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 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.

A mathematical model is developed for the nanofluid flow and heat transfer due to the impulsive motion of an infinite vertical porous plate in its own plane in the presence of a magnetic field and viscous dissipation. The governing unsteady, coupled, nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations, with appropriate boundary conditions. A robust Galerkin finite element numerical solution is developed. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction ranges less than or equal to 0.04 are considered. The Tiwari-Das nanofluid model is employed. The velocity and temperature profiles as well as the skin friction coefficient and Nusselt number are examined for different parameters such as nanoparticle volume fraction, nanofluid type, magnetic parameter, thermal Grashof number, Eckert number and suction parameter. The present simulations are relevant to magnetic nanomaterials thermal flow processing in the chemical engineering and metallurgy industries.

In this paper, the problem of nanofluid flow and heat transfer due to the impulsive motion of a semi-infinite vertical plate in its own plane in the presence of magnetic field is analyzed by the implicit finite-difference numerical method. 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. The Tiwari-Das nanofluid model is employed. The velocity and temperature profiles as well as the skin friction coefficient and Nusselt number are examined for different parameters such as nanoparticle volume fraction, nanofluid type, magnetic parameter and thermal Grashof number. The present simulations are relevant to magnetic nanomaterials thermal flow processing in the chemical and metallurgical industries.

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