A problem of oblique wave scattering by a rectangular breakwater floating in water of uneven depth is solved by applying matched eigenfunction expansion method. Three positions of breakwater are considered. The width and draft of breakwater are assumed to be finite, whereas its length is infinite. Breakwater is studied in the settings of without backwall and with a backwall. By using matching conditions at interface boundaries and making use of orthogonal property of eigenfunctions, the problem is converted to a system of algebraic equations. Breakwater’s position is proposed for which wave reflection, transmission, and force on wall are optimized. The breakwater with certain width and draft reflects more wave energy than the one with zero-draft. In the case of absence of wall, breakwater at lee side to the step induces least transmission of waves. In the case of presence of wall, suitable position of breakwater is suggested based on a range of wave frequency to mitigate force on wall. Optimum distances between wall and breakwater are found to attain less force on wall. Using Green’s identity, energy balance relation is derived to check accuracy in results. The findings are likely to be useful to assess the performance of a breakwater in different positions in water of uneven depth.

The aim of this paper is to study the momentum and the heat transfer characteristics in incompressible electrically conducting boundary layer flow over an exponentially stretching sheet under the effect of magnetic field with thermal radiation through porous medium. The governing boundary layer equations are converted into self-similar nonlinear ordinary differential equations, using similarity transformations in exponential form and then solved numerically using shooting method. The velocity profile, skin friction-co-efficient and rate of heat transfer are computed numerically and then graphically studied with respect to similarity variable (η) for different cases of velocity ratio parameter (β)

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