This investigation deals with the Falkner-Skan flow of a Maxwell fluid in the presence of nonuniform applied magnetic fi？eld with heat transfer. Governing problems of flow and heat transfer are solved analytically by employing the homotopy analysis method (HAM). Effects of the involved parameters, namely, the Deborah number, Hartman number, and the Prandtl number, are examined carefully. A comparative study is made with the known numerical solution in a limiting sense and an excellent agreement is noted. 1. Introduction The Falkner-Skan problem under various aspects has attracted the attention of several researchers . This problem under various aspects has been discussed extensively for viscous fluid. The interested readers may consult the studies in [2–11] for detailed information in viscous fluids. There are several materials which do not obey the Newton's law of viscosity, for example, biological products like blood and vaccines, foodstuffs like honey, ketchup, butter, and mayonnaise, certain paints, cosmetic products, pharmaceutical chemicals and so forth. These fluids are characterized as the non-Newtonian fluids. Investigation of such fluids is very useful in industrial, engineering, and biological applications. However, such fluids cannot be studied by employing a single constitutive relationship. This is due to diverse properties of non-Newtonian fluids in nature. These non-Newtonian fluid models are discussed in view of three main categories, namely, the differential, the rate, and the integral types. The simplest subclass of rate type fluids is called Maxwell. The Maxwell fluid allows for the relaxation effects which cannot be predicted in differential type fluids, namely, second, third, and fourth grades. Recently, there has been an increasing interest in the theory of rate type fluids and, in particular, a Maxwell fluid model has been accorded much attention. The Falkner-Skan wedge flow of a non-Newtonian fluid was firstly investigated by Rajagopal et al. . Massoudi and Ramezan  discussed the effect of injection or suction on the Falkner-Skan flows of second grade fluids. The Falkner-Skan wedge flow of power-law fluids embedded in a porous medium is investigated by Kim . Olagunju  studied this flow problem for viscoelastic fluid. In [10–15], the attention has been given to the differential type fluids. To the best of our knowledge, no one investigated the Falkner-Skan flow problem for rate type fluids. In , Yao has examined the Falkner-Skan wedge flow. He established series solution for the velocity and temperature by
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