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IntroductionTotal subtalar dislocation without fracture of the ankle is a rare clinical entity; it is usually due to a traumatic high-energy mechanism. Standard treatment is successful closed reduction under general anesthesia followed by non-weight bearing and ankle immobilization with a below-knee cast for 6 weeks.Case presentationWe present the case of a 30-year-old Moroccan woman who was involved in a road traffic accident. She subsequently received a radiological assessment that objectified a total subtalar dislocation without fracture of her ankle. She was immediately admitted to the operating theater where an immediate reduction was performed under sedation, and immobilization in a plaster boot was adopted for 8 weeks. The management of this traumatic lesion is discussed in the light of the literature.ConclusionsMedial subtalar dislocation is a rare dislocation and is not commonly seen as a sports injury because it requires transfer of a large amount of kinetic energy. The weaker talocalcaneal and talonavicular ligaments often bear the brunt of the energy and are more commonly disrupted, compared to the relatively stronger calcaneonavicular ligament. Urgent reduction is important, and closed reduction under general anesthesia is usually successful, often facilitated by keeping the knee in flexion to relax the gastrocnemius muscle. Long-term sequelae include talar avascular necrosis and osteochondral fracture, as well as chronic instability and pain.

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.

In this paper, the unsteady boundary-layer flow over a semi-infinite flat plate is solved by means of an analytic approach. Via an ad hoc technique based on the boundary-layer flow evolution, an analytic expression of the velocity profile is proposed. The proposed formula verifies well the results given by Rayleigh, Blasius, and Williams–Rhyne for all time, thus for all Strouhal number values, which is the characteristic of the studied problem. As the main results, the local skin friction depending on a Strouhal number is given in an aim to show an explanation on the flow evolutions from the initial solution to the steady solution in the whole spatial region. This approach permits us to take many applications in engineering technology when the analytic expressions of the velocity, temperature, and matter are looked for.