Laminar boundary-layer separation phenomenon is one of the interesting and important aspects of boundary-layer flows. It occurs in various physical situations because of decreasing wall shear stress. Retarded flow velocities are one of the reasons to happen this event. Flow separation can be prevented or delayed by utilizing bodies of revolution as surface transverse curvature produces the effects of the nature of favorable pressure-gradient which in turn increases wall shear stress that keeps the flow attached to the surface. Bodies of revolution whose body contour follows power-law form also play a vital role to delay flow separation. Bodies of revolution of varying cross-sections and involving surface transverse curvature (TVC) are utilized to examine their effects on flow separation. Particularly, a convex transverse curvature has been considered due to its effects of the nature of favorable pressure-gradient which causes to delay the flow separation. A retarded flow velocity of Görtler’s type is considered in this study to investigate flow separation process. A detailed analysis is provided to understand the flow separation by calculating separation points under various assumptions. It has been observed that the body contours exponent n and the convex transverse curvature parameter k play an assistive role in the delaying of boundary-layer separation even under the influence of strong retardation. Results are presented through various Tables and graphs in order to highlight the role of the power-law exponent of external velocity m, the convex transverse curvature parameter k, and the body contours exponent n on separation points.
Theoretical investigations of fundamental boundary-layer flows are always given prime importance in the field of boundary-layer theory. In particular, among the boundary-layer flows occurring on planner geometries, importance had been given to the flows occurring over the surfaces of finite length. The boundary-layer flows due to moving continuous surfaces were introduced about half a century later to the famous Blasius flow. Unfortunately, no significant attention had been given to these flows with regard to the investigation of boundary-layer properties in these flows. Consequently, a great gap has been created between these two important categories of boundary-layer flows. It is a matter of fact that the flows due to moving continuous surfaces are richer in physics; offer favorable impact, and involve interesting technological applications. One of the important hallmarks of these flows is that they offer a significantly increased wall skin-friction as compared to the flows over surfaces of finite length. Therefore these flows appear to be profitable in situations that are more vulnerable to flow separation. To explore this fact the current study considers a variety of retarded wall velocities to calculate the delay in flow separation for the flows due to moving continuous surfaces in comparison to those occurring on a surface of finite length. It is observed that in the flows due to a moving continuous surface the flow separation is greatly delayed in comparison to the flows over surfaces of finite length. Moreover, the role of wall suction velocity, in this regard, is to be further amplified in these flows. Overall, it is concluded that the continuous surfaces are more useful in order to delay flow separation as compared to the surfaces of finite length.
Heat transfer analysis in a retarded laminar boundary layer over bodies of revolution with a variable radius subject to retarded surface temperature is presented. This study focuses to develop numerical data for local Nusselt number Nu_x under the influence of retarded free stream velocity and decreasing surface temperature along with body contour and surface transverse curvature. With the use of such retarded velocities and body contour the similarity of flow phenomenon does not sustain, and the problem becomes non-similar in nature which has been solved using an efficient numerical scheme, commonly known as Keller-Box. The effects of pertinent parameters such as exponent of free stream velocity m, exponent of surface temperature q, body contour n, and surface transverse curvature k on temperature profile, rate of heat transfer at the surface, and energy thickness of thermal boundary layer are presented through various graphs and tables. The rate of heat transfer and the energy thickness of the thermal boundary layer are observed to decrease with increasing levels of retardation. Furthermore, the rate of heat transfer decreases as the body contour parameter increases, whereas the surface transverse curvature parameter exhibits the opposite trend.
Boundary layer flows induced due to retarded motion of the continuous surfaces ultimately seize at some subsequent downstream location which is equivalent to the phenomenon of flow separation on a surface of finite length, thus leading to increased drag on the aero-dynamical vehicles. The literature has established that the boundary layer formed over a moving continuous surface is more energetic than that formed on a stationary surface of finite length. This implies that for the sustainability of the transport phenomenon in such a retarded flow, which has to ultimately meet the flow separation, a moving continuous surface is preferable to a stationary surface of finite length. Therefore, this study intends to perform heat transfer analysis in a retarded laminar boundary layer formed due to a moving continuous cylinder of constant radius. Wall temperature of uniform nature is considered in this investigation. In the majority of the boundary layer flows the self-similarity of the flow does not persist because of choosing the reference velocity of the desired character. Thus, the problem becomes non-similar in nature. In general, the non-similarity of a flow may appear due to various aspects of the problem such as the retarded nature of the reference velocity, the surface temperature, the curvature of the body, etc. Surface transverse curvature imparts favorable consequences on the separating boundary layer and hence on the seizing flow character. Therefore, this study focuses on investigating the impact of surface transverse curvature (TVC) k and the wall velocity power index m on temperature profiles, rate of heat transfer at the surface Nux(local Nusselt number), the thermal layer thickness, and the thermal diffusivity of heat in a retarded boundary layer. In addition to this, the influence of Prandtl number Pr and Stanton number St has also been investigated.
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