Abstract:
It has been established that a $DF$-space having a fully-$lambda(P)$-basis is $lambda(P)$-nuclear wherein $P$ is a stable nuclear power set of infinite type. It is shown that a barrelled $G_1$-space $lambda(Q)$ is uniformly $lambda(P)$-nuclear iff ${e_i,e_i}$ is a fully-$lambda(P)$-basis for $lambda(Q)$. Suppose $lambda$ is a $mu$-perfect sequence space for a perfect sequence space $mu$ such that there exist $uin lambda^mu$ and $vin mu^x$ with $u_ige varepsilon >0$ and $v_ige iota >0$ for some $varepsilon$ and $iota$ and for all $i$. Then the following results are found to be true. (i) A sequentially complete space having a fully-$(lambda,sigma mu)$-basis is $lambda(P)$-nuclear, provided $mu$ is a $DF$-space in which ${e_i,e_i}$ is a semi-$lambda(P)$-basis. (ii) Suppose ${e_i,e_i}$ is a fully-$(lambda, sigma mu)$-basis for a barrelled $G_i$-space $lambda(Q)$. If $mu$ is barrelled and ${e_i,e_i}$ is a semi-$lambda(P)$-basis for $mu$ then $lambda(Q)$ is uniformly $lambda(P)$-nuclear. (iii) A $DF$-space with a fully-$(lambda, sigmamu)$-basis is $lambda(P)$-nuclear wherein $(lambda,sigmamu)$ is barrelled in which ${e_i,e_i}$ is a semi-$lambda(P)$-basis.

Abstract:
Efforts have been directed to study and analyze the squeeze film performance between rotating transversely rough curved porous annular plates in the presence of a magnetic fluid lubricant considering the effect of elastic deformation. A stochastic random variable with nonzero mean, variance, and skewness characterizes the random roughness of the bearing surfaces. With the aid of suitable boundary conditions, the associated stochastically averaged Reynolds' equation is solved to obtain the pressure distribution in turn, which results in the calculation of the load-carrying capacity. The graphical representations establish that the transverse roughness, in general, adversely affects the performance characteristics. However, the magnetization registers a relatively improved performance. It is found that the deformation causes reduced load-carrying capacity which gets further decreased by the porosity. This investigation tends to indicate that the adverse effect of porosity, standard deviation and deformation can be compensated to certain extent by the positive effect of the magnetic fluid lubricant in the case of negatively skewed roughness by choosing the rotational inertia and the aspect ratio, especially for suitable ratio of curvature parameters. 1. Introduction It was Archibald [1] who presented the behaviour of squeeze films between various geometrical configurations for the flat surfaces. Wu [2] analyzed the performance of the squeeze film for rotating porous annular disks. Prakash and Vij [3] made use of the well-known Morgan Cameron approximation assuming the porous facing small. Murti [4] investigated the squeeze film performance in curved circular plates describing the film thickness by an exponential expression. His analysis was based on the assumption that the central film thickness was constant instead of minimum film thickness as considered by Hays [5]. Gupta and Vora [6] extended this analysis to the corresponding problem for annular plates. Patel and Deheri [7] studied the behavior of squeeze film between curved circular plates considering the film thickness described by a hyperbolic expression. All the above studies dealt with conventional lubricants. The use of magnetic fluid as a lubricant modifying the performance of the bearing system has drawn considerable attention. Agrawal [8] investigated the performance of a porous-inclined slider bearing with a magnetic fluid lubricant. Verma [9] discussed squeeze film performance in the presence of a magnetic fluid lubricant. Bhat and Deheri [10] analyzed the squeeze film behaviour taking

Abstract:
An endeavour has been made to study and analyze the behaviour of a magnetic fluid-based squeeze film between curved transversely rough rotating circular plates when the curved upper plate lying along a surface determined by an exponential function approaches the curved lower plate along the surface governed by a secant function. A magnetic fluid is used as the lubricant in the presence of an external magnetic field oblique to the radial axis. The random roughness of the bearing surfaces is characterised by a stochastic random variable with nonzero mean, variance, and skewness. The associated nondimensional averaged Reynolds equation is solved with suitable boundary conditions in dimensionless form to obtain the pressure distribution, leading to the expression for the load carrying capacity. The results establish that the bearing system registers an enhanced performance as compared to that of the bearing system dealing with a conventional lubricant. This investigation proves that albeit the bearing suffers due to transverse surface roughness, there exist sufficient scopes for obtaining a relatively better performance in the case of negatively skewed roughness by properly choosing curvature parameters and the rotation ratio. It is appealing to note that the negative variance further enhances this positive effect. 1. Introduction Archibald [1] presented a study on the squeeze film behaviour between various geometrical configurations of flat surfaces. Hays [2] modified the analysis of Archibald [1] to discuss the squeeze film phenomena between curved plates considering the curvature of sine form and keeping minimum film thickness as constant. Murti [3] investigated the squeeze film performance in curved circular plates describing the film thickness by an exponential expression. Indeed, his analysis was based on the assumption that the central film thickness instead of minimum film thickness considered by Hays [2] was constant. It was established that the load carrying capacity rose sharply with the curvature in the case of concave pads. In the above investigation the lower plate was assumed to be flat. Ajwaliya [4] extended the analysis of Murti [3] by choosing the lower plate along a surface determined by an exponential function. Patel and Deheri [5] developed this approach to analyze the squeeze film behaviour between curved circular plates lying along the surfaces determined by hyperbolic function. The analysis of Murti [3] was simplified to a larger extent by Prakash and Vij [6] by incorporating the well-known Morgan-Cameron approximation when the

Abstract:
An attempt has been made to analyze the performance of a magnetic fluid-based-squeeze film between longitudinally rough elliptical plates. A magnetic fluid is used as a lubricant while axially symmetric flow of the magnetic fluid between the elliptical plates is taken into consideration under an oblique magnetic field. Bearing surfaces are assumed to be longitudinally rough. The roughness of the bearing surface is characterized by stochastic random variable with nonzero mean, variance, and skewness. The associated averaged Reynolds’ equation is solved with appropriate boundary conditions in dimensionless form to obtain the pressure distribution leading to the calculation of the load-carrying capacity. The results are presented graphically. It is clearly seen that the magnetic fluid lubricant improves the performance of the bearing system. It is interesting to note that the increased load carrying capacity due to magnetic fluid lubricant gets considerably increased due to the combined effect of standard deviation and negatively skewed roughness. This performance is further enhanced especially when negative variance is involved. This paper makes it clear that the aspect ratio plays a prominent role in improving the performance of the bearing system. Besides, the bearing can support a load even when there is no flow. 1. Introduction The transient load carrying capacity of a fluid film between two surfaces having a relative normal velocity plays a crucial role in frictional devices such as clutch plates in automatic transmissions. Archibald [1] studied the behaviour of squeeze film between various geometrical configurations. Subsequently, Wu [2, 3] investigated the squeeze film performance mainly for two types of geometries, namely, annular and rectangular when one of the surfaces was porous faced. Prakash and Vij [4] discussed the load carrying capacity and time height relations for squeeze film performance between porous plates. In that study various geometries such as circular, annular, elliptical, rectangular, conical, and truncated conical were considered. Besides, a comparison was made between the squeeze film performance of various geometries of equivalent surface area and it was established that the circular geometry registered the highest transient load carrying capacity, other parameters remaining same. The above studies dealt with conventional lubricant. Verma [5] considered the application of magnetic fluid as a lubricant. The magnetic fluid consisted of fine magnetic grains coated with a surfactant and dispersed in a non-conducting magnetically

Abstract:
An effort has been made to study and analyze the performance of a magnetic fluidbased infinitely short hydrodynamic slider bearing. The Reynolds’ equation is solved withappropriate boundary conditions. The expressions for various performance characteristicssuch as pressure, load carrying capacity and friction are obtained. Results are presentedgraphically. It is clearly seen that the load carrying capacity increases considerably due tothe magnetic fluid lubricant. Further, the film thickness ratio increases the load carryingcapacity. It is found that the load carrying capacity increases as the ratio of the length tooutlet film thickness increases while it decreases with respect to the increasing values of theratio of the width to the outlet film thickness. In addition, it is investigated that the magneticfluid lubricant unalters the friction. Lastly, this article makes it clear that the negativeeffect induced by the ratio of the width to the outlet film thickness can be neutralized up to aconsiderably large extent by the combined positive effect of the magnetization parameter,the film thickness ratio and the ratio of the length to outlet film thickness. This studyprovides ample scope for extending the life period of the bearing system.

Abstract:
This investigation aims at analyzing the behaviour of a magnetic fluid based squeeze film between two rotating transversely rough porous circular plates taking bearing deformation into consideration. The results presented in graphical form inform that the transverse surface roughness introduces an adverse effect on the performance characteristics while the magnetic fluid lubricant turn in an improved performance. It is found that the combined effect of rotation and deformation causes significantly reduced load carrying capacity. However, this investigation establishes that the adverse effect of porosity, deformation and standard deviation can be compensated up to some extent by the positive effect of magnetic fluid lubricant in the case of negatively skewed roughness by choosing curvature parameters. To compensate, the rotational inertia needs to have smaller values.

Abstract:
We make an effort to analyze the behavior of hydromagnetic squeeze film between two conducting porous truncated conicalplates. The plates are considered electrically conducting and the clearance space between them is filled by an electricallyconducting lubricant. A uniform transverse magnetic field is applied between the plates. An attempt has been made to solvethe associated Reynolds’ equation with appropriate boundary conditions to obtain the pressure distribution which in turn, isused to get the expression for load carrying capacity which is then used to calculate the response time. The results arepresented graphically as well as in tabular form. The results suggest that the bearing system registers an enhancedperformance as compared to that of a bearing system working with a conventional lubricant. Further, it is seen that aspectratio tends to increase the load carrying capacity substantially. It is observed that the combined effect of the semi-verticalangle and the magnetization parameter is relatively better than that of the combined effect of the aspect ratio and porosity.Besides, the conductivity increases the load carrying capacity significantly. The analysis incorporated in this paper presentsample scope for improving the performance of the bearing system considerably by choosing a suitable combination ofmagnetization parameter, the aspect ratio, semi-vertical angle and the conductivities of the plates