Closure relations problem of hydrodynamical models in semiconductors is considered by expressing third- and fourth-order closure relations for the moments of the distribution function in terms of second-order Lagrange multipliers using a generalized Maxwell-Boltzmann distribution function within information theory. Calculation results are commented and compared with others to justify the accuracy of the approach developed in this paper. The comparison involves, in the first part with good agreements, the closure relations results obtained within extended thermodynamics which were checked by means of Monte Carlo simulations, in the second part, the results obtained by Grad's method which expands the distribution function up to fourth-order in Hermite polynomials. It is seen that the latter method cannot give any restriction on closure relations for higher-order moments, within the same conditions proposed in our approach. The important role of Lagrange multipliers for the determination of all closure relations is asserted.
{"title":"Nonlinear Closure Relations for Electron Transport in Hydrodynamical Models","authors":"A. Salhoumi","doi":"10.1155/2013/915297","DOIUrl":"https://doi.org/10.1155/2013/915297","url":null,"abstract":"Closure relations problem of hydrodynamical models in semiconductors is considered by expressing third- and fourth-order closure relations for the moments of the distribution function \u0000in terms of second-order Lagrange multipliers using a generalized Maxwell-Boltzmann distribution \u0000function within information theory. Calculation results are commented and compared with \u0000others to justify the accuracy of the approach developed in this paper. The comparison involves, \u0000in the first part with good agreements, the closure relations results obtained within extended \u0000thermodynamics which were checked by means of Monte Carlo simulations, in the second part, \u0000the results obtained by Grad's method which expands the distribution function up to fourth-order \u0000in Hermite polynomials. It is seen that the latter method cannot give any restriction on closure \u0000relations for higher-order moments, within the same conditions proposed in our approach. The \u0000important role of Lagrange multipliers for the determination of all closure relations is asserted.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77428280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet have been considered. The effect of thermal radiation is also investigated. Implementing similarity transformations, the governing momentum, and energy equations are transformed to self-similar nonlinear ODEs and numerical computations are performed to solve those. The investigation reveals many important aspects of flow and heat transfer. If velocity ratio parameter (B) and magnetic parameter (M) increase, then the velocity boundary layer thickness becomes thinner. On the other hand, for Casson fluid it is found that the velocity boundary layer thickness is larger compared to that of Newtonian fluid. The magnitude of wall skin-friction coefficient reduces with Casson parameter (β). The velocity ratio parameter, Casson parameter, and magnetic parameter also have major effects on temperature distribution. The heat transfer rate is enhanced with increasing values of velocity ratio parameter. The rate of heat transfer is enhanced with increasing magnetic parameter M for B > 1 and it decreases with M for B < 1. Moreover, the presence of thermal radiation reduces temperature and thermal boundary layer thickness.
{"title":"MHD Stagnation-Point Flow of Casson Fluid and Heat Transfer over a Stretching Sheet with Thermal Radiation","authors":"K. Bhattacharyya","doi":"10.1155/2013/169674","DOIUrl":"https://doi.org/10.1155/2013/169674","url":null,"abstract":"The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet have been considered. The effect of thermal radiation is also investigated. Implementing similarity transformations, the governing momentum, and energy equations are transformed to self-similar nonlinear ODEs and numerical computations are performed to solve those. The investigation reveals many important aspects of flow and heat transfer. If velocity ratio parameter (B) and magnetic parameter (M) increase, then the velocity boundary layer thickness becomes thinner. On the other hand, for Casson fluid it is found that the velocity boundary layer thickness is larger compared to that of Newtonian fluid. The magnitude of wall skin-friction coefficient reduces with Casson parameter (β). The velocity ratio parameter, Casson parameter, and magnetic parameter also have major effects on temperature distribution. The heat transfer rate is enhanced with increasing values of velocity ratio parameter. The rate of heat transfer is enhanced with increasing magnetic parameter M for B > 1 and it decreases with M for B < 1. Moreover, the presence of thermal radiation reduces temperature and thermal boundary layer thickness.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83518437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Magneto-thermoelastic interactions in an initially stressed isotropic homogeneous elastic half-space with two temperatures are studied using mathematical methods under the purview of the L-S model of linear theory of generalized thermoelasticity. The formalism deals with the state space approach with the purpose of counteracting the difficulties of handling the displacement potential functions. Of specific concern here is the propagation of waves owing to ramp type increase in temperature and load. The medium is considered to be permeated by a uniform magnetic field. The expressions for different field parameters such as displacement, temperature, strain, and stress in the physical domain are obtained by applying a numerical inversion technique. Results of some earlier workers have been deduced from the present formulation. Numerical work is also performed for a suitable material with the aim of illustrating the results.
{"title":"Two Temperature Magneto-Thermoelasticity with Initial Stress: State Space Formulation","authors":"S. Deswal, K. K. Kalkal","doi":"10.1155/2013/754798","DOIUrl":"https://doi.org/10.1155/2013/754798","url":null,"abstract":"Magneto-thermoelastic interactions in an initially stressed isotropic homogeneous elastic half-space with two temperatures are studied using mathematical methods under the purview of the L-S model of linear theory of generalized thermoelasticity. The formalism deals with the state space approach with the purpose of counteracting the difficulties of handling the displacement potential functions. Of specific concern here is the propagation of waves owing to ramp type increase in temperature and load. The medium is considered to be permeated by a uniform magnetic field. The expressions for different field parameters such as displacement, temperature, strain, and stress in the physical domain are obtained by applying a numerical inversion technique. Results of some earlier workers have been deduced from the present formulation. Numerical work is also performed for a suitable material with the aim of illustrating the results.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82199826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A simple theoretical model is developed to study the size and shape dependence of vibrational and thermodynamic properties of nanomaterials. To show the real connection with the nanomaterials we have studied Debye temperature, Debye frequency, melting entropy, and enthalpy in different shapes, namely, spherical, nanowire, and nanofilm of -Fe, Sn, Ag, and In. The results obtained are compared with the experimental data. A good agreement between the model predictions and the experimental data supports the theory developed in the present paper.
{"title":"Effect of Size and Shape on the Vibrational and Thermodynamic Properties of Nanomaterials","authors":"R. Kumar, G. Sharma, M. Kumar","doi":"10.1155/2013/328051","DOIUrl":"https://doi.org/10.1155/2013/328051","url":null,"abstract":"A simple theoretical model is developed to study the size and shape dependence of vibrational and thermodynamic properties of nanomaterials. To show the real connection with the nanomaterials we have studied Debye temperature, Debye frequency, melting entropy, and enthalpy in different shapes, namely, spherical, nanowire, and nanofilm of -Fe, Sn, Ag, and In. The results obtained are compared with the experimental data. A good agreement between the model predictions and the experimental data supports the theory developed in the present paper.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87906573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
�� �� value in the present investigation was less than one, indicating that the adsorption of the metal ion onto ATS is favorable. After treatment with ATS the levels of heavy metals were observed to decrease by 88% (Ni), 82.9% (Cd), 81.5% (Cu), 74.5% (Cr), and 68.9% (Pb). Results indicate that the freely abundant, locally available, low-cost adsorbent , Teff straw can be treated as economically viable for the removal of metal ions from textile effluents.
{"title":"Research Article Batch Sorption Experiments: Langmuir and Freundlich Isotherm Studies for the Adsorption of Textile Metal Ions onto Teff Straw (Eragrostis tef) Agricultural Waste","authors":"M. Desta","doi":"10.1155/2013/375830","DOIUrl":"https://doi.org/10.1155/2013/375830","url":null,"abstract":"�� �� value in the present investigation was less than one, indicating that the adsorption of the metal ion onto ATS is favorable. After treatment with ATS the levels of heavy metals were observed to decrease by 88% (Ni), 82.9% (Cd), 81.5% (Cu), 74.5% (Cr), and 68.9% (Pb). Results indicate that the freely abundant, locally available, low-cost adsorbent , Teff straw can be treated as economically viable for the removal of metal ions from textile effluents.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83280745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.
{"title":"Shear Thickening in Concentrated Soft Sphere Colloidal Suspensions: A Shear Induced Phase Transition","authors":"J. Kaldasch, B. Senge, J. Laven","doi":"10.1155/2015/153854","DOIUrl":"https://doi.org/10.1155/2015/153854","url":null,"abstract":"A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91514642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Densities, viscosities, and speed of sound have been determined at T = (303.15, 308.15, and 313.15) K for the binary mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether over the entire range of composition. Using these measured values, excess volume , deviation in viscosities , excess Gibb’s free energy of activation for viscous flow , and deviation in isentropic compressibility have been calculated. These calculated binary data have been fitted to Redlich-Kister equation to determine the appropriate coefficients. The values of excess volume and deviation in viscosities are negative over the entire range of composition for all the binary systems at the studied temperatures. The behavior of these parameters with composition of the mixture has been discussed in terms of molecular interactions between the components of liquids.
{"title":"Studies on Excess Volume, Viscosity, and Speed of Sound of Binary Mixtures of Methyl Benzoate in Ethers at and K","authors":"M. V. Rathnam, Devappa R. Ambavadekar, M. Nandini","doi":"10.1155/2013/413878","DOIUrl":"https://doi.org/10.1155/2013/413878","url":null,"abstract":"Densities, viscosities, and speed of sound have been determined at T = (303.15, 308.15, and 313.15) K for the binary mixtures of methyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether over the entire range of composition. Using these measured values, excess volume , deviation in viscosities , excess Gibb’s free energy of activation for viscous flow , and deviation in isentropic compressibility have been calculated. These calculated binary data have been fitted to Redlich-Kister equation to determine the appropriate coefficients. The values of excess volume and deviation in viscosities are negative over the entire range of composition for all the binary systems at the studied temperatures. The behavior of these parameters with composition of the mixture has been discussed in terms of molecular interactions between the components of liquids.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83262850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with the steady two-dimensional stagnation point flow of nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via similarity variables and solved analytically via HAM. Effects of governing parameters such as heat generation/absorption λ, stretching parameter e, thermophoresis , Lewis number Le, Brownian motion , and Prandtl number Pr on heat transfer and concentration rates are investigated. The obtained results indicate that in contrast with heat transfer rate, concentration rate is very sensitive to the abovementioned parameters. Also, in the case of heat generation , despite concentration rate, heat transfer rate decreases. Moreover, increasing in stretching parameter leads to a gentle rise in both heat transfer and concentration rates.
{"title":"Stagnation Point Flow of a Nanofluid toward an Exponentially Stretching Sheet with Nonuniform Heat Generation/Absorption","authors":"A. Malvandi, F. Hedayati, G. Domairry","doi":"10.1155/2013/764827","DOIUrl":"https://doi.org/10.1155/2013/764827","url":null,"abstract":"This paper deals with the steady two-dimensional stagnation point flow of nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via similarity variables and solved analytically via HAM. Effects of governing parameters such as heat generation/absorption λ, stretching parameter e, thermophoresis , Lewis number Le, Brownian motion , and Prandtl number Pr on heat transfer and concentration rates are investigated. The obtained results indicate that in contrast with heat transfer rate, concentration rate is very sensitive to the abovementioned parameters. Also, in the case of heat generation , despite concentration rate, heat transfer rate decreases. Moreover, increasing in stretching parameter leads to a gentle rise in both heat transfer and concentration rates.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72637568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Experimental values of densities (ρ) and viscosities (η) in the binary mixtures of n-octane, n-decane, n-dodecane, and n-tetradecane with octan-2-ol are presented over the whole range of mixture composition at K. From these data, excess molar volume (), deviations in viscosity , and excess Gibbs free energy of activation have been calculated. These results were fitted to Redlich-Kister polynomial equations to estimate the binary coefficients and standard errors. Jouyban-Acree model is used to correlate the experimental values of density and viscosity at K. The values of have been analyzed using Prigogine-Flory-Patterson (PFP) theory. The results of the viscosity composition are discussed in the light of various viscosity equations suggested by Grunberg-Nissan, Tamara and Kurata, Hind et al., Katti and Chaudhri, Heric, Heric and Brewer, and McAllister multibody model. The values of have also been analyzed using Bloomfield and Dewan model. The experiments on the constituted binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.
{"title":"Excess Molar Volumes and Viscosities for the Binary Mixtures of n-Octane, n-Decane, n-Dodecane, and n-Tetradecane with Octan-2-ol at 298.15 K","authors":"A. R. Mahajan, S. Mirgane","doi":"10.1155/2013/571918","DOIUrl":"https://doi.org/10.1155/2013/571918","url":null,"abstract":"Experimental values of densities (ρ) and viscosities (η) in the binary mixtures of n-octane, n-decane, n-dodecane, and n-tetradecane with octan-2-ol are presented over the whole range of mixture composition at K. From these data, excess molar volume (), deviations in viscosity , and excess Gibbs free energy of activation have been calculated. These results were fitted to Redlich-Kister polynomial equations to estimate the binary coefficients and standard errors. Jouyban-Acree model is used to correlate the experimental values of density and viscosity at K. The values of have been analyzed using Prigogine-Flory-Patterson (PFP) theory. The results of the viscosity composition are discussed in the light of various viscosity equations suggested by Grunberg-Nissan, Tamara and Kurata, Hind et al., Katti and Chaudhri, Heric, Heric and Brewer, and McAllister multibody model. The values of have also been analyzed using Bloomfield and Dewan model. The experiments on the constituted binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87355820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A local similarity solution of unsteady MHD natural convection heat and mass transfer boundary layer flow past a flat porous plate within the presence of thermal radiation is investigated. The effects of exothermic and endothermic chemical reactions with Arrhenius activation energy on the velocity, temperature, and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing locally similarity transformation (Maleque (2010)). Numerical solutions to the reduced nonlinear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are obtained for both steady and unsteady cases then presented graphically in the form of velocity, temperature, and concentration profiles. Comparison has been made for steady flow () and shows excellent agreement with Bestman (1990), hence encouragement for the use of the present computations.
{"title":"Effects of Exothermic/Endothermic Chemical Reactions with Arrhenius Activation Energy on MHD Free Convection and Mass Transfer Flow in Presence of Thermal Radiation","authors":"K. Maleque","doi":"10.1155/2013/692516","DOIUrl":"https://doi.org/10.1155/2013/692516","url":null,"abstract":"A local similarity solution of unsteady MHD natural convection heat and mass transfer boundary layer flow past a flat porous plate within the presence of thermal radiation is investigated. The effects of exothermic and endothermic chemical reactions with Arrhenius activation energy on the velocity, temperature, and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing locally similarity transformation (Maleque (2010)). Numerical solutions to the reduced nonlinear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are obtained for both steady and unsteady cases then presented graphically in the form of velocity, temperature, and concentration profiles. Comparison has been made for steady flow () and shows excellent agreement with Bestman (1990), hence encouragement for the use of the present computations.","PeriodicalId":17290,"journal":{"name":"Journal of Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82513036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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