The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T _Wx and surface injectionv _Wx(–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

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Der Effekt des Oberflächenstoffaustausches bei auftriebsinduzierter Strömung in einem variablen porösen Medium, das an eine vertikale, beheizte Platte angrenzt

Zusammenfassung Es wird der Effekt des Oberflächenstoffaustausches in auftriebsinduzierter Strömung in einem variablen porösen Medium, das an eine vertikale, beheizte Platte angrenzt, für große Reynoldszahlen untersucht. Ähnliche Lösungen werden im Rahmen der Grenzschicht-Theorie, durch Variation des Potenzansatzes der Oberflächentemperatur,T _Wx , und der Oberflächengeschwindigkeit,v _Wx(–1/2), erreicht. Die Analyse vereinigt sowohl den Ausdruck, der Porösität und Permeabilität verbindet, als auch den Ausdruck, der Porösität und Wärmeleitfähigkeit miteinander verbindet. Der Einfluß der Temperaturverteilung auf Strömung und Wärmeübergangskennzahlen wird ebenfalls im Detail analysiert. Als Ergebnis der vorliegenden Untersuchung ergibt sich die Tatsache, daß variable Porösität Wärmeübertragungsrate und Betrag der Geschwindigkeit in Wandnähe steigert. Die bestimmenden Gleichungen, sowohl für das Darcysche Strömungsmodell als auch für das Forchheimersche Strömungsmodell, werden mit Hilfe eines implizierten Differenzenschemas gelöst. Die Berechnung wird für die beiden Fälle, isotherme Oberfläche und undurchlässige vertikale Platte, angewandt. Der Einfluß der Terme für die Trägheitskräfte im Forchheimerschen Modell senkt Wärmeübergangs- und Durchgangsrate, wogegen die Wärmeübergangsrate durch den Einfluß der Temperaturverteilung erhöht wird.

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Nomenclature a constant defined by Eq. (12) - A constant defined by Eq. (12) - B constant defined by Eq. (3) - b _s/_f ratio of thermal conductivities - C constant defined by Eq. (1) - C _P specific heat of the convective fluid - d particle diameter - f dimensionless function defined by Eq. (14) - f _w lateral mass flux parameter - g acceleration due to gravity - k ₀ mean permeability of the mediumk ₀= ₀ ³ d ²/150 (1– ₀)² k ₀=1.75d/(1– ₀) 150 (Inertia parameter) - L length of the source or sink - m mass transfer - n constant defined in Eq. (12) - k (y) permeability of the porous medium - k (y) interial coefficient in the Ergun expression - Gr modified Grashof numberGr=(g k ₀ k ₀ (T _w–))/ ² - R _a Rayleigh number (g k ₀ x T _w–)/ - R _ad modified Rayleigh number (g k ₀ d|T _w–|)/ - N _u Nusselt number - s x/d - Q overall heat transfer rate - T temperature - T _w surface temperature - T ambient fluid temperature - u velocity in vertical direction - v velocity in horizontal direction - x vertical coordinate - y horizontal coordinate Greek symbols ₀ mean thermal diffusivity _f/ C_p - coefficient of thermal expansion - constant defined in Eq. (4) - ratio of particle to bed diameter - _e effective thermal conductivity - f thermal conductivity of fluid - _s thermal conductivity of solid - dimensionless similarity variable in Eq. (13) - value of at the edge of the boundary layer - constant defined in Eq. (1) - _e effective molecular thermal diffusivity - (y) porosity of the medium - ₀ mean porosity of the medium - viscosity of the fluid - ₀ density of the convective fluid - stream function - w condition at the wall - condition at infinity     

Microwave‐Assisted Expedite Synthesis of 2‐Phenylimidazo[1,2‐a]pyridylquinoxalin‐2(1H)‐ones

An efficient methodology has been developed for the synthesis of quinoxalin‐2(1H)‐one derivatives of 2‐phenylimidazo[1,2‐a]pyridines by microwave‐irradiated Hinsberg heterocyclization between 2‐phenylimidazo[1,2‐a]pyridine‐3‐glyoxalates and o‐phenylenediamine using either montmorillonite K‐10 or Yb(OTf)₃ as catalysts. Montmorillonite K‐10 was proven to be an efficient catalyst for the heterocyclization reaction between sterically hindered glyoxalate and o‐phenylenediamine only under microwave conditions. The use of Yb(OTf)₃/tetrahydrofuran was also found to be an effective catalyst for the above chemical transformation among a series of Lewis acids screened under microwave conditions; however, comparatively lesser yields were obtained as compared with the use of montmorillonite K‐10.     

Anion‐ and Spacer‐Directed Host–Guest Complexes of Bipyridine with Pyrogallol[4]arene

New oval‐shaped capsular and bilayer‐type hydrogen‐bonded arrangements of C‐propyl‐ol‐pyrogallol[4]arene (PgC3‐OH) with bipyridine‐type spacer complexes are reported here. These complexes are engineered by virtue of derivatization of C‐alkyl tails of pyrogallol[4]arene and the use of divergent spacer ligands. Complexes of PgC3‐OH, PgC3‐OH with bpy (4,4′‐bipyridine) and PgC3‐OH with bpa (1,2‐bis(4‐pyridyl)acetylene) have bilayer type arrangements; however, the use of hydrogen chloride causes protonation of bpy molecule, which is then entrapped flat within an offset oval‐shaped dimeric hydrogen‐bonded PgC3‐OH nanocapsule. The presence of chloride anion in the crystal lattice controls the geometry of the resultant nanoassembly.     

Efficient synthesis of acridinediones in aqueous media

An efficient synthesis of acridinediones in two steps have been achieved using water as a reaction media without chromatographic purification. First step involves the reaction of dimedone with ammonium acetate to yield enaminone in water which on further reaction with various aldehydes yields acridinedione in aqueous media. The reaction merits the use of water as solvent, no additive catalyst and provides high yield of products with good purity.     

Why to consider environmental pollution in cholera modeling?

We propose a deterministic model to study the impact of environmental pollution on the dynamics of cholera. We consider both human to human and human‐environment‐human transmission modes in our model. We obtain the expression for the basic reproduction number of the proposed model. The study of our model reveals that environmental pollution plays a significant role in the spread of cholera and should not be ignored. Although various dimensions of cholera has been studied using mathematical models but scanty efforts have been made to understand impact of environmental pollution on this disease. Through this study, we try to bridge this gap.     

Quality by Design enabled enhanced bioanalytical extraction and UFLC determination of vilazodone from rat serum

An ultrafast liquid chromatographic bioanalytical method was developed and validated for the determination of vilazodone in Wistar rat serum. Principles of quality by design were implemented for enhancing the bioanalytical liquid–liquid extraction of vilazodone from rat serum. A Box–Behnken design was utilized in the studies by selecting extraction time, centrifugation speed, and vortex time as the critical method variables for evaluating their effect on the analytical attribute, i.e., %recovery of vilazodone. Chromatographic separation was achieved within a run time of 10?min using a C-18 column and mobile phase comprising of methanol:phosphate buffer of pH 7 (85:15 v/v) flowing at 1.5?mL/min. Photodiode array detection was performed at 242?nm. Results of validation studies were satisfactory. The method was linear over a concentration of 100–2,000?ng/mL with acceptable accuracy and precision. Limits of detection and quantitation for the developed method were 50 and 100?ng/mL, respectively. This QbD-based approach was found suitable for routine bioanalysis of vilazodone in the biological matrix.     

Effect of electric field on reentrance transition in a binary mixture of liquid crystals

Employing a phenomenological mean field theory, we analyze the effect of an electric field on the N ? SmA phase transition for pure liquid crystal and on the reentrant nematic phase in a binary mixture of liquid crystals exhibiting the phase sequence I ? N ? SmA ? N_R on cooling. The basic idea of the work is to explain the phase transition behavior of the system by assuming that certain Landau coefficients associated with the order parameters coupling terms of the free-energy density expansion are field dependent. These parameters play a crucial role and show a rapid variation at the SmA ? N_R transition as compared to the SmA ? N transition.     

A facile one‐pot reactive solution blending approach for main‐chain donor–acceptor polymeric materials

A high‐temperature solution blending process has been used to synthesize a series of copolymers incorporating varying mole ratios of perylenebisimide (PBI) into the backbone of an engineering thermoplastic polyester [poly(1,4‐cyclohexylenedimethylene‐1,4‐cyclohexanedicarboxylate)] (PCCD). A random donor–acceptor copolymer incorporating oligo(p‐phenylene vinylene) (OPV) and PBI was also synthesized. The chemical incorporation of these chromophores into PCCD was confirmed by carrying out the melt condensation using 1,4‐cyclohexanedimethanol and 1,4‐dimethylcyclohexane dicarboxylate with hydroxyl‐functionalized PBI and OPV derivatives. Higher extent of incorporation of PBI (35 mol %) could be achieved using the blending approach retaining solubility, film‐forming ability, and higher molecular weights. The PBI polymers produced using the two different approaches exhibited structural variations. The polymers formed from the solution blending approach had a semicrystalline nature with blocks of PCCD separating the PBI units, whereas those produced using the melt condensation route were amorphous polymers. This structural variation was reflected in their photophysical properties also with the reactive solution‐blended polymers exhibiting higher fluorescence quantum yields. These results demonstrate the easy incorporation of suitably functionalized donor and acceptor moieties into a completely aliphatic polyester backbone to produce free‐standing films of hitherto nonprocessable polymers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Intermolecular organization of triphenylene-based discotic mesogens by interdigitation of alkyl chains

Two homologous series of 2,3,6,7,10,11-hexa-alkyloxy-substituted triphenylenes have been synthesized, such that alkyl chains of two different lengths alternate around the rigid triphenylene core in order to allow interdigitation of the chains between neighbouring columns in a hexagonal columnar mesophase. We report here the dependence of structural and thermal properties on the extent of interdigitation, as investigated by X-ray diffraction, polarized optical microscopy and differential scanning calorimetry.     

Synthesis of macroporous LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript> with avian egg membrane as a template

Avian eggshell membrane as a template for the synthesis of a macroporous network of crystalline LiMn₂O₄ is demonstrated. Well-formed crystals of average size 600 nm formed a network structure whose average pore size was 2–4 μm. The unique porous structure should make it an attractive cathode material for lithium-ion batteries. In fact, for an 80% cutoff in capacity retention, LiMn₂O₄ obtained by a 10-h calcination at 800°C sustained 83 cycles.