This investigation purposes to study the magnetic fluid based squeeze film behavior on transversely rough stepped plates with the influence of couple stress. Using the well-known stochastic model of Christensen and Tonder the roughness effect has been evaluated. The magnetic fluid flow model of Neuringer -Roseinweig has been adopted to obtain the influence of magnetization. The governing Reynolds' type equation is derived on the basis of stokes microcontinum theory for couple stress fluid. For the expression of pressure distribution, the stochastically averaged Reynolds' type equation is solved. which results in calculation of load carrying capacity. The graphical outcomes also presented in tabular form suggest that although the bearing suffers on account of roughness, the magnetization and couple stress effect save the situation, as this combination does not allow the load carrying capacity to fall rapidly. However, in the case of negatively skewed roughness the magnetization goes a long way in dropping the adversarial influence of roughness by selecting an appropriate value of couple stress parameter when variance (-ve) is involved. It is found that the couple stress effect, alone may not be sufficient to counter the negative influence of transverse roughness and porosity. However, in almost all situations the ferrofluid lubrication adds significantly to the positive effect of couple stress to overcome the adversarial outcome of porosity and roughness. Further, the position of step plays a vital role for an all-round enhancement of the bearing performance.

This study intents to scrutinize the impact of ferrofluid in the presence of couple stress for longitudinally rough porous circular stepped plates. The influence of longitudinal surface roughness is developed using the stochastic model of Christensen and Tonder for nonzero mean, variance and skewness. Neuringer-Roseinweig model is adopted for the influence of ferrofluid. The couple stress effect is characterized by Stoke’s micro continuum theory. The modified Reynolds’ type equation is stochastically averaged and solved by no-slip boundary conditions. The closed form solutions for load bearing capacity and film pressure are obtained as a function of different parameters and plotted graphically. It is perceived that the load capacity gets elevated owing to the combined influence of magnetization and couple stress when the proper choice of roughness parameters (negatively skewed, standard deviation) is in place. Porosity and roughness (positively skewed) adversely affect bearing’s performance. The graphical and tabular analysis shows that there is a significant growth in load bearing capacity compared to the conventional lubricant case.

This article discusses the theoretical study of a ferrofluid based squeeze film between longitudinally rough stepped plates with couple stress effect. For the roughness effect Christensen and Tonder stochastic model has been employed. While the magnetic fluid flow is governed by the model of Neuringer -Roseinweig. On the basis of Stokes microcontinuum model for couple stress fluid the Reynolds' type equation is established. The solution of this equation with suitable boundary conditions results in the computation of load bearing capacity. The graphical and tabular representation asserts that joint influence of magnetization and couple stress is to rise the load bearing capacity irrespective of the situation. It is noticed that the couple stress effect alone fails to be sufficient in overcoming the adverse influence of the roughness and porosity. However, it is the ferrofluid lubrication which adds to the optimistic effect of couple stress there by countering the above said adverse effect. This investigation underlines that one needs to consider the position of step carefully for design point of view. It is motivating to note that the standard deviation related with roughness tends to rise the load bearing capacity which, is in contrast to the situation of transverse roughness.

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