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The motion of a surfactant-laden viscous droplet in the presence of background non-isothermal Poiseuille flow is studied analytically and numerically. Specifically, the effect of interfacial Marangoni stress due to non-uniform distribution of surfactants and temperature at the droplet interface on the velocity and direction of motion of the droplet along the centerline of imposed Poiseuille flow is investigated in the presence of linearly varying temperature field. In the absence of thermal convection, fluid inertia and shape deformation, the interfacial transport of bulk-insoluble surfactants is governed by the surface Péclet number which represents the relative strength of the advective transport of surfactant over the diffusive transport. We obtain analytical solution for small and large values of the surface Péclet number. Numerical solution is obtained for arbitrary surface Péclet number, which compares well with the analytical solution. Depending on the direction of temperature gradient with respect to the imposed Poiseuille flow, the surfactant-induced Marangoni stress affects the droplet velocity differently. When the imposed temperature increases in the direction of imposed Poiseuille flow, surfactants retard the droplet motion as compared with a surfactant-free droplet. However, when the imposed temperature decreases in the direction of imposed Poiseuille flow, presence of surfactants may increase or decrease the magnitude of droplet velocity depending on the relevant governing parameters. Further, for particular values of governing parameters, we observe change in direction of droplet motion due to presence of surfactants, which may bear significant consequences in the design of droplet based microfluidic systems.

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A numerical model has been developed to predict the shape and size of the raceway zone (a void space) created by the force of the blast air injected through the tuyeres in the packed coke bed of a blast furnace. The model is based on the solution of conservation equations of both gas and solid phases as interpenetrating continua on a Eulerian–Eulerian frame. A modified k–ε model has been adopted for gas phase turbulence. The solid phase constitutive equation is characterized by the solid pressure, bulk viscosity and shear viscosity, which are evaluated from the kinetic theory of random motions of granular materials in a fluid flow. The influences of the air blast velocity, initial porosity of the coke bed and the bed height on the shape and size of the raceway zone have been predicted.

An entropy balance and subsequent exergy analysis of the process of combustion of a liquid fuel droplet in a quiescent gaseous surrounding at high temperature has been performed in order to determine the second-law efficiency of the process. Velocity and species concentration fields for the gas phase and the temperature field both for the gas and for the droplet phases have been evaluated from the numerical solution of the equations of conservation of mass, momentum and heat, accordingly. The rate of generation of entropy due to transport processes and chemical reaction in the gas phase has been determined from the generalized entropy transport equation. A theoretical model for exergy analysis of the process of droplet combustion has been developed in order to predict the second-law efficiency in terms of the pertinent controlling parameters, namely, the ratio of free stream to initial droplet temperatures and the initial Damkohler number. It has been observed that, in a typical diffusion-controlled droplet combustion process, in which the rate of chemical reaction is much faster than the rates of diffusion of heat, mass and momentum, the irreversibility rate has, in contrast, a lower value due to chemical reaction than that due to diffusion processes taken together. A low value of the initial Damkohler number (as close as possible to its limiting value for initiation of ignition) and a high value of free stream temperature should be preferred for the process of droplet combustion from the viewpoint of energy economy in relation to thermodynamic utilization of available energy.