The odd log-logistic Topp–Leone G family of distributions: heteroscedastic regression models and applications

We introduce a new class of distributions and provide a comprehensive treatment of its mathematical properties. The maximum likelihood method is discussed to estimate the parameters of the new model by means of Monte-Carlo simulation study. The heteroscedastic regression models with long-term survival are introduced to model data sets with the non homogeneity of the error variances in the presence of cured individuals. The potentiality of the proposed models is illustrated by means of four real data sets.     

Falkner-Skan equation for flow past a moving wedge with suction or injection

The characteristics of steady two-dimensional laminar boundary layer flow of a viscous and incompressible fluid past a moving wedge with suction or injection are theoretically investigated. The transformed boundary layer equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of Falkner-Skan power-law parameter (m), suction/injection parameter (f0) and the ratio of free stream velocity to boundary velocity parameter (λ) are discussed in detail. The numerical results for velocity distribution and skin friction coefficient are given for several values of these parameters. Comparisons with the existing results obtained by other researchers under certain conditions are made. The critical values off ₀,m and λ are obtained numerically and their significance on the skin friction and velocity profiles is discussed. The numerical evidence would seem to indicate the onset of reverse flow as it has been found by Riley and Weidman in 1989 for the Falkner-Skan equation for flow past an impermeable stretching boundary.     

Flow and heat transfer over a rotating porous disk in a nanofluid

The steady flow of an incompressible viscous fluid due to a rotating disk in a nanofluid is studied. The transformed boundary layer equations are solved numerically by a finite difference scheme, namely the Keller-box method. Numerical results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction parameter φ and suction/injection parameter h₀. Two models for the effective thermal conductivity of the nanofluid, namely the Maxwell-Garnett model and the Patel model, are considered. It is found that for the Patel model, the heat transfer rate at the surface increases for both suction and injection, whereas different behaviors are observed for the Maxwell-Garnett model, i.e. increasing the values of φ leads to a decrease in the heat transfer rate at the surface for suction, but increases for injection. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Book reviews

Boundary Layers of Flow and Temperature. By Alfred Walz. (The M.I.T. Press, 1970.) [Pp. 297.] £8.4. Scope: Treatise/textbook Level: Specialist/postgraduate.

Interpretation of X-ray Powder Diffractian Pattern. By H. Lipson and H. Steeple. (London: Macmillan; New York: St. Martin's Press, 1970.) [Pp. viii + 335.1 £4.00. Scope: Textbook. Level: Specialist.     

Flow and heat transfer of nanofluid past stretching/shrinking sheet with partial slip boundary conditions

The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.     

Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

The magnetohydrodynamic(MHD) mixed convection flow past a shrinking vertical sheet with thermal radiation is considered. Besides, the effects of Cu-Al₂O₃ nanoparticles and dust particles are considered. The similarity variables reduce the governing equations to the similarity equations, which are then solved numerically. The outcome shows that, for the shrinking case, the solutions are not unique. The rate of heat transfer and the friction factor enlarge with increasing the...