In this study, the impact of a complex wavy surface on natural convection flow in micropolar fluid is investigated and the function of the complex wavy surface is considered as a sum of the fundamental wave and its first harmonic. The mathematical model in terms of nonlinear governing PDEs is made dimensionless by introducing scaling variables and solved numerically using the finite difference scheme base on central and backward difference approximations. The effects of micropolar parameter R, and amplitudes of complex wavy surface are discussed through tables and graphs. It is observed that total heat transfer rate decreases by enhancing the effects of microploar parameter and noted that in case of dominant amplitude of fundamental wave, it decreases 8.5 and 22% approximately for R = 1 and R = 4 as compared to Newtonian fluid and in case of dominant amplitude of harmonic wave it decreases 8.5-9% and 22-23%. In micropolar fluid by keeping the value of R fixed, total heat transfer rate increases in case of dominant amplitude of harmonic wave and in this case its percentage increase w.r.t. single sinusoidal surface is much greater than to the case of dominant amplitude of fundamental wave.

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Two-dimensional hydromagnetic flow and heat transfer of Walters-B fluid towards a stagnation point region over a stretching cylinder is discussed. Constitutive equations are transformed into dimensionless form by means of suitable similarity transformations. Spectral quasi-linearization method is employed to obtain the solution of similarity equations. Comparison of computed results with existing results in the limiting case of a flat sheet is also provided. Analysis of obtained results is performed through graphs to discuss the influence of emerging parameters on the velocity and temperature profiles. The flow and heat transfer characteristics are analyzed through parameters representing curvature of cylinder, velocity ratio parameter, magnetic parameter, and Weissenberg number. The curvature of the cylinder has significant impact on the velocity and temperature. A magnetic field applied externally suppresses the bulk motion and alters the momentum boundary layer thickness. The drag and heat transfer rate on the surface of the cylinder are examined through skin friction and heat transfer coefficients. Furthermore, streamlines are drawn to see the flow pattern.

The primary goal of this study is to perform the analysis of heat transfer in free convection flow of micropolar nanofluid along a complex roughened surface. A micropolar nanofluid is made by adding nanoparticles namely SWCNTs (single-walled carbon nanotubes) in ethylene glycol (EG) base micropolar fluid. A mathematical model for micropolar nanofluid can be developed in terms of nonlinear partial differential equations by extending Navier-Stokes equations along with micro inertia effects, angular momentum equation and Tiwari and Das model. After using the suitable transformation, the resulting nonlinear PDEs are made dimensionless and solved numerically using finite difference scheme. Micropolar nanofluids have a capability to improve the thermophysical properties and heat transportation capacity instead of base fluids. The impacts of numerous pertinent parameters on velocity, microrotation and temperature profiles also on physical quantities namely wall couple stress, local and average Nusselt numbers, total heat transfer and skin friction coefficient are discussed graphically. It is noted that total heat transfer rate becomes high in case of dominant amplitude of harmonic wave as compared to fundamental. It is also noted that total heat transfer rate decreases by increasing micropolar parameter and can be enhanced by adding SWCNTs in EG based micropolar fluid and that enhancement is reported approximately 27 and 26% in dominant amplitude of fundamental and harmonic waves as compared to ethylene glycol fluid.

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