 1 As i igue 7 u igi-ee ouay coiios 9 euaio ow ie a ose; ase emeaue oie 1 sue- imose o ow ie 0 = 1; k = 75; Er = 5; e =--- 5; ciica wae ume a =5 1 euaio ow ie a ose; ase emeaue oie 1 sue- imose o ow ie /3 = 1; k = 1355; Er = 5; e = 5; ciica wae ume a =1 11 euaio ow ie a ose; ase emeaue oie 1 sue- imose o ow ie = 1; k = 71; Er = 5; e 5; ciica wae ume a =199 5 1 euaio ow ie a ose; ase emeaue oie 1 sue- imose o ow ie = 1; k = 13; er = 5; e = 5; ciica wae ume a =3 5 31 ieecic emiiiy o wae s emeaue; 33 3 ieecic oss aco o wae s emeaue; 33 33 Uisue emeaue oies o wae; /3 = 1 3 3 Seay-sae cues o wae (0, vs. x); 8 = 1. 3 35 Seay-sae cues o wae ( ° s u; 3 1 3 3 Gow ae cues igi-igi case; )3 = 1; k = 1; Pr = 7 5 i igue age 37 eua saiiy cues i e -a ae o wae; k = 1 7 3 eua cues i e — k ae o wae igi-igi case /3 = 1; k = 1 39 eua cues o wae (ciica wae ume s k), igi-igi case = 1; k = 1 9 31 eua cues o wae (eig o maimum emeaue s k igi- igi case /3 = 1; k = 1 9 311 eua cues o wae (maimum emeaue s k), igi-igi case /3 = 1; k = 1 5 1 e geomey o e meig oem 53 e ysics goeig e moig o 53 3 Seay-sae cues (cosa come emiiiy wi ayig io ume Tb„ = —5; k = 1 Seay-sae cues (cosa come emiiiy wi ayig ouay coiio 3 = 1; k = 1 1 5 Seay-sae cues (cosa come emiiiy cases )3 = 1; k = 1; Tb,, = —5 1 Meig o osiio S s eiaie S': )3 = 1; k = 1 7 Seay-sae cues (cosa a aiae come emiiiy cases = 1; k = w = — 5 7 Meig o osiio S s ime (cosa come ieecic emi- tivity): (3 = 1; k = 1 7 9 Meig o osiio S s ime (emeaue eee come ieecic emiiiy =; 13 = 1; k = 1 7 1 Meig o osiio S s ime : = ; /3 = 1; k = 1; w = — 5 • 7 11 Meig o osiio S s ime = ; /3 = 1; k = 1; w = .
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