Effects of Magnetohydrodynamics and Heat Transfer in Casson Fluid Through a Channel

Unsteady flow of Casson fluid past through a vertical channel has been studied by some researchers due to its importance of applications in science and technology. Therefore, the main purpose of this paper is to obtain exact solutions for unsteady free convection flows of Casson fluid with effects of magnetohydrodynamics (MHD) past through vertical channel. This paper is continued study from published article [18] with additional effects of magnetohydrodynamics (MHD). Dimensional governing equations are converted into dimensionless forms by using appropriate dimensionless variables. Dimensionless parameters are obtained through dimensionless process such as Casson fluid, time, Prandtl number, Grashof number and magnetic field. Laplace transform method is used to solve the dimensionless equations with associated initial and boundary conditions. Solutions for velocity and temperature profiles are obtained. Skin friction and Nusselt number are also calculated. The obtained analytical results for velocity and temperature are plotted graphically to discuss the influence of dimensionless parameters on profiles. It is observed that fluid velocity increases with increases of Grashof number, Gr and time, t whereas it decreases with increases of Casson parameter, γ, magnetic field parameter, M and Prandtl number, Pr. Besides that, it is found that temperature profiles decrease with high value of Prandtl number, Pr while increases with high value of time, t. In order to validate the results, the obtained results in limiting cases are compared with the published results and it is found to be in a mutual agreement.

A simple model for desulphurisation of flue gas using reactive filters

Desulphurisation of flue gas is essential before it can be released safely into the atmosphere. One way of removing sulphur dioxide is to use a purification device incorporating a reactive filter, in which the flue gas stream passes in front of a porous-catalyst-filled structure which converts the gaseous sulphur dioxide into liquid sulphuric acid. In this paper, we build and solve a simple mathematical model to describe the operation of a paradigm reactive filter. Our model captures the transport of sulphur dioxide through the device via advection in the main “outer” flow and diffusion through the catalyst structure along with the production of sulphuric acid. This sulphuric acid gradually accumulates in the filter rendering it less efficient. We determine the clogging time for an individual channel (that is, the time at which the entrance to the channel becomes completely filled with liquid) and explore how the concentrations of sulphur dioxide and oxygen and the thickness of the sulphuric acid layer change as the key dimensionless parameters are varied, comparing numerical and asymptotic results where appropriate. We then turn our attention to the device scale and solve our model numerically to determine the overall lifetime of the device. We vary the key dimensionless parameters and explore how they affect the efficiency of the device. In the physically relevant parameter regime, we find an explicit solution to the outer flow problem which agrees well with numerical solutions and provides a formula for the lifetime of the device. Finally, we propose a formula for determining the catalyst reaction rate, given data on the concentration of sulphur dioxide exiting the device.

Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms

This investigation aims to present the thermally developed bioconvection flow of Williamson nanoliquid over an inclined stretching cylinder in presence of linear mixed convection and nonuniform heat source/sink. The activation energy and suspension of gyrotactic microorganisms are accounted with applications of bioconvection phenomenon. Appropriate nondimensional variables are opted to attain the dimensionless form of flow equations. The resulting momentum, energy, concentration and motile density equations are abridged to highly coupled and nonlinear in nature. The numerical treatment is followed for the solution procedure by employing the shooting method. The influence of some relevant dimensionless parameters is discoursed graphically along with physical justifications. Moreover, the impact of several dimensionless parameters on skin friction and Nusselt number is obtained and listed in tables. It is observed that the velocity of fluid shows a decreasing variation for Williamson fluid parameter. The change in unsteadiness parameter and heat source parameter enhanced the nanofluid temperature. The motile microorganisms profile declines with bioconvection constant and bio-convection Lewis number.

Application of the Buckingham ∏ theorem to model multiple effect vacuum membrane distillation

This study aims to develop a dimensionless model of the V-MEMD performance indicator through which a preliminary prediction of the most critical performance indicators can be attained. Buckingham ∏ theorem was utilized to define dimensionless parameters that allow the predicted relationships associating independent input parameters to describe the essential performance indicators of the V-MEMD system. The obtained compact model reduces the design parameters from ten to two effective dimensionless parameters to realize the realistic and actual behavior of the designated system. The self-sustained model stands as a short-cut tool for design and performance analysis avoiding time consuming experimentations and/or complicated theoretical models. The compatibility of the generated model is assessed by matching the expected response of output dimensionless parameters (e.g., recovery ratio, R, and gain output ratio, GOR) to variation in pressure ratio and cooling process. The model is validated with other works, and discrepancies are remarked to be within ±10% and ±25% for recovery ratio and gain output ratio, respectively. Furthermore, the specific thermal energy consumption, STEC is correlated to GOR assuming constant vaporization enthalpy and density of the distillate water. The correlation can predict STEC within 5% accuracy over different operating conditions for the supplied hot water.

On sCO2 Compressor Performance Maps at Variable Intake Thermodynamic Conditions

Unconventional aero-thermodynamic phenomena affect the performance of compressors that operate with carbon dioxide (CO2) close to its thermodynamic critical point. As a consequence, whether compressor performance maps based on conventional scaling parameters, such as flow coefficient and peripheral Mach number, still posses general features remains an open question. In this work, we show that additional dimensionless parameters are needed to ensure full similarity conditions when intake thermodynamic conditions vary. Thanks to a combination of three-dimensional turbulent flow simulations, analytical developments and physical flow considerations, three main phenomena are shown to affect compressor operation when changing the upstream total state: (i) non-ideal effects that can modify the fluid compressibility from liquid-like to gas-like and vice versa, (ii) the extent of the two-phase region within the blade channel, (iii) the resulting compressibility of the two-phase mixture. Three dimensionless parameters are introduced to separately account for these effects and their relationship is highlighted. The influence of these parameters on compressor performance maps is widely discussed, shedding light on the way they act in the modification of the ideal similarity based only on the flow coefficient and the peripheral Mach number. As a general result, two additional dimensionless parameters are needed to guarantee similarity conditions in presence of non-ideal flows of CO2 subject to phase change. These findings are expected to be relevant for the plant regulation in off-design conditions and for planning experimental campaigns at different thermodynamic conditions.

Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination

The widely cited Haken–Kelso–Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.