An efficient methodology for the synthesis of novel substituted pyrido[ 3,2,1-jk]carbazoles via Friedel–Crafts cyclialkylations is reported. The methodology was realized by a three-step protocol involving the addition of carbazole to 3-methylcrotononitrile. The resulting nitrile was subjected to alcoholysis to the desired ester, followed by addition of Grignard reagents to afford tertiary alcohols and/or reacted directly with different Grignard reagents to form the desired ketones. The latter ketones were converted to both secondary and tertiary alcohols by reduction with lithium aluminum hydride (LAH) and addition of Grignard reagents, respectively. These alcohols were cyclialkylated under Friedel–Crafts conditions catalyzed by AlCl3/CH3NO2, p-toluenesulfonic acid (PTSA) or polyphosphoric acid (PPA) to give tri- and tetrasubstituted pyrido[3,2,1-jk]carbazoles.

The unsteady magnetohydrodynamic flow of a nanofluid past an oscillatory moving vertical permeable semi-infinite flat plate with constant heat source in a rotating frame of reference is theoretically investigated. The velocity along the plate (slip velocity) is assumed to oscillate on time with a constant frequency. The analytical solutions of the boundary layer equations are assumed of oscillatory type and they are obtained by using the small perturbation approximations. The influence of various relevant physical characteristics are presented and discussed

The boundary-layer flow and heat transfer in a viscous fluid contains metal nanoparticles over a nonlinear stretching sheet is analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. A similarity solution is presented which depends on the nonlinear stretching parameter n, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. The boundary layer velocity, temperature and nanoparticle volume fraction profiles are then determined numerically. The influence of various relevant parameters are discussed and comparison with published results is presented

We study the effects of higher-order chemical reaction and heat generation on coupled heat and mass transfer by MHD mixed convection from a permeable radiating inclined plate with the thermal convective boundary condition. The governing boundary layer equations are formulated and transformed into a set of similarity equations using dimensionless similarity variables developed by Lie group analysis. The resulting equations are then solved numerically using Maple 13 which uses a fourth–fifth order Runge–Kutta–Fehlberg algorithm for solving nonlinear boundary value problems. A representative set of numerical results are displayed graphically and discussed to show some interesting aspects of the parameters: convective heat transfer (γ), the angle of inclination (α), generation order of chemical reaction (n), reaction rate (λ), the Prandtl number (Pr), and the Schmidt number (Sc) on the dimensionless axial velocity, the temperature, and the concentration profiles. Also effects of pertinent parameters on the skin friction factor, the rate of heat, and the rate of mass transfer are obtained and displayed in tabular form. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res

The boundary-layer flow and heat transfer in a viscous fluid containing metallic nanoparticles over a nonlinear stretching sheet are analyzed. The stretching velocity is assumed to vary as a power function of the distance from the origin. The governing partial differential equation and auxiliary conditions are reduced to coupled nonlinear ordinary differential equations with the appropriate corresponding auxiliary conditions. The resulting nonlinear ordinary differential equations (ODEs) are solved numerically. The effects of various relevant parameters, namely, the Eckert number Ec, the solid volume fraction of the nanoparticles φ, and the nonlinear stretching parameter n are discussed. The comparison with published results is also presented. Different types of nanoparticles are studied. It is shown that the behavior of the fluid flow changes with the change of the nanoparticles type

The steady laminar combined convective flow with heat and mass transfer of a Newtonian viscous incompressible fluid over a permeable flat plate with linear hydrodynamic and thermal slips has been investigated numerically. The velocity of the external flow, the suction/injection velocity and the temperature of the plate surface are assumed to vary nonlinearly following the power law with the distance along the plate from the origin. Lie group analysis is used to develop the similarity transformations and the governing momentum, the energy conservation and the mass conservation equations are converted to a system of coupled nonlinear ordinary differential equations with the associated boundary conditions. The resulting equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method. The effects of hydrodynamic slip parameter (a), thermal slip parameter (b), suction/injection parameter (fw), power law parameter (m), buoyancy ratio parameter (N), Prandtl number (Pr) and Schmidt number (Sc) on the fluid flow, heat transfer and mass transfer characteristics are investigated and presented graphically. We have also shown the effects of the Reynolds number (Re) and the power law parameter (m) on the velocity slip and the thermal slip factors. Good agreement is found between the numerical results of the present paper and published results

The problem of viscous flow & heat transfer over a 2-D steady free convection boundary layer from a vertical surface is studied taking into account slip boundary conditions & exponential decay internal heat generation on variation of fluid viscosity with temperature. The governing equations of the problem are steady reduced to couple non-linear moment & the energy equation to be similar by introducing suitable similarity transformation. Dimensionless velocity and temperature profiles are presented graphically for various values of Prandtl number()Pr, velocity slip parameter ()a & temperature slip parameter ()b with & without internal heat generation. Velocity gradient & temperature gradient are also discussed & are given in tables

The problem of viscous flow and heat transfer over an 1-D unsteady free convection boundary layer from vertical surface has been studied by taking slip conditions & variable suction into consideration. The exponential decay with heat generation term was incorporated in the energy equation. The governing equations of the problem the unsteady nonlinear momentum & energy equations are reduced to be similar by introducing a time dependent length scale & by the usual method of similarity transformation. Maple solutions are obtained for a range value of suction parameter()0V, Prandtl number()Pr, velocity slip parameter ()a & temperature slip parameter ()b with & without internal heat generation. Flow & heat transfer characteristics are discussed & are given in figures & tables. Numerical result show that the internal heat generation effects have significant impacts on velocity profiles, temperature profiles & heat transfer rates from vertical surface

The two dimensional steady laminar MHD free convection heat and mass transfer flow over a vertical plate in an incompressible, viscous and electrically conducting fluid is examined considering the wall temperature and concentration distribution proportional to  x utilizing the similarity transformations. The transformed nonlinear boundary layer equations have been obtained by solving the governing equations using numerical technique. Numerical calculations are carried out for different values of dimensionless parameters and an analysis of the results obtained shows that the flow is influenced of magnetic parameter, mixed convection parameter, Lewis, Dufour and Soret number in the fluid. The obtained results are presented graphically and in tabular form.

This article presents the similarity solutions for the steady two-dimensional Falkner–Skan boundary layer flow of a nanofluid over wedge with convective boundary condition. The model used for the nanofluid is the one that incorporates the variable viscosity and nanoparticle volume fraction parameter. Numerical results for the dimensionless velocity and temperature as well as skin friction and Nusselt number are presented graphically for different values of the controlling parameters. Four different types of nanoparticles, namely, copper (Cu), alumina (Al2O3), titania (TiO2) and silver (Ag) as well as two different types of the base fluid, namely, water and ethylene glycol are considered. It is shown that the skin friction and dimensionless heat transfer rate increase with an increase in nanoparticle volume fraction, wedge, viscosity and convective parameters. Comparisons with the published results for the skin friction and Nusselt number are presented and found to be in good agreement