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The scattering of incident surface water waves due to small bottom undulation on the porous bed of a laterally unbounded ocean in the presence of surface tension at the free surface is investigated within the framework of two-dimensional linearized water wave theory. Perturbation analysis in conjunction with the Fourier transform technique is employed to derive the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. One special type of bottom topography is considered as an example and the related coefficients are determined in detail. These coefficients are presented in graphical forms. The theoretical observations are validated computationally. The results for the problem involving scattering of water waves by bottom deformations on an impermeable ocean bed are obtained as a particular case.

This article examines the influence of single-walled carbon nanotube (SWCNT)/multi-walled carbon nanotube (MWCNT) nanoparticles shapes on the radiative up and down flow of nanofluids past a thin needle. This nanofluid flow is considered in the presence of Darcy-Forchheimer effects, thermal radiation, Wu's slip, and non-uniform heat source/sink. Brick, cylinder, platelet, and blade shapes of nanoparticles are considered. Numerical solutions are attained by a wellknown shooting technique. A comprehensive discussion regarding the effects of physical parameters on velocity, temperature, skin friction coefficient, and local Nusselt number is carried out. Outcomes reveal that fluid velocities of SWCNT/MWCNT-Water nanofluids behave in the opposite manner in up and down flows of nanofluids in the order of brick, cylinder, platelet and blade-shaped nanoparticles. The porosity parameter regulates the heat transfer rate efficaciously.The surface viscous drag intensifies for the nanofluids involving the nanoparticles in the order of their shapes as brick, blade, cylinder, and platelet.

Because of accelerated demands of advanced technologies like power station, chemical production and microelectronics, it necessitates the need of novel type of fluids with more heat transfer capability. Due to synergistic effect, ternary composite nanofluids (TCNFs) ensure better thermophysical and Rheology properties thereby acting as better suitable heat transfer fluid in wire coating, metal spinning, aerodynamics, medicine and engineering industries, etc. In view of such relevance, flow and heat transfer aspects of TCNF MWCNT + Al2O3 + TiO2 + water induced by linear and nonlinear slips over arbitrarily inclined moving thin needle are investigated in this study. Thompson and Troian nonlinear slip model is modified by developing it in polar coordinates. Quadratic thermal radiation phenomenon is adopted. Fourth-order Runge–Kutta method is used to obtain requisite numerical solution. Major outcomes indicate that fluid velocity of TCNF whittles down with amplification of magnetic parameter due to the flow induced by either linear or nonlinear slips. Lower value of Reynolds number favoring linear slip leads to effective intensification of nondimensional temperature distributions. Surface viscous drag and heat transfer rate get ameliorated with growth in size of thin needle under the influence of both linear and nonlinear slips.

Reiner–Rivlin nanofluid flow due to rotating disk has significance in manufacturing of computer disks, pumping of liquid metals, spin coating, centrifugal machinery, turbo-machinery, crystal growth and rotational viscometer. In light of such real and relevant industrial applications, this study deals with the numerical investigation of unsteady rotationally symmetric flow of Reiner–Rivlin nanofluid over a stretchable rotating disk. The purpose of this investigation is to explore heat transfer characteristics of Reiner–Rivlin nanofluid subject to radial stretched surface implementable in several thermal systems. For facilitation of heat transport in complex thermal systems, mathematical models, such as Cattaneo–Christov, Buongiorno and nonlinear thermal radiation models, are assumed to be introduced. Runge–Kutta–Fehlberg technique along with shooting method is used for numerical computation of the transformed equations. It is captivating that radial and circumferential velocities decelerate with rise in Reiner–Rivlin and stretching strength parameters, respectively. Amplified thermal relaxation and Reiner–Rivlin parameters led to diminution of wall temperature gradient. Nanoparticle concentration profiles exhibit opposite behavior in response to escalation of activation energy and reaction rate parameters.