In the present paper approximate solutions for the fluid and thermal boundary layers in an incompressible laminar plane wall jet with isothermal and adiabatic walls have been studied respectively, and comparisons with the known exact solutions have been made wherever possible. It is found that the present method is simple and straightforward, and gives results being in good agreement with the exact solutions. For moderate values of the Prandtl number the method may be used for calculating the heat transfer from an isothermal wall and temperature recovery factor for an adiabatic wall respectively.

Approximate solutions of heat and momentum transfer in laminar plane wall jet

Millipedes, the ancient arthropods which belong to class Diplopoda, are the third most diverse class of terrestrial arthropods, following Insecta and Arachnida (Golovatch and Kime, Soil Org 81(3):565–597, 2009). They have a long and distinguished history on our planet and existed on earth more than 100 times longer than man, and their fossil records demonstrate their worldwide distribution (Almond, 1985; Hannibal, 1986). With an estimated total of more than 80,000 extant species, only about 12,000 millipede species have been formally described in 3005 genera, 145 families and 16 orders (Shelley, 2007; Sierwald and Bond, 2007). They also constitute one of the major groups of soil and litter fauna in temperate and tropical environments. Millipedes play an important role in energy flow as well as in the humification of soil and circulation of minerals in terrestrial ecosystems.

Millipedes: Diversity, Distribution and Ecology

The flow of a laminar viscous, incompressible, electrically conducting fluid, in the presence of a uniform transverse magnetic field, in a plane-wall jet is studied. A perturbation on the Akatnow-Glauert model is applied and numerical solutions for first- and second-order perturbation terms are obtained. Expressions for the velocity field, shearing stress and the volume flux are given and the range of the magnetic interaction parameter, for which the results are physically acceptable, is determined.

On the hydromagnetic laminar plane-wall jet

Couche limite avec reaction de surface: Extension de la methode de rosner au cas compressible a gradient thermique. Application au jet parietal

In the present note the temperature distribution in a laminar plane wall jet has been studied. It is found that a similarity solution of the energy equation exists. The resulting ordinary differential equation is reduced to a hypergeometric equation by a suitable transformation of the similarity variable and the solution, for arbitrary values of the Prandtl number, is obtained. It is concluded that the heat transfer at the wall at a given section and the product of volume and heat-flux through any cross-section of the boundary layer increase with the increase in the value of Prandtl number respectively.

S. S. Tak

Papers

Temperature distribution in a laminar plane wall jet