Rudra Kanta Deka

Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction

An exact solution to the flow due to impulsive motion of an infinite vertical plate in its own plane in the presence of i) species concentration ii) constant heat flux at the plate iii) chemical reaction of first order, has been derived by the Laplace-transform technique. Velocity and concentration profiles are shown on graphs. It is observed that due to the presence of first order chemical reaction, the velocity decreases but the skin-friction being positive at large values of the chemical reaction parameter, there may not occur separation of the flow near the plate.

Flow past an accelerated horizontal plate in a rotating fluid

SummaryA semi-infinite mass of an incompressible viscous fluid bounded by an infinite flat plate is initially rotating with uniform angular velocity Ω about an axis normal to the plate. An analysis is presented for the subsequent flow when the plate started impulsively from rest relative to the rotating fluid moves with uniform acceleration in its own plane. It is found that when Ω≠0, the velocity profiles for varying times are nonsimilar in contrast to the velocity profiles which are similar in the absence of rotation (Ω=0). At a given instant, the velocity component along the direction of motion of the plate decreases with an increase in rotation but the transverse velocity component (induced by the Coriolis force) increases with increasing rotation. Due to the gradual thinning of the boundary layer with rotation, both the skin-friction components along and transverse to the direction of motion of the plate increase with increasing rotation. A study of the asymptotic behavior of the velocity field for large time reveals a novel feature of the flow; it develops inertial oscillations with frequency 2Ω, which grow with time. This behavior has not been reported in the absence of rotation.

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.

Stability of Taylor–Couette Magnetoconvection With Radial Temperature Gradient and Constant Heat Flux at the Outer Cylinder

An analysis is made of the linear stability of wide-gap hydromagnetic (MHD) dissipative Couette flow of an incompressible electrically conducting fluid between two rotating concentric circular cylinders in the presence of a uniform axial magnetic field. A constant heat flux is applied at the outer cylinder and the inner cylinder is kept at a constant temperature. Both types of boundary conditions viz; perfectly electrically conducting and electrically nonconducting walls are examined. The three cases of μ 0 (co-rotating), and μ=0 (stationary outer cylinder) are considered. Assuming very small magnetic Prandtl number Pm, the wide-gap perturbation equations are derived and solved by a direct numerical procedure. It is found that for given values of the radius ratio η and the heat flux parameter N, the critical Taylor number Tc at the onset of instability increases with increase in Hartmann number Q for both conducting and nonconducting walls thus establishing the stabilizing influence of the magnetic field. Further it is found that insulating walls are more destabilizing than the conducting walls. It is observed that for given values of η and Q, the critical Taylor number Tc decreases with increase in N. The analysis further reveals that for μ=0 and perfectly conducting walls, the critical wave number ac is not a monotonic function of Q but first increases, reaches a maximum and then decreases with further increase in Q. It is also observed that while ac is a monotonic decreasing function of μ for N=0, in the presence of heat flux (N=1), ac has a maximum at a negative value of μ (counter-rotating cylinders).

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.

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.

Effects of Mass Transfer and Heat Flux on Convective Flow Past a Moving Vertical Cylinder with Chemical Reaction

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