Hyperbolic Boundary Conditions Research Articles

Influence of relaxation‐retardation viscous dissipation on chemically reactive flow of Oldroyd‐B nanofluid with hyperbolic boundary conditions

AbstractThe present analysis is meant to explore the computational solution of the problem dealing with the impact of relaxation‐retardation viscous dissipation and chemical reaction on the flow of Oldroyd‐B nanofluid over a Riga plate. Hyperbolic time‐varying boundary conditions are taken into consideration. The basic modeled problem being transformed into nonlinear differential equations are solved numerically by efficient fourth‐order Runge‐Kutta method along with shooting technique. Characteristics of controlling parameters on velocity, temperature, and concentration along with skin friction, Nusselt number, and Sherwood number profiles are presented with the help of well‐featured graphs. The relaxation and retardation parameters affect well flow profiles. In addition, an accelerated flow pattern is accomplished due to the augmentation of the modified Hartmann number. Furthermore, the presence of relaxation‐retardation viscous dissipation improves the temperature field.

Flow and heat transfer of Oldroyd-B nanofluid with relaxation-retardation viscous dissipation and hyperbolic boundary conditions

In the present research article, modeling and computations are presented to introduce the novel concept of relaxation-retardation viscous dissipation and hyperbolic time variation boundary conditions on the magnetohydrodynamic transient flow of Oldroyd-B nanofluid past a vertical stretched plate for the first time. In the present work, firstly we implement Buongiorno’s model to illustrate Brownian motion and thermophoretic diffusion which take vital role in heat and mass transportation process. Nonlinear non-dimensional governing equations are solved by fourth order Runge-Kutta method along with shooting technique. We investigate the behavior of influential variables on the velocity, thermal and solutal fields through graphical illustrations. Our results indicate that relaxation and retardation Deborah numbers exhibit completely reverse trend in the flow field. Especially, augmented relaxation-retardation viscous dissipation invigorates the temperature gradient. The results of the current theoretical study may be instrumental for worthful practical applications.

Shape effects of the conductance of a quantum ballistic constriction in a two-dimensional electron gas

A hyperbolic model is used to describe the shape effect of the quantized conductance of a microscopic constriction in a two-dimensional electron gas. The constriction is given by two hyperbolas of β = β 0 and π - β 0 in elliptic coordinates (α, β). The conductance G of the constriction is calculated by using Mathieu's functions which satisfy Schrödinger's equation and the hyperbolic boundary conditions. It is found that the number of channels N C depends not only on the constriction width W but also the slope-related coordinate β 0. It is also found that tunnelling is the important factor to determine the shape of the quantized G graph and depends on β 0. Quantization of G is more possible for the large- β 0 constriction (i.e. the long and smooth shape) than for the small- β 0 constriction (i.e. the short and steep shape). For comparison, we calculate G of the hyperbolic constrictions using the adiabatic approximation that the shape is smooth enough for quantization. All adiabatic results for every β 0 have almost the same G curve, which is similar to one obtained by the first scheme for smoothly changing shape, say β 0 = 45°.