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The phenomena of unsteady magnetohydrodynamics (MHD) natural convection flow in an inclined square cavity filled with nanofluid and containing a heated circular obstacle at its center with heat generation/absorption impact are examined numerically. The cavity's right and left walls are maintained at low temperatures, while the remaining walls are adiabatic. The volumetric external force, MHD, is applied across the inclined cavity. A penalty formulation-based finite element method is used to solve the nonlinear set of governing equations iteratively. The numerical scheme and results are validated through a comparison with the benchmark results, and it shows that our solutions are in good agreement with them. The results are shown in terms of contours of streamlines, isotherms, and average Nusselt number. It is observed that MHD alters the streamlines, isotherms, and average Nusselt number and dominates the flow as compared to any other physical parameter. The average Nusselt number is found sensitive to the central obstacle's size, and it reduces sufficiently when the radius of the inner cylinder increases. For all the parameters, the streamlines' symmetric pattern holds, such that the anti-clockwise cells on the left side of the cavity have their symmetric clockwise cells on the right side. [ABSTRACT FROM AUTHOR]

Natural convective flow and heat transfer around a locally heated circular cylinder kept in a rectangular enclosure are investigated. At first, a problem valid for a rectangular domain is formulated and then an analytical coordinate transformation is introduced to map the rectangular domain to the physical domain considered here. Based on the coordinate transformation, a set of governing equations is obtained which is further simulated by imposing appropriate conditions on the walls of the cavity and the inner solid bodies. Numerical solutions are validated through comparison of the present results with the available published data. It is found that streamlines and isotherms are greatly influenced by the width (w) and breadth (b) of the heat source and the Rayleigh number (Ra). The Nusselt number (Nu) is computed at the surface of the inner and outer cylinders, revealing that it grows considerably when controlling parameters w, b, and Ra are increased. The strength and number of the vortices generated within the velocity field heavily depend on the size and location of the outer cylinder. The span-wise local Nusselt number variation shows some sharp rises compared to the neighboring values in Nui and Nuo, which is due to the large temperature gradient at those points. [ABSTRACT FROM AUTHOR]

A mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of Ri = 1.0 \mathrm{Ri}=1.0 , the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic. [ABSTRACT FROM AUTHOR]

A boundary-layer analysis is presented for steady, two-dimensional, Marangoni convection along an irregular surface. Thick radiation limit is considered to express the radiative heat flux. A coordinate transformation is adopted to convert the physical domain into computational domain. Implicit finite difference method is then used to obtain the solutions of the problem. The main purpose of this study is to demonstrate the radiation effects on the dissipative layers. Numerical solutions are presented in the form of skin friction coefficient, heat transfer coefficient, velocity and temperature profiles, streamlines and isotherms. It is observed that thermal radiation has a pronounced effect on the flow field and amplitude of the harmonic oscillations also decay with R d $R_d$. The momentum and thermal boundary-layer thickness increases as R d $R_d$ gets augmented. [ABSTRACT FROM AUTHOR]

The problem considered in this paper deal with the transient behavior of heat transfer by natural convection flow of fluid along an infinite vertical heated wavy surface. The governing equations are transformed into dimensionless form and solutions are obtained for the two dimensional flow for both pure (α = 0) and uneven surface (α ≠ 0). For pure vertical surface boundary layer equations are solved in the (i) upstream (small τ) (ii) downstream (large τ) and (iii) entire (0<τ<∞) regimes using analytical and numerical techniques. A very good agreement is found when results of above mentioned regimes are compared. Further, for wavy surface solutions are obtained for the entire time regime and results are discussed in terms of average Nusselt number coefficient and isotherms. Numerical results are served to reveal the influence of the physical parameters such as the Prandtl number, Pr, and wavy geometry, α, for the surface conditions. [ABSTRACT FROM AUTHOR]

This article provides the computational results of laminar, boundary layer flow of a dilute gas-particle mixture over a semi-infinite vertical wavy surface. The governing parabolic partial differential equations are switched into another frame of reference by using primitive variable formulations (PVF). Two-point finite difference scheme is applied to acquire the unknown quantities of the carrier and the particle phase. The results are obtained for the cases: (i) water-metal mixture and (ii) air-metal mixture and are displayed in the form of wall shear stress, wall heat transfer, velocity profile, temperature profile, streamlines and isotherms for different emerging physical parameters. The solutions are compared, as well, with the available data in the literature. Quantitative comparison shows good compatibility between the present and the previous results. For the dusty fluid model it is found that the rate of heat transfer reduces considerably when the amplitude of the sinusoidal waveform increases from 0 to 0.5. [ABSTRACT FROM AUTHOR]