Series solution of unsteady free convection flow with mass transfer along an accelerated vertical porous plate with suction

The problem of unsteady free convection flow is considered for the series solution (analytic solution). The flow is induced by an infinite vertical porous plate which is accelerated in its own plane. The series solution expressions for velocity field, temperature field and concentration distribution are presented. The influence of important parameters is seen on the velocity, temperature, concentration, skin friction coefficient and temperature gradient with the help of graphs and tables. Convergence is also properly checked for different values of the important parametes for velocity field, temperature and concentration with the help of ħ-curves.     

Heat transfer in fluctuating flow of an elastico-viscous fluid past an infinite plate with constant suction

An analysis of heat transfer in a two dimensional flow of an elastico-viscous fluid (Walters liquid B) past an infinite porous plate has been carried out under the following conditions: (1) constant suction, (2) free stream oscillates in time about a constant mean, (3) the plate is thermally insulated. Approximate solutions to the temperature field have been derived on taking into consideration viscous dissipative terms. The mean wall temperature has been shown graphically and it is observed that it decreases with increasing frequency.     

Perturbation technique for unsteady MHD mixed convection periodic flow, heat and mass transfer in micropolar fluid with chemical reaction in the presence of thermal radiation

An analytical study is presented for the problem of unsteady hydromagnetic heat and mass transfer for a micropolar fluid bounded by semi-infinite vertical permeable plate in the presence of first-order chemical reaction, thermal radiation and heat absorption. A uniform magnetic field acts perpendicularly to the porous surface which absorbs the micropolar fluid with a time-dependent suction velocity. The basic partial differential equations are reduced to a system of nonlinear ordinary differential equations which are solved analytically using perturbation technique. Numerical calculations for the analytical expressions are carried out and the results are shown graphically. The effects of the various dimensionless parameters related to the problem on the velocity, angular velocity, temperature and concentration fields are discussed in detail.     

EHD convection in dielectric micropolar fluid layer

The onset of instability in a layer of dielectric micropolar fluid under the simultaneous action of an AC electric field and temperature gradient has been investigated. The dispersion relation has been derived and various critical values of non-dimensional Rayleigh number in the fluid layer have been determined. The influence of micropolar viscosity and electric Rayleigh number on the onset of convection has been analyzed. Thermal Rayleigh number has been computed for various values of electric Rayleigh number for the onset of instability. The stabilizing and destabilizing effects of electric Rayleigh number, micropolar viscosity and Prandtl number have been discussed.     

Heat transfer and fluid flow of benard-cell convection in rectangular container with free surface sensed by infrared thermography

The natural convection flow phenomena that occur inside an enclosed space are very interesting examples of complex fluid systems that may yield to analytical, empirical and numerical solutions, and many reports have looked into this basic problem. In the present study, heat transfer and fluid flow for natural convection in a horizontal rectangular container with a free surface are investigated using infrared thermography. The temperature field was measured and visualized at a gas-liquid (air — silicon oil) interface using infrared thermography. The heat transfer phenomena were also investigated by statistically analyzing the temperature data. The applicability of the infrared thermography to quantitative heat transfer measurement at the gas-liquid interface was evaluated. It is revealed that infrared thermography is effective not only in visualization of a gas-liquid interface but also in heat transfer measurement. A new heat transfer correlation is proposed for the gas-liquid interface of this flow system. The coefficient of heat transfer can be summarized by a specific heat transfer correlation formula regardless of several conditions, including container aspect ratio, fluid viscosity and fluid layer depth.     

Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet

The steady two-dimensional mixed convection flow of a micropolar fluid over a non-linear stretching sheet is investigated. The governing non-linear equations and their associated boundary conditions are transformed into coupled non-linear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy analysis method (HAM). The convergence of the obtained series solutions is carefully checked. The physical significance of interesting parameters on the flow and the thermal fields are shown through graphs and discussed in detail. The values of wall shear stress, couple wall stress and the local Nusselt number are tabulated. Comparison is also made with the corresponding results of viscous fluid with no mixed convection and an excellent agreement is noted.     

Temperature and concentration gradient effects on heat and mass transfer in micropolar fluid

We report here the development of collinear laser spectroscopy (CLS) system at VECC for the study of hyperfine spectrum and isotopic shift of stable and unstable isotopes. The facility is first of its kind in the country allowing measurement of hyperfine splitting of atomic levels using atomic beams. The CLS system is installed downstream of the focal plane of the existing isotope separator online (ISOL) facility at VECC and is recently commissioned by successfully resolving the fluorescence spectrum of the hyperfine levels in \(^{85,87}\)Rb. The atomic beams of Rb were produced by charge exchange of 8 keV Rb ion beam which were produced, extracted and transported to the charge exchange cell using the ion sources, extractor and the beam-line magnets of the ISOL facility. The laser propagating opposite to the ion / atom beam direction was allowed to interact with the atom beam and fluorescence spectrum was recorded. The experimental set-up and the experiment conducted are reported in detail. The measures needed to be carried out for improving the sensitivity to a level necessary for studying short-lived exotic nuclei have also been discussed.     

Unsteady flow of a viscous incompressible fluid past a porous plate with constant suction

An exact solution of the flow of an incompressible viscous fluid past an infinite porous plate has been derived on taking into account a step-change in suction velocity. It has been observed that the skin-friction decreases with increasingS, the suction parameter.     

Magnetohydrodynamic flow of a viscoelastic fluid

The non-linear differential equation for the magnetohydrodynamic Poiseuille flow of Phan-Thein-Tanner (PTT) conducting fluid is derived. Using the homotopy analysis method (HAM), the series solution is developed and its convergence is discussed. Also, the results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

Poiseuille flow of a micropolar fluid

We use non-equilibrium molecular dynamics simulations to study the flow of a micropolar fluid and to test an extended Navier-Stokes theory (ENS) for such fluids. The angular streaming velocity (which is of course missing in the classical Navier-Stokes theory) and the translational streaming velocity are found to be in good agreement with the predictions of ENS theory. Besides, owing to molecular rotation, the translational streaming velocity profile is shown to deviate from the classical parabolic profile. Finally, temperature profiles calculated using three different expressions (a kinetic translational, a kinetic rotational and a recently derived configurational expression) are found to be in excellent agreement, demonstrating that the equipartition principle still holds in this non-equilibrium system. No deviation from the classical quartic temperature profile is observed.     

MHD oscillatory flow on free convection–radiation through a porous medium with constant suction velocity

Unsteady two-dimensional hydromagnetic free convection and thermal radiation flow of an electrically conducting viscous-incompressible fluid, through a highly porous medium bounded by a vertical plane surface of constant temperature are presented. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Expressions for the velocity and temperature are obtained. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Effects of varying R (radiative parameter), G (Grashof number), k′ (permeability of the porous medium) and M (magnetic parameter upon the velocity field and the effect of varying R and Pr (Prandtl number) on the temperature are discussed.     

Collisional granular flow as a micropolar fluid

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.     

Marangoni flow and mass transfer of power-law non-Newtonian fluids over a disk with suction and injection

We scrutinize the approximate analytical solutions by the optimal homotopy analysis method (OHAM) for the flow and mass transfer within the Marangoni boundary layer of power-law fluids over a disk with suction and injection in the present paper. Concentration distribution on the surface of a disk varies in a power-law form. The non-Newtonian fluid flow is due to the surface concentration gradient without considering gravity and buoyancy. According to the conservation of mass, momentum and concentration, the governing partial differential equations are established, and the appropriate generalized Kármán transformation is found to reduce them to the nonlinear ordinary differential equations. OHAM is used to access the approximate analytical solution. The influences of Marangoni the number, suction/injection parameters and power-law exponent on the flow and mass transfer are examined.     

Magnetohydrodynamic plane Couette flow of an elasto-viscous fluid

Summary Using the Laplace transform, an analytical solution of the Navier-Stokes equation is obtained for a two-dimensional incompressible elasto-viscous fluid past between two infinite parallel walls. It is assumed that the lower wall is moving with velocity which is a function of any given free stream velocity. As an application of the solution, two cases for the stream velocity are studied.     

Magnetohydrodynamic flow of burgers fluid with heat source and power law heat flux

Here magnetohydrodynamic (MHD) two-dimensional (2D) flow of an incompressible Burgers material bounded by a permeable stretched surface is addressed. The boundary layer flow equations are modelled. Heat transfer is discussed for power law heat flux at the surface and heat source. Convergent series solutions are constructed. Clarification of different emerging variables is presented through graphs of velocity, temperature and local Nusselt number. The present solutions are matched with the available published work in a limiting case.     

Magnetohydrodynamic tangent hyperbolic fluid flow past a stretching sheet

In this article, we investigate the MHD tangent hyperbolic fluid flow along a stretching sheet with suction/injection effect at the boundary. The governing nonlinear partial differential equations are transformed into a set of nonlinear ordinary differential equations using the similarity transformation developed by the Lie group analysis. The transformed non-dimensional ordinary differential equations are solved numerically by a shooting technique. The impacts of the governing parameters on the fluid flow and heat transfer characteristics are investigated and discussed, with the help of graphical representations.     

Heat transfer at a laminar free convection and separated flow past a rib in a vertical channel with isothermal walls

The results of numerical computations of a free laminar convection and heat transfer between two parallel isothermal plates in the presence of a single rib on the channel surface are presented. The investigations have been conducted for a channel with the aspect ratio AR = L/w = 10, where L is the channel height, and w is the distance between the plates. An infinitely thin adiabatic rib was located on one of the channel walls in the middle of its height. The relative rib height l/w was varied in the range 0÷0.8. The wall temperature was higher than the ambient temperature, and the Rayleigh number was varied in the range Ra = 10²÷10⁵. The main attention has been paid to the study of the influence of the rib height and the Rayleigh number on local and integral heat transfer and the Reynolds number in the channel (the convective thrust). A fundamental difference in the heat transfer over the channel height has been shown on the ribbed wall and on a smooth surface. The computational results have been compared with the case of a symmetric distribution of the ribs on the both walls with the integral height equal to a single rib.     

Free convection and mass transfer effects on the oscillatory flow of a dissipative fluid past an infinite vertical porous plate (II)

The effects of free convection and mass transfer on the mean steady flow of an incompressible, dissipative, viscous fluid past an infinite vertical, porous plate, with constant suction, was studied in the preceding paper, while in the present work an analysis for the unsteady flow is presented. The solutions for the transient velocity profiles, transient temperature profiles, the amplitude and the phase of the skin friction and the rate of heat transfer are obtained here by using the assumptions and results of the preceding paper. The effects of Grashof number (Gr), modified Grashof number (Gc), Eckert number (E), Schmidt number (Sc) and the frequency (), on the unsteady flow field, are discussed for the case of air (P = 0·71), when the plate is cooled by the free convection currents (Gr > 0).     

Free convection and mass transfer effects on the oscillatory flow of a dissipative fluid past an infinite vertical porous plate (I)

The effects of free convection and mass transfer on the oscillatory flow of an incompressible, dissipative, viscous fluid past an infinite vertical, porous plate with constant suction, is studied. The solution of the problem is obtained with assumption that there exists a mean steady flow and on it superimposed the unsteady oscillatory flow. The mean steady flow is studied in this paper and the effects of Grashof number (Gr), modified Grashof number(Gc), Eckert number(E) and Schmidt number(Sc) are discussed for the case of air (P = 0·71). The study of the expression of the unsteady parts of the velocity, temperature and related quantities will be given in a subsequent paper.Nomenclature C non-dimensional species concentration - C _p specific heat of the fluid at constant pressure - D chemical molecular diffusivity - E Eckert number - g gravitational acceleration - G _r Grashof number - G _c modified Grashof number - k thermal conductivity - P Prandtl number - S _c Schmidt number - t ^* time - temperature - u ^* velocity component inx'-direction - U ^* free-stream velocity - U ₀ mean free-stream velocity - ^* velocity component iny-direction - ₀ suction velocity - x ^* co-ordinate axis along the plate - y ^* co-ordinate axis normal to the plate - ^* volumetric coefficient of thermal expansion - ₁ ^* volumetric coefficient of expansion with concentration - viscosity of the fluid - v kinematic viscosity of the fluid - density of the fluid     

Thermosolutal convection of micropolar fluids in hydromagnetics

The thermosolutal convection in a layer of electrically conducting micropolar fluids heated and soluted from below in the presence of a uniform vertical magnetic field is considered. The presence of coupling between thermosolutal and micropolar effects may bring overstability in the system. The magnetic field also introduces oscillatory modes in the system and the Rayleigh number is found to increase with the increase in magnetic field. The possibility of oscillatory motions and the increase in Rayleigh number with increase in magnetic field is depicted graphically.