Ashish Paul

Stability of Dean Flow Between Two Porous Concentric Cylinders With Radial Flow and a Constant Heat Flux at the Inner Cylinder

A linear analysis for the instability of viscous flow between two porous concentric circular cylinders driven by a constant azimuthal pressure gradient is presented when a radial flow through the permeable walls of the cylinders is present. In addition, a constant heat flux at the inner cylinder is applied. The linearized stability equations form an eigenvalue problem, which is solved by using the classical Runge–Kutta–Fehlberg scheme combined with a shooting method, which is termed the unit disturbance method. It is found that for a given value of the constant heat flux parameter N, even for a radially weak outward flow, there is a strong stabilizing effect and the stabilization is greater as the gap between the cylinders increases. However, in the presence of a weak inward flow for a wider gap, the constant heat flux has no role on the onset.

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

This paper presents an analytical solution of unsteady one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless coupled linear governing partial differential equations are solved by Laplace transform technique for unit Prandtl number and Schmidt number. Effects of various physical parameters are presented with graphs. Numerical values of boundary layer thickness for different parameters are presented in table. Due to the effects of thermal and mass stratifications, the velocity, temperature, and skin friction, Nusselt number shows oscillatory behaviour at smaller times and then reaches steady state at larger times.

Transient Free Convective MHD Flow Past an Exponentially Accelerated Vertical Porous Plate with Variable Temperature through a Porous Medium

This paper is concerned with analytical solution of one-dimensional unsteady laminar boundary layer MHD flow of a viscous incompressible fluid past an exponentially accelerated infinite vertical plate in presence of transverse magnetic field. The vertical plate and the medium of flow are considered to be porous. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The governing boundary layer equations are first converted to dimensionless form and then solved by Laplace transform technique. Numerical values of transient velocity, temperature, skin friction, and Nusselt number are illustrated and are presented in graphs for various sets of physical parametric values, namely, Grashof number, accelerating parameter, suction parameter, permeability parameter, radiation parameter, magnetic parameter, and time. It is found that the velocity decreases with increases of the suction parameter for both cases of cooling and heating of the porous plate whereas skin friction increases with increase of suction parameter.

Chemical Reaction Effect on Transient Free Convective Flow past an Infinite Moving Vertical Cylinder

An analysis is performed to study the heat and mass transfer on the flow past an infinite moving vertical cylinder, in the presence of first-order chemical reaction. The closed-form solutions of the dimensionless governing partial differential equations are obtained in terms of Bessel’s functions and modified Bessel’s functions by the Laplace transform technique. The transient velocity profiles, temperature profiles, and concentration profiles are studied for various sets of physical parameters, namely, the chemical reaction parameter, Prandtl number, Schmidt number, thermal Grashof number, mass Grashof number, and time. The skin friction, Nusselt number, and Sherwood number are also obtained and presented in graphs. It is observed that in presence of as well as increase in chemical reaction the flow velocity decreases. Also, in presence of destructive chemical reaction the concentration profile and Sherwood number tend to the steady state at large time.