• M SHAHZAD

      Articles written in Pramana – Journal of Physics

    • Numerical interpretation of autocatalysis chemical reaction for nonlinear radiative 3D flow of cross magnetofluid

      W A KHAN M ALI F SULTAN M SHAHZAD M KHAN M IRFAN

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      A simple relation of chemical processes for three-dimensional flow of a cross magnetofluid over bidirectional stretched surface is constructed. The impact of convective heat transport in the manifestation of non-linear thermal radiation and features of heat source–sink are also considered for heat transfer mechanism.Furthermore, in this research paper, the innovative relation between heterogeneous and homogeneous responses with equivalent diffusivities for reactant and autocatalysis is exploited. Apposite alterations are guaranteed to obtain ordinary differential equations (ODEs) with high nonlinearity. Numerically, the bvp4c technique is exploited to the interpret the structure of ODEs. Portrayals of temperature and concentration for cross liquid equivalent to abundant somatic parameters are presented graphically as well as in tabular form. Our results reveal that the temperature of the cross fluid decreases with fluctuation in the heat sink parameter. Furthermore, it is perceived from the figuresthat the concentration of the cross fluid reduces for higher values of chemical reaction parameters.

    • Theoretical aspects of thermophoresis and Brownian motion for three-dimensional flow of the cross fluid with activation energy

      F SULTAN W A KHAN M ALI M SHAHZAD M IRFAN M KHAN

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      The current review proclaims the forced convective flow and heat–mass transfer characteristics of cross nanofluid past a bidirectional stretched surface. The most significant aim of the current review is to incorporatethe features of Buongiorno relation, activation energy, nonlinear thermal radiation and heat sink–source for a three-dimensional flow of the cross fluid. Appropriate transformations are employed to transform the modelledpartial differential equations (PDEs) of momentum, temperature and concentration into coupled nonlinear ordinary differential equations (ODEs). The governing boundary value problem is numerically integrated with the help of bvp4c scheme. The obtained numerical data are plotted for the temperature and concentration profiles of nanofluid for various converging values of physical parameters. The dependence of increasing thermophysical parameters on temperature and concentration profiles of the cross nanofluid is graphically demonstrated. Furthermore, detailedstudy reveals that the concentration of the cross nanofluid decreases for increasing values of Brownian motion parameter. It is also perceived from the sketches that the concentration of the cross nanofluid decreases for higher values of chemical reaction parameter. The validity of the achieved numerical outcomes is ensured by making a comparison with the existing work as special cases.

    • C-matrix and invariants in chemical kinetics: A mathematical concept

      M SHAHZAD F SULTAN I HAQ M ALI W A KHAN

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      To treat a realistic chemical system, such as a liquid phase dehydrogenation reaction, a chemical scheme, which describes the chemical kinetics in terms of the small number of reaction progress variables is needed. Based onthe matrix algebra, we analyse the key components, elements and reactions in the mechanism, C-matrix. Reduction techniques exploit the time-scale separation into fast and slow modes by computing the dimension reduced model via the elimination of fast mode subjecting them to the slow one. The two-step reversible reaction mechanism is considered for model reduction and to simplify the complexity of reaction mechanisms. They give a meaningful picture, but for maximum clarity, the phase flow of the solution trajectories near the equilibrium point is exploited. The Lyapunov function is applied for the stability analysis. To describe the physical behaviour of the reaction mechanism, graphical results are measured while refinement of the initial approximation is tabulated at the end.

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