Search results for: Exciting Boundary Layer

Authors: R. Resmi, M. R. Baiju

Abstract:

The thermal damping of a dynamic vibrating micromirror is an important factor affecting the design of MEMS based actuator systems. In the development process of new micromirror systems, assessing the extent of energy loss due to thermal damping accurately and predicting the performance of the system is very essential. In this paper, the depth of the thermal penetration layer at different eigenfrequencies and the temperature variation distributions surrounding a vibrating micromirror is analyzed. The thermal penetration depth corresponds to the thermal boundary layer in which energy is lost which is a measure of the thermal damping is found out. The energy is mainly dissipated in the thermal boundary layer and thickness of the layer is an important parameter. The detailed thermoacoustics is used to model the air domain surrounding the micromirror. The thickness of the boundary layer, temperature variations and thermal power dissipation are analyzed for a Si based torsional mode micromirror. It is found that thermal penetration depth decreases with eigenfrequency and hence operating the micromirror at higher frequencies is essential for reducing thermal damping. The temperature variations and thermal power dissipations at different eigenfrequencies are also analyzed. Both frequency-response and eigenfrequency analyses are done using COMSOL Multiphysics software.

Keywords: Eigen frequency analysis, micromirrors, thermal damping, thermoacoustic interactions.

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Authors: Siti Khuzaimah Soid, Zanariah Mohd Yusof, Ahmad Sukri Abd Aziz, Seripah Awang Kechil

Abstract:

A steady two-dimensional magnetohydrodynamics flow and heat transfer over a stretching vertical sheet influenced by radiation and porosity is studied. The governing boundary layer equations of partial differential equations are reduced to a system of ordinary differential equations using similarity transformation. The system is solved numerically by using a finite difference scheme known as the Keller-box method for some values of parameters, namely the radiation parameter N, magnetic parameter M, buoyancy parameter l , Prandtl number Pr and permeability parameter K. The effects of the parameters on the heat transfer characteristics are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M and permeability parameter K increase. Heat transfer rate at the surface decreases as the radiation parameter increases.

Keywords: Keller-box, MHD boundary layer flow, permeability stretching.

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Authors: O. Miraliyari

Abstract:

This article attempts to analyze functionally graded beam thermal buckling along with piezoelectric layers applying based on the third order shearing deformation theory considering various boundary conditions. The beam properties are assumed to vary continuously from the lower surface to the upper surface of the beam. The equilibrium equations are derived using the total potential energy equations, Euler equations, piezoelectric material constitutive equations and third order shear deformation theory assumptions. In order to fulfill such an aim, at first functionally graded beam with piezoelectric layers applying the third order shearing deformation theory along with clamped -clamped boundary conditions are thoroughly analyzed, and then following making sure of the correctness of all the equations, the very same beam is analyzed with piezoelectric layers through simply-simply and simply-clamped boundary conditions. In this article buckling critical temperature for functionally graded beam is derived in two different ways, without piezoelectric layer and with piezoelectric layer and the results are compared together. Finally, all the conclusions obtained will be compared and contrasted with the same samples in the same and distinguished conditions through tables and charts. It would be noteworthy that in this article, the software MAPLE has been applied in order to do the numeral calculations.

Keywords: Thermal buckling, functionally graded beam, piezoelectric layer, various boundary conditions.

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Authors: Ezad Hafidz Hafidzuddin, Roslinda Nazar, Norihan M. Arifin, Ioan Pop

Abstract:

In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: Boundary Layer, Exponentially Stretching/Shrinking Sheet, Generalized Slip, Heat Transfer, Numerical Solutions.

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Authors: Andrea Dal Monte, Marco Raciti Castelli, Ernesto Benini

Abstract:

The present paper deals with the most adopted technical solutions for the enhancement of the lift force of a wing. In fact, during several flight conditions (such as take off and landing), the lift force needs to be dramatically enhanced. Both trailing edge devices (such as flaps) and leading edge ones (such as slats) are described. Finally, the most advanced aerodynamic solutions to avoid the separation of the boundary layer from aircraft wings at high angles of attack are reviewed.

Keywords: High lift devices, Trailing Edge devices, Leading Edge devices, Boundary Layer Control devices

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Authors: Saeed Sarabadan, Mehran Nikarya, Kouroah Parand

Abstract:

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this paper, we solve this equation via spectral collocation method based on Bessel functions of the first kind. In this approach, we reduce the solution of the nonlinear MHD Falkner-Skan equation to a solution of a nonlinear algebraic equations system. Then, the resulting system is solved by Newton method. We discuss obtained solution by studying the behavior of boundary layer flow in terms of skin friction, velocity, various amounts of magnetic field and angle of wedge. Finally, the results are compared with other methods mentioned in literature. We can conclude that the presented method has better accuracy than others.

Keywords: MHD Falkner-Skan, nonlinear ODE, spectral collocation method, Bessel functions, skin friction, velocity.

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Authors: M. Si Abdallah, B. Zeghmati

Abstract:

A numerical analysis used to simulate the effects of wavy surfaces and thermal radiation on natural convection heat transfer boundary layer flow over an inclined wavy plate has been investigated. A simple coordinate transformation is employed to transform the complex wavy surface into a flat plate. The boundary layer equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm with relaxation coefficient. Effects of the wavy geometry, the inclination angle of the wavy plate and the thermal radiation on the velocity profiles, temperature profiles and the local Nusselt number are presented and discussed in detail.

Keywords: Free convection, wavy surface, inclined surface, thermal radiation.

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Authors: C. K. Chear, S. S. Dol

Abstract:

For a bluff body, dimples behave like roughness elements in stimulating a turbulent boundary layer, leading to delayed flow separation, a smaller wake and lower form drag. This is very different in principle from the application of dimples to streamlined body, where any reduction in drag would be predominantly due to a reduction in skin friction. In the present work, a car model with different dimple geometry is simulated using k-ε turbulence modeling to determine its effect to the aerodynamics performance. Overall, the results show that the application of dimples manages to reduce the drag coefficient of the car model.

Keywords: Aerodynamics, Boundary Layer, Dimple, Drag, Kinetic Energy, Turbulence.

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Authors: Harpreet Kaur, Vinod Mishra, R. C. Mittal

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In this paper, we have proposed a Haar wavelet quasilinearization method to solve the well known Blasius equation. The method is based on the uniform Haar wavelet operational matrix defined over the interval [0, 1]. In this method, we have proposed the transformation for converting the problem on a fixed computational domain. The Blasius equation arises in the various boundary layer problems of hydrodynamics and in fluid mechanics of laminar viscous flows. Quasi-linearization is iterative process but our proposed technique gives excellent numerical results with quasilinearization for solving nonlinear differential equations without any iteration on selecting collocation points by Haar wavelets. We have solved Blasius equation for 1≤α ≤ 2 and the numerical results are compared with the available results in literature. Finally, we conclude that proposed method is a promising tool for solving the well known nonlinear Blasius equation.

Keywords: Boundary layer Blasius equation, collocation points, quasi-linearization process, uniform haar wavelets.

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Authors: Diego Garijo

Abstract:

A numerical approach for solving constant-coefficient differential equations whose solutions exhibit boundary layer structure is built by inserting Bernstein Partition of Unity into Galerkin variational weak form. Due to the reproduction capability of Bernstein basis, such implementation shows excellent accuracy at boundaries and is able to capture sharp gradients of the field variable by p-refinement using regular distributions of equi-spaced evaluation points. The approximation is subjected to convergence experimentation and a procedure to assemble the discrete equations without a background integration mesh is proposed.

Keywords: Bernstein polynomials, Galerkin, differential equation, boundary layer.

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Authors: G. Revathi, P. Saikrishnan

Abstract:

An analysis is performed to study the influence of nonuniform double slot suction on a steady laminar boundary layer flow over a rotating sphere when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Nonsimilar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. The present investigation shows that the point of ordinary separation can be delayed by nonuniform double slot suction if the mass transfer rate is increased and also if the slots are positioned further downstream. In addition, the investigation reveals that double slot suction is found to be more effective compared to a single slot suction in delaying ordinary separation. As rotation parameter increase the point of separation moves upstream direction.

Keywords: Boundary layer, suction, mass transfer, rotating sphere.

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Authors: M. Arabghahestani, A. Darwish Ahmad, N. K. Akafuah

Abstract:

In this work, small-scale experiments of fire whirl were conducted to study the spinning fire phenomenon and to gain comprehensive understandings of fire tornadoes and the factors that affect their behavior. High speed imaging was used to track the flames at both temporal and spatial scales. This allowed us to better understand the role of the near-ground height in creating a boundary layer flow profile that, in turn contributes to formation of vortices around the fire, and consequent fire whirls. Based on the results obtained from these observations, we were able to spot the differences in the fuel burning rate of the fire itself as a function of a newly defined specific non-dimensional near-ground height. Based on our observations, there is a cutoff non-dimensional height, beyond which a normal fire can be turned into a fire whirl. Additionally, the results showed that the fire burning rate decreases by moving the fire to a height higher than the ground level. These effects were justified by the interactions between vortices formed by, the back pressure and the boundary layer velocity profile, and the vortices generated by the fire itself.

Keywords: Boundary layer profile, fire whirls, near-ground height, vortex interactions.

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Authors: F. Kadioglu, M. Z. Polat, A. R. Gunay

Abstract:

Correct measurement of a structural damping value is an important issue for the reliable design of the components exposed to vibratory and noise conditions. As far as a vibrating beam technique is concerned, the specimens under the test somehow are interacted with measuring and exciting devices, and also with boundary conditions of the test set-up. The aim of this study is to propose a vibrating beam method that offers a non-contact dynamic measurement of solid beam specimens. To evaluate the possible effects of the clamped portion of the specimens with clamped-free ends on the dynamic values (damping and the elastic modulus), the same measuring devices were used, and the results were compared to those with the free-free ends. First, the governing equations of beam specimens related to the free-free and clamped-free boundary conditions were expressed to be able to find their natural frequencies, flexural modulus and damping values. To get a clear idea of the sensitivity of the boundary conditions to the damping values at low, medium and high levels, representative materials were subjected to the tests. The results show that the specimens with low damping values are especially sensitive to the boundary conditions and that the most reliable structural damping values are obtained for the specimens with free-free ends. For the damping values at the low levels, a deviation of about 368% was obtained between the specimens with free-free and clamped-free ends, yet, for those having high inherent damping values, comparable results were obtained. It was obvious that the set-up with clamped-free boundary conditions was not able to produce correct/reliable damping values for the specimens with low inherent damping. 

Keywords: Boundary conditions, damping, dynamic values, non-contact measuring systems, vibrating beam technique.

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Authors: Ferhat Kadioglu, Ahmet Reha Gunay

Abstract:

Correct measurement of a structural damping value is an important issue for the reliable design of the components exposed to vibratory and noise conditions. As far as a vibrating beam technique is concerned, the specimens under the test somehow are interacted with measuring and exciting devices and also with boundary conditions of the test set-up. The aim of this study is to propose a vibrating beam method that offers a non-contact dynamic measurement of solid beam specimens. To evaluate possible effects of the clamped portion of the specimens with clamped-free ends on the dynamic values (damping and the elastic modulus), the same measuring devices were used, and the results were compared to those with the free-free ends. To get clear idea about the sensitivity of the boundary conditions to the damping values at low, medium and high levels, representative materials were subjected to the tests. The results show that the specimens with low damping values are especially sensitive to the boundary conditions and the most reliable structural damping values are obtained for the specimens with free-free ends. For the damping values at the low levels, a deviation of about 368% was obtained between the specimens with free-free and clamped-free ends, yet, for those having high inherent damping values, comparable results were obtained.

Keywords: Vibrating beam technique, dynamic values, damping, boundary conditions, non-contact measuring systems.

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Authors: N. Patten, T. M. Young, P. Griffin

Abstract:

Preliminary results for a new flat plate test facility are presented here in the form of Computational Fluid Dynamics (CFD), flow visualisation, pressure measurements and thermal anemometry. The results from the CFD and flow visualisation show the effectiveness of the plate design, with the trailing edge flap anchoring the stagnation point on the working surface and reducing the extent of the leading edge separation. The flow visualization technique demonstrates the two-dimensionality of the flow in the location where the thermal anemometry measurements are obtained. Measurements of the boundary layer mean velocity profiles compare favourably with the Blasius solution, thereby allowing for comparison of future measurements with the wealth of data available on zero pressure gradient Blasius flows. Results for the skin friction, boundary layer thickness, frictional velocity and wall shear stress are shown to agree well with the Blasius theory, with a maximum experimental deviation from theory of 5%. Two turbulence generating grids have been designed and characterized and it is shown that the turbulence decay downstream of both grids agrees with established correlations. It is also demonstrated that there is little dependence of turbulence on the freestream velocity.

Keywords: CFD, Flow Visualisation, Thermal Anemometry, Turbulence Grids.

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Authors: Bhausaheb L. Pangarkar, M. G. Sane, Saroj B. Parjane, Rajendra M. Abhang, Mahendra Guddad

Abstract:

Vacuum membrane distillation (VMD) process can be used for water purification or the desalination of salt water. The process simply consists of a flat sheet hydrophobic micro porous PTFE membrane and diaphragm vacuum pump without a condenser for the water recovery or trap. The feed was used aqueous NaCl solution. The VMD experiments were performed to evaluate the heat and mass transfer coefficient of the boundary layer in a membrane module. The only operating parameters are feed inlet temperature, and feed flow rate were investigated. The permeate flux was strongly affected by the feed inlet temperature, feed flow rate, and boundary layer heat transfer coefficient. Since lowering the temperature polarization coefficient is essential enhance the process performance considerable and maximizing the heat transfer coefficient for maximizes the mass flux of distillate water. In this paper, the results of VMD experiments are used to measure the boundary layer heat transfer coefficient, and the experimental results are used to reevaluate the empirical constants in the Dittus- Boelter equation.

Keywords: Desalination, heat and mass transfer coefficient, temperature polarization, membrane distillation

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Authors: Norihan Md Arifin, Norfifah Bachok

Abstract:

The onset of Marangoni convection in a horizontal fluid layer with internal heat generation overlying a solid layer heated from below is studied. The upper free surface of a fluid is nondeformable and the bottom boundary are rigid and no-slip. The resulting eigenvalue problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the internal heating, depth ratio and conductivity ratio. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability with internal heating are studied in detail.

Keywords: Linear stability, Marangoni convection, Internal Heatgeneration.

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Authors: G. Sarojamma, K. Vendabai

Abstract:

An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt.

Keywords: Casson nanofluid, Boundary layer flow, Internal heat generation/absorption, Exponentially stretching cylinder, Heat transfer, Brownian motion, Thermophoresis.

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Authors: M. A. Talha, M. Osman Gani, M. Ferdows

Abstract:

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: Convection flow, internal heat generation, similarity, spectral method, numerical analysis, Williamson nanofluid.

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Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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Authors: A. Bumbová, J. Kellner, J. Navrátil, D. Pluskal, M. Kozubková, E. Kozubek

Abstract:

The paper deals with the possibilities of modelling vapour propagation of explosive substances in the FLUENT software. With regard to very low tensions of explosive substance vapours the experiment has been verified as exemplified by mononitrotoluene. Either constant or time variable meteorological conditions have been used for calculation. Further, it has been verified that the eluent source may be time-dependent and may reflect a real situation or the liberation rate may be constant. The execution of the experiment as well as evaluation were clear and it could also be used for modelling vapour and aerosol propagation of selected explosive substances in the atmospheric boundary layer.

Keywords: atmospheric boundary layer, explosive substances, FLUENT software, modelling of propagation

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Authors: Dong Ming, Su Caihong

Abstract:

The scenario of bypass transition is generally described as follows: the low-frequency disturbances in the free-stream may generate long stream-wise streaks in the boundary layer, which later may trigger secondary instability, leading to rapid increase of high-frequency disturbances. Then possibly turbulent spots emerge, and through their merging, lead to fully developed turbulence. This description, however, is insufficient in the sense that it does not provide the inherent mechanism of transition that during the transition, a large number of waves with different frequencies and wave numbers appear almost simultaneously, producing sufficiently large Reynolds stress, so the mean flow profile can change rapidly from laminar to turbulent. In this paper, such a mechanism will be figured out from analyzing DNS data of transition.

Keywords: boundary layer, breakdown, bypass transition, stability, streak.

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Authors: M. Raciti Castelli, S. Mogno, S. Giacometti, E. Benini

Abstract:

A boundary layer wind tunnel facility has been adopted in order to conduct experimental measurements of the flow field around a model of the Panorama Giustinelli Building, Trieste (Italy). Information on the main flow structures has been obtained by means of flow visualization techniques and has been compared to the numerical predictions of the vortical structures spread on top of the roof, in order to investigate the optimal positioning for a vertical-axis wind energy conversion system, registering a good agreement between experimental measurements and numerical predictions.

Keywords: Boundary layer wind tunnel, flow around buildings, atmospheric flow field, vertical-axis wind turbine (VAWT).

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Authors: S. Dey, P. Sibanda, S. Gupta, A. Chakraborty

Abstract:

The occurrence of high nocturnal surface ozone over a tropical urban area (23̊ 32′16.99″ N and 87̊ 17′ 38.95″ E) is analyzed in this paper. Five incidences of nocturnal ozone maxima are recorded during the observational span of two years (June, 2013 to May, 2015). The maximum and minimum values of the surface ozone during these five occasions are 337.630 μg/m³ and 13.034 μg/m³ respectively. HYSPLIT backward trajectory analyses and wind rose diagrams support the horizontal transport of ozone from distant polluted places. Planetary boundary layer characteristics, concentration of precursor (NO₂) and meteorology are found to play important role in the horizontal and vertical transport of surface ozone during nighttime.

Keywords: Nocturnal ozone, planetary boundary layer, horizontal transport, meteorology, urban area.

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Authors: Norfifah Bachok, Norihan Md. Arifin

Abstract:

In this paper we use classical linear stability theory to investigate the effects of uniform internal heat generation on the onset of Marangoni convection in a horizontal layer of fluid heated from below. We use a analytical technique to obtain the close form analytical expression for the onset of Marangoni convection when the lower boundary is conducting with free-slip condition. We show that the effect of increasing the internal heat generation is always to destabilize the layer.

Keywords: Marangoni convection, heat generation, free-slip

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Authors: N. K. Singh, S. Sarkar

Abstract:

Direct numerical simulation (DNS) is used to study the evolution of a boundary layer that was laminar initially followed by separation and then reattachment owing to generation of turbulence. This creates a closed region of recirculation, known as the laminar-separation bubble. The present simulation emulates the flow environment encountered in a modern LP turbine blade, where a laminar separation bubble may occur on the suction surface. The unsteady, incompressible three-dimensional (3-D) Navier-Stokes (NS) equations have been solved over a flat plate in the Cartesian coordinates. The adverse pressure gradient, which causes the flow to separate, is created by a boundary condition. The separated shear layer undergoes transition through appearance of ╬ø vortices, stretching of these create longitudinal streaks. Breakdown of the streaks into small and irregular structures makes the flow turbulent downstream.

Keywords: Adverse pressure gradient, direct numerical simulation, laminar separation bubble.

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Authors: S. C. Kattimani

Abstract:

This article deals with the analysis of active constrained layer damping (ACLD) of smart multiferroic or magneto-electro-elastic doubly curved shells. The kinematics of deformations of the multiferroic doubly curved shell is described by a layer-wise shear deformation theory. A three-dimensional finite element model of multiferroic shells has been developed taking into account the electro-elastic and magneto-elastic couplings. A simple velocity feedback control law is employed to incorporate the active damping. Influence of layer stacking sequence and boundary conditions on the response of the multiferroic doubly curved shell has been studied. In addition, for the different orientation of the fibers of the constraining layer, the performance of the ACLD treatment has been studied.

Keywords: Active constrained layer damping, doubly curved shells, magneto-electro-elastic, multiferroic composite, smart structures.

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

Abstract:

This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: Boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation.

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Authors: Ampon Dhamacharoen, Kanittha Chompuvised

Abstract:

In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.

Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.

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Authors: A. T. Eswara

Abstract:

This paper analyses the unsteady, two-dimensional stagnation point flow of an incompressible viscous fluid over a flat sheet when the flow is started impulsively from rest and at the same time, the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. The partial differential equations governing the laminar boundary layer forced convection flow are non-dimensionalised using semi-similar transformations and then solved numerically using an implicit finitedifference scheme known as the Keller-box method. Results pertaining to the flow and heat transfer characteristics are computed for all dimensionless time, uniformly valid in the whole spatial region without any numerical difficulties. Analytical solutions are also obtained for both small and large times, respectively representing the initial unsteady and final steady state flow and heat transfer. Numerical results indicate that the velocity ratio parameter is found to have a significant effect on skin friction and heat transfer rate at the surface. Furthermore, it is exposed that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state (large time solution).

Keywords: Forced flow, Keller-box method, Stagnation point, Stretching flat sheet, Unsteady laminar boundary layer, Velocity ratio parameter.

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