Flow Past a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Two-Phase Model

The steady two-dimensional flow and heat transfer over a stretching/shrinking sheet in a nanofluid is investigated using Buongiorno’s nanofluid model. Different from the previously published papers, in the present study we consider the case when the nanofluid particle fraction on the boundary is passively rather than actively controlled, which make the model more physically realistic. The governing partial differential equations are transformed into nonlinear ordinary differential equations by a similarity transformation, before being solved numerically by a shooting method. The effects of some governing parameters on the fluid flow and heat transfer characteristics are graphically presented and discussed. Dual solutions are found to exist in a certain range of the suction and stretching/shrinking parameters. Results also indicate that both the skin friction coefficient and the local Nusselt number increase with increasing values of the suction parameter.     

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

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.     

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables.     

Unsteady Boundary Layer Flow and Heat Transfer of a Casson Fluid past an Oscillating Vertical Plate with Newtonian Heating

In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.     

Mixed Convection Boundary Layer Flow over a Moving Vertical Flat Plate in an External Fluid Flow with Viscous Dissipation Effect

The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.     

Effects of Convective Heat and Mass Transfer in Flow of Powell-Eyring Fluid Past an Exponentially Stretching Sheet

The aim here is to investigate the effects of convective heat and mass transfer in the flow of Eyring-Powell fluid past an inclined exponential stretching surface. Mathematical formulation and analysis have been performed in the presence of Soret, Dufour and thermal radiation effects. The governing partial differential equations corresponding to the momentum, energy and concentration are reduced to a set of non-linear ordinary differential equations. Resulting nonlinear system is computed for the series solutions. Interval of convergence is determined. Physical interpretation is seen for the embedded parameters of interest. Skin friction coefficient, local Nusselt number and local Sherwood number are numerically computed and examined.     

Three-Dimensional Flow of an Oldroyd-B Nanofluid towards Stretching Surface with Heat Generation/Absorption

This article addresses the steady three-dimensional flow of an Oldroyd-B nanofluid over a bidirectional stretching surface with heat generation/absorption effects. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved analytically by using the homotpy analysis method (HAM). Graphically results are presented and discussed for various parameters, namely, Deborah numbers and , heat generation/absorption parameter Prandtl parameter , Brownian motion parameters, thermophoresis parameter and Lewis number . We have seen that the increasing values of the Brownian motion parameter and thermophoresis parameter leads to an increase in the temperature field and thermal boundary layer thickness while the opposite behavior is observed for concentration field and concentration boundary layer thickness. To see the validity of the present work, the numerical results are compared with the analytical solutions obtained by Homotopy analysis method and noted an excellent agreement for the limiting cases.     

Thermal and Concentration Stratifications Effects in Radiative Flow of Jeffrey Fluid over a Stretching Sheet

In this article we investigate the heat and mass transfer analysis in mixed convective radiative flow of Jeffrey fluid over a moving surface. The effects of thermal and concentration stratifications are also taken into consideration. Rosseland''s approximations are utilized for thermal radiation. The nonlinear boundary layer partial differential equations are converted into nonlinear ordinary differential equations via suitable dimensionless variables. The solutions of nonlinear ordinary differential equations are developed by homotopic procedure. Convergence of homotopic solutions is examined graphically and numerically. Graphical results of dimensionless velocity, temperature and concentration are presented and discussed in detail. Values of the skin-friction coefficient, the local Nusselt and the local Sherwood numbers are analyzed numerically. Temperature and concentration profiles are decreased when the values of thermal and concentration stratifications parameters increase. Larger values of radiation parameter lead to the higher temperature and thicker thermal boundary layer thickness.     

Convective Flow of Sisko Fluid over a Bidirectional Stretching Surface

The present investigation focuses the flow and heat transfer characteristics of the steady three-dimensional Sisko fluid driven by a bidirectional stretching sheet. The modeled partial differential equations are reduced to coupled ordinary differential equations by a suitable transformation. The resulting equations are solved numerically by the shooting method using adaptive Runge Kutta algorithm in combination with Newton''s method in the domain [0,∞). The numerical results for the velocity and temperature fields are graphically presented and effects of the relevant parameters are discussed in detail. Moreover, the skin-friction coefficient and local Nusselt number for different values of the power-law index and stretching ratio parameter are presented through tabulated data. The numerical results are also verified with the results obtained analytically by the homotopy analysis method (HAM). Additionally, the results are validated with previously published pertinent literature as a limiting case of the problem.     

Impact of Cattaneo-Christov Heat Flux in Jeffrey Fluid Flow with Homogeneous-Heterogeneous Reactions

Two-dimensional stretched flow of Jeffrey fluid in view of Cattaneo-Christov heat flux is addressed. Effects of homogeneous-heterogeneous reactions are also considered. Suitable transformations are used to form ordinary differential equations. Convergent series solutions are computed. Impact of significant parameters on the velocity, temperature, concentration and skin friction coefficient is addressed. Analysis of thermal relaxation is made. The obtained results show that ratio of relaxation to retardation times and Deborah number have inverse relation for velocity profile. Temperature distribution has decreasing behavior for Prandtl number and thermal relaxation time. Also concentration decreases for larger values of strength of homogeneous reaction parameter while it increases for strength of heterogeneous reaction parameter.     

Polycondensation and peptide chain-length distribution under prebiotic conditions

An open-ended system of differential equations is formulated for the number of polymers of length n, n = 1,2,..., under the assumption that all monomers are kinetically equivalent. Although this assumption does not hold in real systems, solutions to the model could provide insights into the processes of polycondensation including polymerizing proteins and polynucleotides. In this paper the equilibrium solution to the system is derived analytically and is used to estimate the concentration of monomers required to obtain a fixed proportion of polymers longer than a given length. Simulation results are also presented to indicate the effects that autocatalytic interactions may have on the dynamics of polycondensation. The results suggest that relatively long-chained peptides (one to several hundred units long) could well have been synthesized under non-template or prebiotic conditions.     

Conjugate Effects of Heat and Mass Transfer on MHD Free Convection Flow over an Inclined Plate Embedded in a Porous Medium

The aim of this study is to present an exact analysis of combined effects of radiation and chemical reaction on the magnetohydrodynamic (MHD) free convection flow of an electrically conducting incompressible viscous fluid over an inclined plate embedded in a porous medium. The impulsively started plate with variable temperature and mass diffusion is considered. The dimensionless momentum equation coupled with the energy and mass diffusion equations are analytically solved using the Laplace transform method. Expressions for velocity, temperature and concentration fields are obtained. They satisfy all imposed initial and boundary conditions and can be reduced, as special cases, to some known solutions from the literature. Expressions for skin friction, Nusselt number and Sherwood number are also obtained. Finally, the effects of pertinent parameters on velocity, temperature and concentration profiles are graphically displayed whereas the variations in skin friction, Nusselt number and Sherwood number are shown through tables.     

Influence of Newtonian Heating on Three Dimensional MHD Flow of Couple Stress Nanofluid with Viscous Dissipation and Joule Heating

The present exploration discusses the influence of Newtonian heating on the magnetohydrodynamic (MHD) three dimensional couple stress nanofluid past a stretching surface. Viscous dissipation and Joule heating effects are also considered. Moreover, the nanofluid model includes the combined effects of thermophoresis and Brownian motion. Using an appropriate transformation, the governing non linear partial differential equations are converted into nonlinear ordinary differential equations. Series solutions using Homotopy Analysis method (HAM) are computed. Plots are presented to portrait the arising parameters in the problem. It is seen that an increase in conjugate heating parameter results in considerable increase in the temperature profile of the stretching wall. Skin friction coefficient, local Nusselt and local Sherwood numbers tabulated and analyzed. Higher values of conjugate parameter, Thermophoresis parameter and Brownian motion parameter result in enhancement of temperature distribution.     

Travelling Waves in Hybrid Chemotaxis Models

Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are investigated. Bacteria are modelled using an agent-based (individual-based) approach with internal dynamics describing signal transduction. In addition to the chemotactic behaviour of the bacteria, the individual-based model also includes cell proliferation and death. Cells consume the extracellular nutrient field (chemoattractant), which is modelled using a partial differential equation. Mesoscopic and macroscopic equations representing the behaviour of the hybrid model are derived and the existence of travelling wave solutions for these models is established. It is shown that cell proliferation is necessary for the existence of non-transient (stationary) travelling waves in hybrid models. Additionally, a numerical comparison between the wave speeds of the continuum models and the hybrid models shows good agreement in the case of weak chemotaxis and qualitative agreement for the strong chemotaxis case. In the case of slow cell adaptation, we detect oscillating behaviour of the wave, which cannot be explained by mean-field approximations.     

On Comparison of Series and Numerical Solutions for Flow of Eyring-Powell Fluid with Newtonian Heating And Internal Heat Generation/Absorption

In this paper, we have investigated the combined effects of Newtonian heating and internal heat generation/absorption in the two-dimensional flow of Eyring-Powell fluid over a stretching surface. The governing non-linear analysis of partial differential equations is reduced into the ordinary differential equations using similarity transformations. The resulting problems are computed for both series and numerical solutions. Series solution is constructed using homotopy analysis method (HAM) whereas numerical solution is presented by two different techniques namely shooting method and bvp4c. A comparison of homotopy solution with numerical solution is also tabulated. Both solutions are found in an excellent agreement. Dimensionless velocity and temperature profiles are plotted and discussed for various emerging physical parameters.     

Human exposure to 2450 MHz CW energy at levels outside the IEEE C95.1 standard does not increase core temperature

Permission was received from the Brooks AFB Institutional Review Board and the AF Surgeon General's Office to exceed the peak power density (PD = 35 mW/cm(2)) we had previously studied during partial body exposure of human volunteers at 2450 MHz. Two additional peak PD were tested (50 and 70 mW/cm(2)). The higher of these PD (normalized peak local SAR = 15.4 W/kg) is well outside the IEEE C95.1 guidelines for partial body exposure, as is the estimated whole body SAR approximately 1.0 W/kg. Seven volunteers (four males, three females) were tested at each PD in three ambient temperatures (T(a) = 24, 28, and 31 degrees C) under our standard protocol (30 min baseline, 45 min RF exposure, 10 min baseline). The thermophysiological data (esophageal and six skin temperatures, metabolic heat production, local sweat rate, and local skin blood flow) were combined with comparable data at PD = 0, 27, and 35 mW/cm(2) from our 1999 study to generate response functions across PD. No change in esophageal temperature or metabolic heat production was recorded at any PD in any T(a). At PD = 70 mW/cm(2), skin temperature on the upper back (irradiated directly) increased 4.0 degrees C in T(a) = 24 degrees C, 2.6 degrees C in T(a) = 28 degrees C, and 1.8 degrees C in T(a) = 31 degrees C. These differences were primarily due to the increase in local sweat rate, which was greatest in T(a) = 31 degrees C. Also at PD = 70 mW/cm(2), local skin blood flow on the back increased 65% over baseline levels in T(a) = 31 degrees C, but only 40% in T(a) = 24 degrees C. Although T(a) becomes an important variable when RF exposure exceeds the C95.1 partial body exposure limits, vigorous heat loss responses of blood flow and sweating maintain thermal homeostasis efficiently. It is also clear that strong sensations of heat and thermal discomfort will motivate a timely retreat from a strong RF field, long before these physiological responses are exhausted. Published 2001 Wiley-Liss, Inc.     

Radiation Effects on the Flow of Powell-Eyring Fluid Past an Unsteady Inclined Stretching Sheet with Non-Uniform Heat Source/Sink

This study investigates the unsteady flow of Powell-Eyring fluid past an inclined stretching sheet. Unsteadiness in the flow is due to the time-dependence of the stretching velocity and wall temperature. Mathematical analysis is performed in the presence of thermal radiation and non-uniform heat source/sink. The relevant boundary layer equations are reduced into self-similar forms by suitable transformations. The analytic solutions are constructed in a series form by homotopy analysis method (HAM). The convergence interval of the auxiliary parameter is obtained. Graphical results displaying the influence of interesting parameters are given. Numerical values of skin friction coefficient and local Nusselt number are computed and analyzed.     

Dispersal, settling and layer formation

Motivated by examples in developmental biology and ecology, we develop a model for convection-dominated invasion of a spatial region by initially motile agents which are able to settle permanently. The motion of the motile agents and their rate of settling are affected by the local concentration of settled agents. The model can be formulated as a nonlinear partial differential equation for the time-integrated local concentration of the motile agents, from which the instantaneous density of settled agents and its long-time limit can be extracted. In the limit of zero diffusivity, the partial differential equation is of first order; for application-relevant initial and boundary-value problems, shocks arise in the time-integrated motile agent density, leading to delta-function components in the motile agent density. Furthermore, there are simple solutions for a model of successive layer formation. In addition some analytic results for a one-dimensional system with non-zero diffusivity can also be obtained. A case study, both with and without diffusion, is examined numerically. Some important predictions of the model are insensitive to the specific settling law used and the model offers insight into biological processes involving layered growth or overlapping generations of colonization.     

Rate theory models for ion transport through rigid pores. I. Time-dependent analysis in the case of vanishing interactions

In this first of a series of papers concerning the theoretical analysis of rate theory models for ion transport through rigid pores, the case of vanishing interactions is investigated. "Rigidity" means that ions crossing membranes through pores see a fixed structure of the pores, not changing in time. A single pore is considered to be a sequence of (n + 1) activation barriers separated by n energy minima. The explicit analytical treatment is restricted to pores with regular internal barrier structure, including the nonequilibrium situation of an applied electric field. In this case the connection with continuum diffusion models is demonstrated by performing in the limit n leads to infinity (n = number of binding sites within the pores) the transition to continuum. Thus, from diffusion equations describing a discrete number of jumps, the corresponding diffusion-like partial differential equations and boundary conditions are generated. For regular pores, from the time dependent solutions of the discrete equations, the corresponding solutions of the continuum equations are explicitly generated. The time-dependent relaxation behaviour of the discrete model is in good agreement with the continuum model if one assumes more than two binding sites in the pores.     

Travelling Waves in Hyperbolic Chemotaxis Equations

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235–248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically.