Volume 71, Issue 7

Supersymmetric cylindrical KdV equation is presented. Decay mode solutions for the supersymmetric KdV equation are derived by supersymmetric Hirota operator.

Heat transfer analysis has been carried out in the Magnetohydrodynamic (MHD) boundary layer formed near the wavy rough plate moving in x -direction. Due to the presence of metallic nanoparticle in the fluid and enhanced surface area of the plate as a consequence of surface texture, an increase in heat transfer rates is expected. However, the calculation of these enhanced rates of heat transfer is not straightforward because the convection phenomena become more complicated due to the motion of nanoparticle in the base fluid and also the waviness of the plate surface. The contribution of nanoparticle toward convective heat transfer is manifold which requires a suitable model in order to capture the correct physics. Famous Tiwari and Das model has been utilised in the current study. Percent increase in the rate of heat transfer is calculated for the nanoparticle of different metals, such as MWCNT, SWCNT, Al 2 O 3 , TiO 2 and Ag. Appreciable increase in the rate of heat transfer is observed, which is 24% at the most for Al 2 O 3 nanoparticle. The effect of applied magnetic field on the velocity profile, skin friction coefficient, and Nusselt number has also been presented through graphs. The concentration of the nanoparticle has been limited up to 10%.

Steady-state parallel plate flow of a third-grade fluid and a Newtonian fluid with temperature-dependent viscosity is considered. Approximate analytical solutions are constructed using the newly developed perturbation-iteration algorithms. Two different perturbation-iteration algorithms are used. The velocity and temperature profiles obtained by the iteration algorithms are contrasted with the numerical solutions as well as with the regular perturbation solutions. It is found that the perturbation-iteration solutions converge better to the numerical solutions than the regular perturbation solutions, in particular when the validity criteria of the regular perturbation solution are not satisfied. The new analytical approach produces promising results in solving complex fluid problems.

The aim of this paper is to investigate the effects of small boundary perturbations on the flow of an incompressible micropolar fluid. The fluid domain is described as follows: we start from a simple rectangular domain and then perturb part of its boundary by the product of a small parameter ϵ and some smooth function h . Using formal asymptotic analysis with respect to ϵ , we derive the effective model in the form of the explicit formulae for the velocity, pressure and microrotation. The asymptotic solution clearly acknowledges the effects of the boundary perturbation and the micropolar nature of the fluid. The obtained results are illustrated by some numerical examples confirming that the considered perturbation has a nonlocal impact on the solution.

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Through imposing on space–time symmetries, a new reduction of the self-dual Yang–Mills equations is obtained for which a Lax pair is established. By a proper exponent transformation, we transform the Lax pair to get a new Lax pair whose compatibility condition gives rise to a set of partial differential equations (PDEs). We solve such PDEs by taking different Lax matrices; we develop a new modified Burgers equation, a generalised type of Kadomtsev–Petviasgvili equation, and the Davey–Stewartson equation, which also generalise some results given by Ablowitz, Chakravarty, Kent, and Newman.

With the help of the characteristic polynomial of Lax matrix for the K (−2, −2) hierarchy, we define a hyperelliptic curve 𝒦 n +1 of arithmetic genus n +1. By introducing the Baker–Akhiezer function and meromorphic function, the K (−2, −2) hierarchy is decomposed into Dubrovin-type differential equations. Based on the theory of hyperelliptic curve, the explicit Riemann theta function representation of meromorphic function is given, and from which the quasi-periodic solutions to the K (−2, −2) hierarchy are obtained.

The way in which solitons propagate and collide is an important theme in various areas of physics. We present a systematic study of the superposition of solitons in systems governed by higher-order equations related to the nonlinear Schrödinger family. We allow for arbitrary amplitudes and relative velocities and include an infinite number of equations in our analysis of collisions and superposed solitons. The formulae we obtain can be useful in determining the influence of subtle effects like higher-order dispersion in optical fibres and small delays in the material responses to imposed impulses.

The structural and elastic properties of V-Si (V 3 Si, VSi 2 , V 5 Si 3 , and V 6 Si 5 ) compounds are studied by using first-principles method. The calculated equilibrium lattice parameters and formation enthalpy are in good agreement with the available experimental data and other theoretical results. The calculated results indicate that the V-Si compounds are mechanically stable. Elastic properties including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are also obtained. The elastic anisotropies of V-Si compounds are investigated via the three-dimensional (3D) figures of directional dependences of reciprocals of Young’s modulus. Finally, based on the quasi-harmonic Debye model, the internal energy, Helmholtz free energy, entropy, heat capacity, thermal expansion coefficient, Grüneisen parameter, and Debye temperature of V-Si compounds have been calculated.

In this paper, based on similarity transformation and auxiliary equation method, we construct many exact solutions of N -coupled nonlinear Schrödinger equations with variable coefficients, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions and combined Jacobi elliptic function solutions. These solutions may give insight into many considerable physical processes.

The electrical conductivity of molten CdCl 2 was measured across a wide temperature range (Δ T =628 K), from 846 K to as high as 1474 K, i.e. 241° above the normal boiling point of the salt. In previous studies, a maximum temperature of 1201 K was reached, this being 273° lower than in the present work. The activation energy of electrical conductivity was calculated.