The paper attempts to enhance the control of convective transport phenomena in magnetothermal devices applying a technique of multibanded magnetic field. For this demonstration, a typical cavity-like thermal system is considered involving linear heating, porous substance, hybrid nanofluid, and magnetic field. Four identical bands of magnetic fields are applied horizontally with uniform inactive zones between the bands. The transport equations of the coupled multiphysics evolving from the thermal buoyancy (due to linear heating at one sidewall and isothermal cooling at the opposite sidewall), filled porous medium, spatially intermittently active magnetic fields, and the engineered working fluid of Cu–Al₂O₃/water hybrid nanofluid are solved by an indigenously developed computing code. The study is conducted using the pertinent dimensionless parameters for the following ranges: Darcy–Rayleigh number (Ra_m = 1–10⁴), Darcy number (Da = 10⁻⁵ − 10⁻¹), Hartmann number (Ha = 0–70), and concentration of hybrid nanoparticles $\varphi$ (= 0–2%). The convective phenomena are analyzed using the heatlines (for heat transport), streamlines (flow pattern), isotherms (static temperature), and the average Nusselt number (for heat transfer). The outcomes of this technique of multibanded magnetic field are rigorously compared with other established application methods of magnetic fields. It establishes different local behaviors along with an improved heat transfer. Heatline visualization reveals the definite portraits of heat flow paths depending upon parametric values. Furthermore, the presence of linear heating is in particular treated to explore the insight of linear heating (that featuring multiple heating and cooling zones along with the linear heater), utilizing the local Nusselt number and heatlines. One of the important advantages of this new technique is it is more energy-efficient particularly for the square or shallow cavity. The multibanded magnetic field shows a promising technique for the control of convective transport phenomena involving coupled multiphysics used during sophisticated applications (such as materials processing, biomedical applications, etc.).

The problem of steady natural convection in a bottom-heated semi-elliptical enclosure has been investigated numerically for a wide range of geometric and flow configurations using the finite volume method. The results are presented for varying Rayleigh numbers, Ra, in the range 1 × 10² ≤ Ra ≤ 5 × 10⁴ and different values of aspect ratio, A = 1, 0.75, 0.5, and 0.25, where the aspect ratio, A, is defined as the ratio of lengths of the semi-minor axis to the semi-major axis of the semi-elliptical enclosure. It has been found that the steady-state solution appears in the form of single or multiple pairs of counter-rotating convection cells depending on the values of physical parameters. For A = 1, 0.75, and 0.5, as the value of Rayleigh number exceeds a critical value, natural convective flow inside the semi-elliptical enclosure exhibits multiple steady solutions with varying pairs of counter-rotating convection cells; however, such multiplicity of steady solutions could not be found for the cases of A = 0.25. The parametric variations of heat transfer and entropy generation rates are studied in detail. It is observed that the average Nusselt number associated with the natural convection in the semi-elliptical cavity is governed by several parameters: aspect ratio, Rayleigh number, number of convection cells, and intensity of convective motion inside the convection cells. The entropy generation due to viscous dissipation is found to be negligible as compared to the entropy generation due to conduction.

Fully developed laminar flow through semi-elliptic annulus formed between two confocal elliptical ducts, driven by a constant pressure-gradient, has been analysed. The elliptic cylindrical coordinate system has been used to determine the exact solutions for 'Wide' and 'Narrow' semi-elliptic annuli with cross-sections being symmetric about the minor and major axes of the confocal elliptic boundaries, respectively. For both the configurations, exact analytical expressions have been obtained for velocity distribution, volume flow rate, shear stress and Poiseuille number. The results are expressed in terms of two non-dimensional physical parameters: ratio of length of semi-minor axis to semi-major axis of the outer boundary, r_o, 0{less than or equal to}r_o<1, and ratio of length of semi-major axes of inner and outer elliptic boundaries, r_ma, c{less than or equal to}r_ma<1, c being the non-dimensional focal distance of the elliptic boundaries. Based on the analytical expressions, the graphical and tabulated results of the flow fields are presented for representative values of r_o and r_ma to illustrate the characteristic features of the flow. Numerical evaluation of the analytical expressions shows that the flow field and the corresponding distributions of velocity and shear stresses are characteristically different for wide and narrow semi-elliptic annuli. In addition to the analytical results, a bivariate Chebyshev pseudospectral method is formulated in the elliptic-cylindrical coordinate system for obtaining numerical solution of the problem. The numerical results show that the proposed method yields 'exponential convergence' or 'infinite order of accuracy', as expected from a spectral method; exact agreement has been observed between the analytical and numerical results.

The Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatory flows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillating cylindrical annulus. In both the cases, in addition to the exact expressions for the velocity profiles, particular emphasis has been given for the determination of approximate velocity distributions for the high frequency and low frequency or quasi-static limits. It is shown that, for sufficiently large value of an appropriate frequency parameter, the velocity distribution inside the axially or longitudinally oscillating cylindrical annulus can be approximated as a superposition of the velocity distribution inside an axially oscillating cylindrical pipe of radius $${\bar R_o}$$R ¯ o and the velocity distribution outside an axially oscillating cylindrical pipe of radius $${\bar R_i}$$R ¯ i , where $${\bar R_i}$$R ¯ i and $${\bar R_o}$$R ¯ o are the inner and outer radii of the axially oscillating annulus, respectively.