Ahmed Alsaedi - Academia.edu (original) (raw)
Papers by Ahmed Alsaedi
Journal of the Taiwan Institute of Chemical Engineers, 2015
PLOS ONE, 2016
This article examines the impact of Cattaneo-Christov heat flux in flows of viscoelastic fluids. ... more This article examines the impact of Cattaneo-Christov heat flux in flows of viscoelastic fluids. Flow is generated by a linear stretching sheet. Influence of thermal relaxation time in the considered heat flux is seen. Mathematical formulation is presented for the boundary layer approach. Suitable transformations lead to a nonlinear differential system. Convergent series solutions of velocity and temperature are achieved. Impacts of various influential parameters on the velocity and temperature are sketched and discussed. Numerical computations are also performed for the skin friction coefficient and heat transfer rate. Our findings reveal that the temperature profile has an inverse relationship with the thermal relaxation parameter and the Prandtl number. Further the temperature profile and thermal boundary layer thickness are lower for Cattaneo-Christov heat flux model in comparison to the classical Fourier's law of heat conduction.
Ecological Indicators, 2014
International Journal of Numerical Methods for Heat & Fluid Flow, 2014
Purpose – This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-th... more Purpose – This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues. Design/methodology/approach – The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined. Findings – It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting proc...
Zeitschrift für Analysis und ihre Anwendungen, 2015
This paper proves a regularity criterion for the density-dependent Hallmagnetohydrodynamics with ... more This paper proves a regularity criterion for the density-dependent Hallmagnetohydrodynamics with positive density.
PloS one, 2015
This research addresses the mixed convection flow of an Oldroyd-B fluid in a doubly stratified su... more This research addresses the mixed convection flow of an Oldroyd-B fluid in a doubly stratified surface. Both temperature and concentration stratification effects are considered. Thermal radiation and chemical reaction effects are accounted. The governing nonlinear boundary layer equations are converted to coupled nonlinear ordinary differential equations using appropriate transformations. Resulting nonlinear systems are solved for the convergent series solutions. Graphs are plotted to examine the impacts of physical parameters on the non-dimensional temperature and concentration distributions. The local Nusselt number and the local Sherwood number are computed and analyzed numerically.
Journal of hazardous materials, Jan 29, 2015
Little information is available concerning co-sorbing oxyanion and metal contaminants in the envi... more Little information is available concerning co-sorbing oxyanion and metal contaminants in the environment, yet in most metal-contaminated areas, co-contamination by phosphate is common. In this study, the mutual effects of phosphate and Zn(II) on their interaction with γ-Al2O3 are investigated by batch experiments and X-ray absorption fine structure spectroscopy (XAFS) technique. The results show that the co-sorption of phosphate on γ-Al2O3 modifies both the extent of Zn(II) sorption and the local atomic structures of sorbed Zn(II) ions. Multiple mechanisms are involved in Zn(II) retention in the presence of phosphate, including electrostatic interaction, binary and ternary surface complexation, and the formation of Zn(II)-phosphate polynuclear complexes. At pH 6.5, type III ternary surface complexation occurs concurrently with binary Zn-alumina surface complexation at low phosphate concentrations, whereas the formation of type III ternary surface complexes is promoted as the phospha...
Nonlinear Analysis: Hybrid Systems, 2014
ABSTRACT
Ecological Indicators, 2014
Abstract With the expansion of urbanization in China, the integrated biogas-utilization system ha... more Abstract With the expansion of urbanization in China, the integrated biogas-utilization system has gained its popularity for both renewable energy production and multi-level utilization of organic waste. To appraise the ecological performance of the integrated biogas system, systematic accounting is undertaken for an integrated “pig–biogas–fish” system in Hubei province, China. Based on Odum's concept of embodied solar energy as a unified measure for environmental resources, human labors and purchased goods, a set of emergetic indicators are employed to quantify the system sustainability. The results reveal that in a 20-year designed lifetime scenario, 94.69% of the total emergy inputs for the “pig–biogas–fish” system are attributed to purchased social resources. Three kinds of products, namely pig, biogas, fish are taken into consideration, and transformity of the “pig–biogas–fish” system is calculated as 1.26E + 05 seJ/J. Compared with the Chinese conventional agriculture system, the integrated biogas system shows a higher sustainability. Given that most biogas systems have a lifespan less than 20 years, for the “pig–biogas–fish” system, six other scenarios with different lifespans are studied to investigate the impact of the lifespan on sustainability. The findings suggest that the “pig–biogas–fish” system should be well operated for at least 8 years to prove its advantage in ecological economy over the conventional agriculture system. This has essential policy implications that local government should strengthen subsequent management on biogas production to extend the practical service life of the biogas system.
Mathematical Physics, Analysis and Geometry, 2014
This paper proves a new regularity criterion for the 3D generalized MHD system with fractional di... more This paper proves a new regularity criterion for the 3D generalized MHD system with fractional diffusion terms (−) α u and (−) β b with 0 < α < 5 4 β.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2014
This article investigates the effects of convective heat and concentration conditions in magnetoh... more This article investigates the effects of convective heat and concentration conditions in magnetohydrodynamic flow of non-Newtonian fluid with nanoparticles. Convective type boundary conditions are utilized for heat and nanoparticles concentration. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by suitable similarity variables. Homotopy analysis method is employed to obtain the dimensionless velocity, temperature and nanoparticles concentration expressions. Graphical results for temperature and nanoparticles concentration are plotted and examined. Numerical values of skin friction coefficient are computed and discussed. Heat transfer and nanoparticles concentration transfer rates at the wall are examined by plotting the graphs of different governing physical parameters. We noticed that the temperature and nanoparticles concentration profiles are enhanced when the values of Biot numbers are increased. An increase in thermophoresis parameter leads to an enhancement in the temperature and nanoparticles concentration. On the other hand the increasing values of Brownian motion parameter has reverse effects on the temperature and nanoparticles concentration fields.
PLoS ONE, 2014
This article studies the viscous flow and heat transfer over a plane horizontal surface stretched... more This article studies the viscous flow and heat transfer over a plane horizontal surface stretched non-linearly in two lateral directions. Appropriate wall conditions characterizing the non-linear variation in the velocity and temperature of the sheet are employed for the first time. A new set of similarity variables is introduced to reduce the boundary layer equations into self-similar forms. The velocity and temperature distributions are determined by two methods, namely (i) optimal homotopy analysis method (OHAM) and (ii) fourth-fifth-order Runge-Kutta integration based shooting technique. The analytic and numerical solutions are compared and these are found in excellent agreement. Influences of embedded parameters on momentum and thermal boundary layers are sketched and discussed.
Thermal Science, 2016
Analysis has been carried out for the magnetohydrodynamic (MHD) boundary layer flow of nanofluid.... more Analysis has been carried out for the magnetohydrodynamic (MHD) boundary layer flow of nanofluid. The flow is caused by a permeable stretching sheet. Convective type boundary conditions are employed in modeling the heat and mass transfer process. Appropriate transformations reduce the nonlinear partial differential equations to ordinary differential equations. The convergent series solutions are constructed. Graphical results of different parameters are discussed. The behaviors of Brownian motion and thermophoretic diffusion of nanoparticles have been examined. The dimensionless expressions of local Nusselt and local Sherwood numbers have been evaluated and discussed.
Applied Mathematics and Computation, 2014
Purpose-In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydro... more Purpose-In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues. Design/methodology/approach-In this paper, the authors used two methods: homotopy analysis method and numerical Keller-box method. Findings-It is observed that skin friction coefficient in Oldroyd-B fluid is larger when compared with viscous fluid. Further, the relaxation and retardation times have opposite effects on the velocity components. Practical implications-A comparative study between the series and numerical solutions for the skin friction is shown in the paper. The results indicated that both solutions are in well agreement. Originality/value-This model is investigated for the first time, as the authors know.
PLoS ONE, 2014
This article addresses the effects of homogeneous-heterogeneous reactions in peristaltic transpor... more This article addresses the effects of homogeneous-heterogeneous reactions in peristaltic transport of Carreau fluid in a channel with wall properties. Mathematical modelling and analysis have been carried out in the presence of Hall current. The channel walls satisfy the more realistic convective conditions. The governing partial differential equations along with long wavelength and low Reynolds number considerations are solved. The results of temperature and heat transfer coefficient are analyzed for various parameters of interest.
PLoS ONE, 2014
This article addresses the boundary layer flow and heat transfer in third grade fluid over an uns... more This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.
PLoS ONE, 2013
This paper looks at the series solutions of three dimensional boundary layer flow. An Oldroyd-B f... more This paper looks at the series solutions of three dimensional boundary layer flow. An Oldroyd-B fluid with variable thermal conductivity is considered. The flow is induced due to stretching of a surface. Analysis has been carried out in the presence of heat generation/absorption. Homotopy analysis is implemented in developing the series solutions to the governing flow and energy equations. Graphs are presented and discussed for various parameters of interest. Comparison of present study with the existing limiting solution is shown and examined.
Journal of Heat Transfer, 2012
We performed a study for the effect of Newtonian heating on the nonsimilar mixed convection Falkn... more We performed a study for the effect of Newtonian heating on the nonsimilar mixed convection Falkner–Skan flow of a Maxwell fluid. Transformation procedure is adopted in obtaining the ordinary differential equations. Homotopic approach is adopted for the series solutions of velocity and temperature. Special emphasis is given to the effects of Prandtl number (Pr) and conjugate parameter (γ) which measure the strength of surface heating. It is observed that temperature and heat transfer rate are enhanced by increasing the conjugate parameter.
International Journal of Thermal Sciences, 2013
This article looks at the thermal analysis of the mixed convection-radiation of an inclined flat ... more This article looks at the thermal analysis of the mixed convection-radiation of an inclined flat plate embedded in a porous medium. The boundary-layer equations are reduced to the nonlinear ordinary differential equations (ODEs) using similarity transformations. The governing equations are solved using the homotopy analysis method (HAM). The dimensionless velocity and temperature profiles are obtained for different values of emerging parameters. The obtained results without the radiation effect are compared with the existing results. Such results show the performance and reliability of HAM. The present results in comparison with the existing solutions admit an excellent accuracy.
International Journal for Numerical Methods in Fluids, 2011
The steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered.... more The steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered. Upper‐convected Maxwell (UCM) fluid is treated as a rheological model. The resulting nonlinear differential system is solved by homotopy analysis method (HAM). The influence of melting parameter (M), Prandtl number (Pr), Deborah number (β) and stretching ratio (A = a/c) on the velocity and temperature profiles is thoroughly examined. It is noticed that fields are effected appreciably with the variation of parameters. Furthermore, it is seen that the local Nusselt number is a decreasing function of melting parameter. Copyright © 2011 John Wiley & Sons, Ltd.
Journal of the Taiwan Institute of Chemical Engineers, 2015
PLOS ONE, 2016
This article examines the impact of Cattaneo-Christov heat flux in flows of viscoelastic fluids. ... more This article examines the impact of Cattaneo-Christov heat flux in flows of viscoelastic fluids. Flow is generated by a linear stretching sheet. Influence of thermal relaxation time in the considered heat flux is seen. Mathematical formulation is presented for the boundary layer approach. Suitable transformations lead to a nonlinear differential system. Convergent series solutions of velocity and temperature are achieved. Impacts of various influential parameters on the velocity and temperature are sketched and discussed. Numerical computations are also performed for the skin friction coefficient and heat transfer rate. Our findings reveal that the temperature profile has an inverse relationship with the thermal relaxation parameter and the Prandtl number. Further the temperature profile and thermal boundary layer thickness are lower for Cattaneo-Christov heat flux model in comparison to the classical Fourier's law of heat conduction.
Ecological Indicators, 2014
International Journal of Numerical Methods for Heat & Fluid Flow, 2014
Purpose – This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-th... more Purpose – This investigation has been carried out for thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects on the boundary layer flow of Jeffrey fluid in the region of stagnation-point towards a stretching sheet. Heat transfer occurring during the melting process due to a stretching sheet is considered. The paper aims to discuss these issues. Design/methodology/approach – The authors convert governing partial differential equations into ordinary differential equations by using suitable transformations. Analytic solutions of velocity and temperature are found by using homotopy analysis method (HAM). Further graphs are displayed to study the salient features of embedding parameters. Expressions of skin friction coefficient, local Nusselt number and local Sherwood number have also been derived and examined. Findings – It is found that velocity and the boundary layer thickness are increasing functions of viscoelastic parameter (Deborah number). An increase in the melting proc...
Zeitschrift für Analysis und ihre Anwendungen, 2015
This paper proves a regularity criterion for the density-dependent Hallmagnetohydrodynamics with ... more This paper proves a regularity criterion for the density-dependent Hallmagnetohydrodynamics with positive density.
PloS one, 2015
This research addresses the mixed convection flow of an Oldroyd-B fluid in a doubly stratified su... more This research addresses the mixed convection flow of an Oldroyd-B fluid in a doubly stratified surface. Both temperature and concentration stratification effects are considered. Thermal radiation and chemical reaction effects are accounted. The governing nonlinear boundary layer equations are converted to coupled nonlinear ordinary differential equations using appropriate transformations. Resulting nonlinear systems are solved for the convergent series solutions. Graphs are plotted to examine the impacts of physical parameters on the non-dimensional temperature and concentration distributions. The local Nusselt number and the local Sherwood number are computed and analyzed numerically.
Journal of hazardous materials, Jan 29, 2015
Little information is available concerning co-sorbing oxyanion and metal contaminants in the envi... more Little information is available concerning co-sorbing oxyanion and metal contaminants in the environment, yet in most metal-contaminated areas, co-contamination by phosphate is common. In this study, the mutual effects of phosphate and Zn(II) on their interaction with γ-Al2O3 are investigated by batch experiments and X-ray absorption fine structure spectroscopy (XAFS) technique. The results show that the co-sorption of phosphate on γ-Al2O3 modifies both the extent of Zn(II) sorption and the local atomic structures of sorbed Zn(II) ions. Multiple mechanisms are involved in Zn(II) retention in the presence of phosphate, including electrostatic interaction, binary and ternary surface complexation, and the formation of Zn(II)-phosphate polynuclear complexes. At pH 6.5, type III ternary surface complexation occurs concurrently with binary Zn-alumina surface complexation at low phosphate concentrations, whereas the formation of type III ternary surface complexes is promoted as the phospha...
Nonlinear Analysis: Hybrid Systems, 2014
ABSTRACT
Ecological Indicators, 2014
Abstract With the expansion of urbanization in China, the integrated biogas-utilization system ha... more Abstract With the expansion of urbanization in China, the integrated biogas-utilization system has gained its popularity for both renewable energy production and multi-level utilization of organic waste. To appraise the ecological performance of the integrated biogas system, systematic accounting is undertaken for an integrated “pig–biogas–fish” system in Hubei province, China. Based on Odum's concept of embodied solar energy as a unified measure for environmental resources, human labors and purchased goods, a set of emergetic indicators are employed to quantify the system sustainability. The results reveal that in a 20-year designed lifetime scenario, 94.69% of the total emergy inputs for the “pig–biogas–fish” system are attributed to purchased social resources. Three kinds of products, namely pig, biogas, fish are taken into consideration, and transformity of the “pig–biogas–fish” system is calculated as 1.26E + 05 seJ/J. Compared with the Chinese conventional agriculture system, the integrated biogas system shows a higher sustainability. Given that most biogas systems have a lifespan less than 20 years, for the “pig–biogas–fish” system, six other scenarios with different lifespans are studied to investigate the impact of the lifespan on sustainability. The findings suggest that the “pig–biogas–fish” system should be well operated for at least 8 years to prove its advantage in ecological economy over the conventional agriculture system. This has essential policy implications that local government should strengthen subsequent management on biogas production to extend the practical service life of the biogas system.
Mathematical Physics, Analysis and Geometry, 2014
This paper proves a new regularity criterion for the 3D generalized MHD system with fractional di... more This paper proves a new regularity criterion for the 3D generalized MHD system with fractional diffusion terms (−) α u and (−) β b with 0 < α < 5 4 β.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2014
This article investigates the effects of convective heat and concentration conditions in magnetoh... more This article investigates the effects of convective heat and concentration conditions in magnetohydrodynamic flow of non-Newtonian fluid with nanoparticles. Convective type boundary conditions are utilized for heat and nanoparticles concentration. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by suitable similarity variables. Homotopy analysis method is employed to obtain the dimensionless velocity, temperature and nanoparticles concentration expressions. Graphical results for temperature and nanoparticles concentration are plotted and examined. Numerical values of skin friction coefficient are computed and discussed. Heat transfer and nanoparticles concentration transfer rates at the wall are examined by plotting the graphs of different governing physical parameters. We noticed that the temperature and nanoparticles concentration profiles are enhanced when the values of Biot numbers are increased. An increase in thermophoresis parameter leads to an enhancement in the temperature and nanoparticles concentration. On the other hand the increasing values of Brownian motion parameter has reverse effects on the temperature and nanoparticles concentration fields.
PLoS ONE, 2014
This article studies the viscous flow and heat transfer over a plane horizontal surface stretched... more This article studies the viscous flow and heat transfer over a plane horizontal surface stretched non-linearly in two lateral directions. Appropriate wall conditions characterizing the non-linear variation in the velocity and temperature of the sheet are employed for the first time. A new set of similarity variables is introduced to reduce the boundary layer equations into self-similar forms. The velocity and temperature distributions are determined by two methods, namely (i) optimal homotopy analysis method (OHAM) and (ii) fourth-fifth-order Runge-Kutta integration based shooting technique. The analytic and numerical solutions are compared and these are found in excellent agreement. Influences of embedded parameters on momentum and thermal boundary layers are sketched and discussed.
Thermal Science, 2016
Analysis has been carried out for the magnetohydrodynamic (MHD) boundary layer flow of nanofluid.... more Analysis has been carried out for the magnetohydrodynamic (MHD) boundary layer flow of nanofluid. The flow is caused by a permeable stretching sheet. Convective type boundary conditions are employed in modeling the heat and mass transfer process. Appropriate transformations reduce the nonlinear partial differential equations to ordinary differential equations. The convergent series solutions are constructed. Graphical results of different parameters are discussed. The behaviors of Brownian motion and thermophoretic diffusion of nanoparticles have been examined. The dimensionless expressions of local Nusselt and local Sherwood numbers have been evaluated and discussed.
Applied Mathematics and Computation, 2014
Purpose-In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydro... more Purpose-In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues. Design/methodology/approach-In this paper, the authors used two methods: homotopy analysis method and numerical Keller-box method. Findings-It is observed that skin friction coefficient in Oldroyd-B fluid is larger when compared with viscous fluid. Further, the relaxation and retardation times have opposite effects on the velocity components. Practical implications-A comparative study between the series and numerical solutions for the skin friction is shown in the paper. The results indicated that both solutions are in well agreement. Originality/value-This model is investigated for the first time, as the authors know.
PLoS ONE, 2014
This article addresses the effects of homogeneous-heterogeneous reactions in peristaltic transpor... more This article addresses the effects of homogeneous-heterogeneous reactions in peristaltic transport of Carreau fluid in a channel with wall properties. Mathematical modelling and analysis have been carried out in the presence of Hall current. The channel walls satisfy the more realistic convective conditions. The governing partial differential equations along with long wavelength and low Reynolds number considerations are solved. The results of temperature and heat transfer coefficient are analyzed for various parameters of interest.
PLoS ONE, 2014
This article addresses the boundary layer flow and heat transfer in third grade fluid over an uns... more This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.
PLoS ONE, 2013
This paper looks at the series solutions of three dimensional boundary layer flow. An Oldroyd-B f... more This paper looks at the series solutions of three dimensional boundary layer flow. An Oldroyd-B fluid with variable thermal conductivity is considered. The flow is induced due to stretching of a surface. Analysis has been carried out in the presence of heat generation/absorption. Homotopy analysis is implemented in developing the series solutions to the governing flow and energy equations. Graphs are presented and discussed for various parameters of interest. Comparison of present study with the existing limiting solution is shown and examined.
Journal of Heat Transfer, 2012
We performed a study for the effect of Newtonian heating on the nonsimilar mixed convection Falkn... more We performed a study for the effect of Newtonian heating on the nonsimilar mixed convection Falkner–Skan flow of a Maxwell fluid. Transformation procedure is adopted in obtaining the ordinary differential equations. Homotopic approach is adopted for the series solutions of velocity and temperature. Special emphasis is given to the effects of Prandtl number (Pr) and conjugate parameter (γ) which measure the strength of surface heating. It is observed that temperature and heat transfer rate are enhanced by increasing the conjugate parameter.
International Journal of Thermal Sciences, 2013
This article looks at the thermal analysis of the mixed convection-radiation of an inclined flat ... more This article looks at the thermal analysis of the mixed convection-radiation of an inclined flat plate embedded in a porous medium. The boundary-layer equations are reduced to the nonlinear ordinary differential equations (ODEs) using similarity transformations. The governing equations are solved using the homotopy analysis method (HAM). The dimensionless velocity and temperature profiles are obtained for different values of emerging parameters. The obtained results without the radiation effect are compared with the existing results. Such results show the performance and reliability of HAM. The present results in comparison with the existing solutions admit an excellent accuracy.
International Journal for Numerical Methods in Fluids, 2011
The steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered.... more The steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered. Upper‐convected Maxwell (UCM) fluid is treated as a rheological model. The resulting nonlinear differential system is solved by homotopy analysis method (HAM). The influence of melting parameter (M), Prandtl number (Pr), Deborah number (β) and stretching ratio (A = a/c) on the velocity and temperature profiles is thoroughly examined. It is noticed that fields are effected appreciably with the variation of parameters. Furthermore, it is seen that the local Nusselt number is a decreasing function of melting parameter. Copyright © 2011 John Wiley & Sons, Ltd.