Shier and published by CRC Press online. This book was released on 11 November with total page pages. Book excerpt: The practice of modeling is best learned by those armed with fundamental methodologies and exposed to a wide variety of modeling experience.
Ideally, this experience could be obtained by working on actual modeling problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines.
The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in practice. These chapters discuss the general components of the modeling process, and the evolutionary nature of successful model building.
The second part provides a rich compendium of case studies, each one complete with examples, exercises, and projects. In keeping with the multidimensional nature of the models presented, the chapters in the second part are listed in alphabetical order by the contributor's last name. Unlike most mathematical books, in which you must master the concepts of early chapters to prepare for subsequent material, you may start with any chapter.
Begin with cryptology, if that catches your fancy, or go directly to bursty traffic if that is your cup of tea. Liao, K. Cheung o Homotopy analysis of nonlinear progressive waves in deep water o J. Math, 45 2 , pp. Liao, I. Pop o Explicit analytic solution for similarity boundary layer equations o Int. Heat Mass Transfer, 46 10 , pp.
Ayub, A. Rasheed, T. Hayat o Exact flow of a third grade fluid past a porous plate using homotopy analysis method o Int. Hayat, M. Khan, M. Ayub o On the explicit analytic solutions of an Oldroyd 6-constant fluid o Int. Sci, 42 , pp. Ayub o Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field o J. Khan, S. Yang, S. Liao o On the explicit purely analytic solution of Von Karman swirling viscous flow o Comm. Non-linear Sci. Liao o A new branch of solutions of boundary-layer flows over an impermeable stretched plate o Int.
Heat Mass Transfer, 48 12 , pp. Liao o An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate o Comm. Cheng, S. Pop o Analytic series solution for unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium o Transp. Porous Media, 61 , pp. Xu, S. Liao, Analytic solutions of magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate, J.
Non-Newtonian Fluid Mech. Rajagopal, T. Fetecau, C. Non-Linear Mech. Fosdick, K. Rajagopal o Thermodynamics and stability of fluids of third grade o Proc. A, , pp. ABSTRACT In this paper, the mixed convection steady boundary layer stagnation point flow and heat transfer of a third grade fluid over an exponentially stretching sheet is investigated. Both the analytical and numerical solutions are carried out. The analytical solutions are obtained through the homotopy analysis method HAM while the numerical solutions are computed by using the Keller box method K-b.
Comparison of the HAM and Keller-box methods is also given. The effects of important physical parameters are presented through graphs and the salient features are discussed. However, due to the practical significance of these non- Newtonian fluids, many authors have presented various non-Newtonian fluid models like Buongiorno , Nadeem and Ali , Nadeem and Akbar , Lukaszewics , Nadeemet al. The third grade fluid model is one of the most significant fluid models that exhibits all the properties of shear thinning and shear thickening fluids.
The effect of the variable magnetic field over the Couette flow of a third grade fluid was studied by Hayat and Kara Moreover, Hayat et al. Recently, Sahoo and Do analyzed slip effects over the flow and heat transfer of an electrically conducting third grade fluid past a stretching sheet. They concluded that slip causes a decrease in the momentum boundary layer thickness while producing an increase in the thermal boundary layer thickness. Furthermore, Hayat et al. Later on, the problem of steady, laminar flow of a third grade fluid through a porous flat channel was encountered by Ariel He considered the case when the injection rate of the fluid at a boundary is the same as the suction rate of the fluid at the other boundary.
Asghar et al. The present work studies the boundary layer stagnation point flow of a third grade fluid through an exponentially stretching sheet. The governing highly nonlinear equations of the third grade fluid model are simplified by using a boundary layer approximation and similarity transformation. The reduced nonlinear equations are solved analytically and numerically. The analytical solutions are obtained by using the homotopy analysis method.
Details of HAM can be found in the works of Nadeem et al. The numerical solutions are calculated with the help of the Keller-box method described in Keller , Cebeci and Bradshaw and Ali The comparisons of both the solutions are also presented through graphs and tables. The particular features of the parameters are discussed through graphs of the velocity and temperature profiles and also through tables.
The Cartesian coordinates x, y are used such that x is along the surface of the sheet, while y is taken as normal to it. Defining the following similarity transformations: With the help of the transformations in Eqs.
Numerical Solution The numerical solution of Equations 9 and 10 subject to the boundary conditions 11 and 12 is obtained through the Keller-box scheme. For this scheme we first reduce these equations to a first order system; the system obtained is then approximated by central differences.
Further, these difference equations are linearized by Newton's method. The resulting tri-diagonal system is then solved using the block-elimination technique. Results obtained from Keller-box are discussed and compare with HAM in the next section. From these figures, we observe that the convergence region is sufficiently large for smaller values of the respective parameters but decreases very rapidly with an increase in these parameters. These figures also guarantee the fact that our numerical and analytical solutions are convergent.
This holds only for small values of the parameters involved. A similar observation holds for the other parameters as well. We note that in both cases increasing the parameters corresponds to a decrease in the temperature profile and the thermal boundary layer thickness.
The coefficient of skin friction is graphed in Fig. From Fig. It is noted that cause an increase in the Nusselt numbers. Table 2 shows the variation in the Nusselt number for different values of the parameters. The skin-friction coefficient for a third grade fluid is greater than that for a viscous fluid.
Both numeric and HAM solutions are in excellent agreement. Warme-und Stoffubertagung, Vol. International Journal of Engineering Science, Vol. Mathematical and Computer Modeling, Vol. Springer-Verlag, New York, A, Emam, T.
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