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A novel numerical computing framework through Lobatto IIIA method is presented for the dynamical investigation of nanofluidic problem with Williamson fluid flow on a stretching sheet by considering the thermal slip and velocity. The impact of thermophoresis and Brownian motion on phenomena of heat transfer are explored by using Buongiorno model. The governing non-linear partial differential system representing the mathematical model of the Williamson fluid is transformed in to a system of ODE by incorporating the competency of non-dimensional similarity variables. The dynamics of the transformed system of ODE are evaluated through the Lobatto IIIA numerically. Sufficient graphical and numerical illustrations are portrayed in order to investigate and analyze the influence of physical parameters: Williamson parameter, Prandtl number, Lewis number, Schmidt number, ratio of diffusivity parameter, ratio of heat capacitance parameter on velocity, temperature, and concentration fields. The numerically computed values of local Nusselt number, local Sherwood number, and skin friction coefficient are also inspected for exhaustive assessment. Moreover, the accuracy, efficiency and stability of the proposed method is analyzed through relative errors.

This article express the outcomes of mixed convective flow of a chemically reacting Oldroyd-B liquid (OBL) with Cattaneo-Christov double flux (CCDF) under the consequence of second order slip (SS), heat absorption (HA)/heat generation (HG) and Newtonian cooling (NC)/Newtonian heating (NH). The governing PDEs are converted into ODEs using suitable variables. The homotopy analysis method (HAM) is employed to solve these resultant equations. The outcomes of diverse physical parameters, like, relaxation time, retardation time, Richardson number, buoyancy ratio, Prandtl number, radiation, heat absorption/generation, Schmidt number, chemical reaction, suction/injection, slip and Newtonian heating are discussed.

Temperature from burning wood cribs will be simulated in this paper by subgrid scale model in fire dynamics simulator. A baseline gas phase uncertainty is determined for simulating wood crib fire spread scenarios. This uncertainty is based on a sensitivity analysis of key input parameters and their subsequent effect on key output variables that are important for fire spread. Effects of different grid systems, computing domains and moisture contents on the predictions were studied first and then used to study the gaseous phase sensitivity. The gaseous phase input variables considered are: Smagorinsky constant, Prandtl number, and Schmidt number. The results show that the predictions for temperature have good agreement with experiment with the values of 0.25, 0.7, 0.4, and 5 for Smagorinsky constant, turbulent Schmidt number, and turbulent Prandtl number, respectively.

In this work, three-dimensional and two-phase nanofluid flow and heat transfer is modeled over a stretching infinite solar plate. The governing equations are presented based on previous studies. The infinite boundary condition and shortcoming of traditional analytical Collocation Method have been overcome in our study by changing the problem into a finite boundary problem with a new analytical method called Optimal Collocation Method (OCM). The accuracy of results is examined by fourth order Runge-kutta numerical method. Effect of some parameters, Pr (Prandtl number), Sc (Schmidt number), Nb (Brownian motion parameter), Nt (Thermophoresis parameter), λ=b/a (ratio of the stretching rate along y to x directions) and n (power-law index), on the velocities, temperature and nanoparticles concentration functions are discussed. As an important outcome of our 3D model analysis, it is found that increase in thermophoretic forces can enhance the thickness of both thermal and nanoparticle volume fraction boundary layers.

In this study, heat and mass transfer characteristic of unsteady nanofluid flow between parallel plates is investigated. The important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. The governing equations are solved via Differential Transformation Method. The validity of this method was verified by comparison previous work which is done for viscous fluid. The analytical investigation is carried out for different governing parameters namely; the squeeze number, Hartmann number, Schmidt number, Brownian motion parameter, thermophoretic parameter and Eckert number. The results indicate that skin friction coefficient has direct relationship with Hartmann number and squeeze number. Also it can be found that Nusselt number increases with increase of Hartmann number, Eckert number and Schmidt number but it is decreases with augment of squeeze number.

This article investigates the flow of Maxwell nanofluid over a moving plate in a calm fluid. Novel aspects of Brownian motion and thermophoresis are taken into consideration. Revised model for passive control of nanoparticle volume fraction at the plate is used in this study. The formulated differential system is solved numerically by employing shooting approach together with fourth-fifth-order-Runge-Kutta integration procedure and Newton’s method. The solutions are greatly influenced with the variation of embedded parameters which include the local Deborah number De , the Brownian motion parameter Nb , the thermophoresis parameter Nt , the Prandtl number Pr and the Schmidt number Sc . We found that the variation in velocity distribution with an increase in local Deborah number De is non-monotonic. Moreover, the reduced Nusselt number has a linear and direct relationship with the local Deborah number De .

An investigation of unsteady MHD free convective flow and mass transfer during the motion of a viscous incompressible fluid through a porous medium, bounded by an infinite vertical porous surface, in a rotating system is presented. The porous plane surface and the porous medium are assumed to rotate in a solid body rotation. The vertical surface is subjected to uniform constant suction perpendicular to it and the temperature at this surface fluctuates in time about a non-zero constant mean. Analytical expressions for the velocity, temperature and concentration fields are obtained using the perturbation technique. The effects of R (rotation parameter), k0 (permeability parameter), M (Hartmann number) and w (frequency parameter) on the flow characteristics are discussed. It is observed that the primary velocity component decreases with the increase in either of the rotation parameter R, the permeability parameter k0, or the Hartmann number M. It is also noted that the primary skin friction increases whenever there is an increase in the Grashof number Gr or the modified Grashof number Gm. It is clear that the heat transfer coefficient in terms of the Nusselt number decreases in the case of both air and water when there is an increase in the Hartmann number M. It is observed that the magnitude of the secondary velocity profiles increases whenever there is an increase in either of the Grashof number or the modified Grashof number for mass transfer or the permeability of the porous media. Concentration profiles decreases with an increase in the Schmidt number.

In this paper, effects of heat and mass transfer on peristaltic transport of Walter's B fluid in an asymmetric channel are investigated. The governing equations are solved using regular perturbation method by taking wave number as a small parameter. Expressions for the stream function, temperature distribution, heat transfer coefficient, and mass concentration are presented in explicit form. Solutions are analyzed graphically for different values of arising parameters such as viscoelastic parameter, Prandtl, Eckert, Soret, Schmidt and Reynolds number. It has been found that these parameters considerably affect the considered flow characteristics. Results show that with an increase in Eckert and Prandtl number temperature and heat transfer coefficient increase while mass concentration decreases. Further, Mass concentration also decreases with increasing Soret and Schmidt number.

An analysis is carried out to study the effect of heat and mass transfer on a non-Newtonian-fluid between two infinite parallel walls, one of them moving with a uniform velocity under the action of a transverse magnetic field. The moving wall moves with constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at permeable surface. The governing equations for the flow are transformed into a system of nonlinear ordinary differential equations by perturbation technique and are solved numerically by using the shooting technique with fourth order Runge-Kutta integration scheme. The effect of non-Newtonian parameter, magnetic pressure parameter, Schmidt number, Grashof number and modified Grashof number on velocity, temperature, concentration and the induced magnetic field are discussed. Numerical results are given and illustrated graphically for the considered Problem.

The control of fluid mechanics and mass transfer in separated and reattaching flow over a backward-facing step by a local forcing, is studied using Large Eddy Simulation (LES). To control the flow, the local forcing is realized by a sinusoidal oscillating jet at the step edge. The Reynolds number is varied in the range 10000 ? Re ? 50000 and the Schmidt number is fixed at 1. The found results show that the flow structure is modified and the local mass transfer is enhanced by the applied forcing. The observed changes depend on the Reynolds number and vary with the frequency and amplitude of the local forcing. For the all Reynolds numbers, the largest recirculation zone size reduction is obtained at the optimum forcing frequency St = 0.25. At this frequency the local mass transfer enhancement attains the maximum.

A numerical solution for the free convective, unsteady, laminar convective heat and mass transfer in a viscoelastic fluid along a semi-infinite vertical plate is presented. The Walters-B liquid model is employed to simulate medical creams and other rheological liquids encountered in biotechnology and chemical engineering. This rheological model introduces supplementary terms into the momentum conservation equation. The dimensionless unsteady, coupled and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature and concentration fields have been studied for the effect of Prandtl number (Pr), viscoelasticity parameter (G), Schmidt number (Sc), Buoyancy ration parameter (N). The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically. It is observed that, when the viscoelasticity parameter (G) increases, the velocity increases close to the plate surface. An increase in Schmidt number is observed to significantly decrease both velocity and concentration.

An analysis is presented for the steady thermal convection heat and mass transfer in a micropolar-fluid-saturated non-Darcian porous medium in the presence of radiation and thermophoresis effects. The governing boundary layer equations for momentum, energy, species transfer and angular momentum (micro-rotation) are transformed from an (x,y), coordinate system into (?), coordinate system. The influence of Darcy number (Da), Forchheimmer number (Fs), local Grashof number (Gr), Prandtl number (Pr), Schmidt number (Sc), radiation (R) and thermophoresis (k), surface parameter (s), on the velocity, temperature, concentration profiles and angular velocity (micro-rotation) are studied graphically. Applications for the problem arise in chemical engineering systems and geothermal energy systems.

An exact solution of unsteady flow past an exponentially accelerated infinite vertical plate with variable temperature has been presented in the presence of uniform mass diffusion. The plate temperature is raised linearly with time and species concentration level near the plate is made to rise Cw. The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles fields are studied for different physical parameters like thermal Grashof number, mass Grashof number, Schmidt number, a and time. It is observed that the velocity increases with increasing values of a or t.

The unsteady flow of a viscous incompressible flow past an infinite isothermal vertical oscillating plate, in the presence of thermal radiation and homogeneous chemical reaction of first order has been studied. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised to Tw and the concentration level near the plate is raised linearly with respect to time. An exact solution to the dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity, temperature, and concentration are studied for different physical parameters like phase angle, radiation parameter, chemical reaction parameter, Schmidt number, thermal Grashof number, mass Grashof number, and time are studied graphically. It is observed that the velocity increases with decreasing phase angle wt.

A modified form of the Bejan number (Be), originally proposed by Bhattacharjee and Grosshandler for momentum processes, is obtained by replacing the dynamic viscosity (m) appearing in the original proposition with the equivalent product of the fluid density (r) and the momentum diffusivity of the fluid (n). This modified form is not only more akin to the physics it represents but it also has the advantage of being dependent on only one viscosity coefficient. Moreover, this simple modification allows for a much simpler extension of Be to other diffusion processes, such as a heat or a species transfer process, by simply replacing the diffusivity coefficient. Consequently, a general Be representation for any process involving pressure-drop and diffusion becomes possible. It is shown that this general representation yields analogous results for any process satisfying the Reynolds analogy (i.e., when Pr = Sc = 1), in which case the momentum, energy and species concentration representations of Be turn out to be the same.

A new definition of Bejan number will be generated by replacing the thermal diffusivity with the mass diffusivity. For example, the Schmidt number is the mass transfer analog of the Prandtl number. For the case of Reynolds analogy (Sc = Pr = = 1), both current and new definitions of Bejan number are the same. This new definition is useful and needed for diffusion of mass (mass diffusion).