B.S. Mazumder

Effect of boundary reaction on solute dispersion in pulsatile flow through a tube

We examine the streamwise dispersion of passive contaminant molecules released in a time-dependent laminar flow through a tube in the presence of boundary absorption or a catalytic wall reaction, which causes a depletion of contaminant in the flow. A finite-difference implicit scheme has been used to solve the unsteady convective-diffusion equation for all time. Here it is shown how the mixing of the cross-sectionally integrated concentration of contaminant molecules is influenced by the frequency of pressure pulsation and the heterogeneous reaction at the boundary

Turbulence statistics of flow over isolated scalene and isosceles triangular-shaped bedforms

The objective of this research is to examine the turbulent flow characteristics over artificial waveform structures and to compare turbulence between two types of isolated geometries. Measurement of turbulent velocity components have been performed over the respective structures of equal crest height and length at the Fluvial Mechanics Laboratory (FML) of the Indian Statistical Institute, Calcutta. The velocity data were analyzed to determine the relative importance of mean flows, Reynolds stresses and the contributions of burst-sweep cycles. The difference in the sizes of the separation zone for these two cases makes significant differences in the mean flow and turbulence. The motivation of this study is to identify the spatial changes of flow and turbulent events over these structures, and to gain better insight in the flow physics, which are different conditions for the process of sediment transport.

Dispersion of contaminant in oscillatory flows

SummaryAn extension of the Aris-Barton method of moments is presented for the study of statustucal behaviour of dispersion of contaminant molecules in oscillatory flows inside uniform conduits. The main idea is to replace the constant pressure gradient which causes the flow simply by the time-dependent one, and then investigate the effects of the amplitude and frequency of the pressure pulsations on the dispersion process. The technique incorporates the case of the time-independent flow also, and gives an exact analysis of the central moments of the distribution of the cloud of contaminant, which are valid for all times after the injection. The general theory is applied to oscillatory laminar flows in tubes, and between parallel plates.

Influence of bed roughness on sediment suspension: experimental and theoretical studies

Flume experiments with five beds of heterogeneous sediment mixtures having different values of bed roughness show that for fixed height and velocity the amount of suspension concentration increases up to a certain value with increase of bed roughness and then decreases with further increase of bed roughness. This indicates depletion of concentration in suspension due to increase of coarse sediment in the bed. Some sort of “critical bed roughness” together with sediment entrapment acting on the sediment beds due to further increase of bed roughness prevent grain sizes from lifting into suspension from the beds. Mathematical models for computation of actual amount (g/l) and size distribution of suspended materials over different sediment beds, based on Hunts diffusion equations for sediments and water, have been developed in this work. Models give results which compare well with the observed values of actual amount and grain-size distributions comprising the wide range of grain sizes. In this study, the parameter γ, the ratio of sediment diffusion coefficient to the momentum diffusion coefficient, has been shown to be a function of normalized settling velocity of particle, and the relation has been used to estimate sediment suspension distribution.

Unsteady convective diffusion in a pulsatile flow through a channel

SummaryThe paper presents an exact analysis of the streamwise dispersion of passive contaminant molecules released in an incompressible viscous fluid flowing through a channel under the influence of a periodic pressure gradient. Using the Aris-Barton method of moments which is valid for all time after the injection of the solute, the dispersion coefficients of a passive contaminant cloud are obtained separately for three different cases: steady, periodic and for comparison the combined effect of steady and periodic currents. Here it is shown how the injected material disperses due to the shear effect caused by the combined effects of flow (steady or periodic) and lateral diffusion about its mean position, and how the centre of gravity of mass moves, when the initial distribution of contaminant is uniform over the cross-section of the channel. The comparison reveals that for all cases the dispersion coefficient asymptotically reaches a stationary state after a certain time, but it changes cyclically with dispersion time even in the stationary state for the case of oscillatory flows. The analysis leads to the interesting result that the dispersion coefficient consists of a steady part and a fluctuating part due to the pulsatility of the flow.

Effect of wall conductances on hydromagnetic flow and heat transfer in a rotating channel

SummaryWall conductance effects on the hydromagnetic flow and heat transfer between two parallel plates in a rotating frame of reference has been studied when the liquid is permeated by a transverse magnetic field. An exact solution of the governing equations has been obtained. It is found that the velocity, current density and the temperature depend only on the sum of the wall conductances φ1 + φ2 = φ but magnetic field depends on the individual values of φ1 and φ2, where φ1 and φ2 are respectively the wall conductance ratios of the upper and lower walls.ZusammenfassungIn der Arbeit wird der Einfluß der Leitfähigkeit der Wände auf die MHD-Strömung sowie auf den Wärmeübergang untersucht für den Fall, daß sich das zähe Medium zwischen zwei rotierenden Platten befindet und ein Magnetfeld parallel zur Rotationsachse angelegt wird. Es wird eine exakte Lösung des Problems gegeben. Es zeigt sich, daß die Geschwindigkeit, die Stromdichte und die Temperatur nur von der Summe der Leitfähigkeiten der Wände + φ2 = φ abhängen, dagegen hängt die magnetische Feldstärke von den individuellen Werten φ1 und φ2 ab, wobei φ1 und φ2 die Leitfähigkeiten der oberen bzw. unteren Wand bezeichnen.

Deposition of Sand by Suspension Currents: Experimental and Theoretical Studies

ABSTRACT Flume experients with heterogeneous sediment mixtures show that all the grain sizes present in suspension are involved in the process of formation of a bed when the flow velocity is decreased. The size distribution deposited closely reflects the one present in suspension. This finding is contradictory to the common belief that the coarser grains are the first to be discarded at decreasing current velocity. The existing equations after Rouse (1938) and Hunt (1969) also tend to overestimate depletion of the coarser grains. A mathematical model for deposition, based on the idea that the process of depletion of the coarser grains is actually dampened in nature, has been developed in this work. This model gives results which compare well (particularly for low velocities) with the observed values comprising wide range of grain sizes. Using the model, it should be possible to estimate the grain-size distribution of the deposited material, given the size distribution present in suspension at a higher velocity. Since the size distribution of the deposits closely reflects that present in suspension, it should also be possible to work out paleoflow velocities of suspension currents from grain-size parameters of ancient deposits, following the relationship established earlier between mean grain size in suspension and the shear velocity (Ghosh and Mazumder 1981).

Flow and heat transfer in the hydromagnetic ekman layer on a porous plate with hall effects

Abstract Flow in the Ekman layer of a conducting liquid past an infinite porous plate is investigated when the liquid is permeated by a transverse magnetic field and the Hall effects are taken into account. It is found that asymptotic solution exists both in the presence of suction or blowing at the plate. For fixed magnetic and suction parameters, the skin friction of the primary flow increases with increase in the Hall parameter ωτ, while that for the secondary flow first increases, reaches a maximum and then decreases with increase in ωτ. Steady distribution of temperature in the flow exists only for suction at the plate and for large Eckert numbers, heat flows from the liquid to the wall even if the wall temperature is higher than that of the ambient stream.

On contaminant dispersion in unsteady generalised Couette flow

Abstract The paper presents the longitudinal dispersion of passive contaminant molecules released in an incompressible viscous fluid flowing through a parallel plate channel under the influence of the oscillation of upper plate in its own plane with a constant velocity and an imposed constant pressure gradient in the axial direction. Analytical solution of unsteady convective–diffusion equation based on the Aris method of moments is presented upto the second moment about the mean and then a finite-difference implicit scheme based on the Crank–Nicholson method has been adopted to solve the remaining equations upto fourth moments for all time periods. Here it is shown how spreading of tracers is influenced by the combined action of imposed pressure gradient, frequency of plate oscillation and the lateral diffusion, when the contaminant is initially uniform over the cross-section of the channel and the Peclet number is large. The behaviour of the dispersion coefficient from the initial to the stationary stage has been examined separately for three different flow regimes: plane Couette flow or simple shear flow, generalised Couette flow and unsteady Couette flow due to the oscillation of the upper wall. The axial distributions of mean concentration have been studied from first four central moments by using Hermite polynomials and the deviations from Gaussianity have also been examined for these flow regimes.

Hall effects on combined free and forced convective hydromagnetic flow through a channel

Abstract Hydromagnetic free and forced convection in a parallel plate channel permeated by a transverse magnetic field has been considered taking Hall effects into account. When there is a uniform axial temperature variation along the walls, the primary flow shows incipient flow reversal at the upper plate for an increase in temperature along that plate. Similarly flow reversal at the lower plate occurs for a decrease in temperature along that plate. Hall currents are found to exert a destabilizing influence on the flow. The skin-friction for the cross-flow increases with the Hall parameter. The induced magnetic field and the heat transfer characteristics in the flow are also determined.