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A mathematical model is presented for unsteady free convective flow and heat transfer of a viscous nanofluid from a moving vertical cylinder in the presence of thermal radiation. A range of nanofluids containing nanoparticles of Al 2 O 3 , Cu, TiO 2 and Ag with nanoparticle volume fraction range less than or equal to 0.04 are considered. The governing partial differential equations with the corresponding initial and boundary conditions are solved numerically by a robust, well-tested, implicit finite difference scheme of Crank-Nicolson type, which is efficient, unconditionally stable and convergent. The obtained results are benchmarked with previously published work for special cases of the problem in order to access the accuracy of the numerical method and found to be in excellent agreement. The influence of significant parameters such as nanoparticle volume fraction, nanofluid type, thermal conduction-radiation parameter and thermal Grashof number on the flow and heat transfer characteristics is discussed. This study is relevant to high-temperature nanofluid materials' processing, chemical engineering coating operations exploiting nanomaterials and so on.

Purpose-The purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite vertical cylinder with heat transfer Design/methodology/approach-The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. The fluid is a water-based nanofluid containing nanoparticles of copper. The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are used. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A robust, well-tested, implicit finite difference method of Crank-Nicolson type, which is unconditionally stable and convergent, is used to find the numerical solutions of the problem. The velocity and temperature profiles are studied for significant physical parameters such as the magnetic parameter, nanoparticles volume fraction and the thermal Grashof number Gr. The local skin-friction coefficient and the Nusselt number are also analysed and presented graphically. Findings-The present computations have shown that an increase in the values of either magnetic parameter M or nanoparticle volume fraction decreases the local skin-friction coefficient, whereas the opposite effect is observed for thermal Grashof number Gr. The local Nusselt number increases with a rise in Gr and f values. But an increase in M reduces the local Nusselt number. Originality/value-This paper is relatively original and presents numerical investigation of transient two-dimensional laminar boundary layer free convective flow of a nanofluid over a moving semi-infinite vertical cylinder in the presence of an applied magnetic field. The present study is of immediate application to all those processes which are highly affected by heat enhancement concept and a Free convective flow 1393

This investigation is undertaken to study the hydromagnetic flow of a viscous incompressible fluid past an oscillating vertical plate embedded in a porous medium with radiation, viscous dissipation and variable heat and mass diffusion. Governing equations are solved by unconditionally stable explicit finite difference method of DuFort - Frankel’s type for concentration, temperature, vertical velocity field and skin - friction and they are presented graphically for different values of physical parameters involved. It is observed that plate oscillation, variable mass diffusion, radiation, viscous dissipation and porous medium affect the flow pattern significantly

Purpose-The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature. Design/methodology/approach-The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations. Findings-The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m. Research limitations/implications-The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. Practical implications-The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods). Originality/value-This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.