This study utilizes an integral transform technique in order to solve the heat conduction equation in cylindrical coordinates. The major assumption is the high speed (i.e., large Peclet number) assumption. The boundary value problem is governed by the parabolic form of the heat equation representing the quasi-stationary state. The boundary conditions are a combination of Neumann and mixed type due to simultaneous heating and cooling on the surface of the cylinder. The surface temperature reaches a peak value over the heat source and gradually decreases to a nearly constant level over the cooling zone. Thermal penetration in the radial direction is shown to be only a few percent of the radius, leaving the bulk of the body at a uniform temperature. The width of the heat source and the total heat input are shown to be effective on the level of temperature whereas the input distribution is shown to be unimportant. The dimensionless numbers involved are the Biot and the Peclet numbers where the solution is governed by the ratio of the Biot number to the square root of the Peclet number.

A Grubin-like EHD inlet analysis utilizing a non-linear viscous fluid model with a limiting shear stress is reported. The shear rheological equation requires only a low shear stress viscosity and the limiting shear stress both functions of pressure. Values employed for these properties are taken from measurements on typical lubricants. Reductions of EHD film thickness are found to be up to 40 percent compared with the standard Grubin prediction for typical operating conditions. Slide-roll ratio, limiting shear stress dependence on pressure, and atmospheric pressure value of limiting shear stress are new variables required to determine film thickness with the first two being more important than the last. The EHD film thickness is reduced by increasing slide-roll ratio and/or decreasing the pressure dependence of the limiting shear stress.

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The two dimensional, transient temperature distribution in the vicinity of a small, stationary, circular heat source is derived. The source is assumed to be acting on the surface of a relatively much larger body which can be treated as semi-infinite. Formulations both with and without surface convection are considered. Successive integral transforms are used to obtain a direct solution of the governing differential equation. The transient of local temperature rise is found to be very short and very localized in the immediate vicinity of the source. The auxiliary problem of pure convective cooling, i.e., no heat input, is also presented. The initial temperature distribution is taken to be the steady distribution already derived with the heat input. The transient of local temperature in cooling-off is found to be even shorter. In both the main and the auxiliary problems, the governing parameters are source radius, heat flux, thermal conductivity and thermal diffusivity. The convective coefficient does not have a significant effect. This study is intended to represent the thermal behavior of a single asperity in an apparent area of contact. The auxiliary problem represents the cooling-off of the asperity as it moves out from the apparent contact; or it may also be the cooling-off between two consecutive asperity collisions within an apparent contact. The analysis can also be applied to multiple sources acting simultaneously, provided that they are located sufficiently far away from each other, and thermal interaction is negligible. Because the heat generated at the asperity interface must be partitioned, a partition coefficient is derived in the appendix.

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