A bio-convective investigation for flow of Casson nanofluid with activation energy applications

Here theoretical analysis of heat, mass and motile microorganisms transfer rates in Casson fluid flow over stretched permeable surface of cylinder is studied. Investigated is carried out in the presence of suspended nanoparticles and self-propelled gyrotactic microorganisms. The effects of buoyancy forces, magnetic field and thermal radiation are considered. The nanoparticles with suitable suspension are stabilized through mutual effects of buoyancy forces and bioconvection. Furthermore, activation energy and Darcy- Forchheimer effects on bio nanofluid flow are accounted. The constitutive theories are executed to develop the model formulation. The obtained model is made dimensionless trough appropriate transformations. The dimensionless flow model is tackled by built-in algorithm of shooting technique. Impact of flow controlling constraints parameters is physically elaborated by making graphical illustrations. The outcomes based on numerical data against essential engineering formulations like surface drag force, Nusselt, density and Sherwood numbers are tabulated. Main outcomes are successfully summarized in terms of closing remarks.

Ordered Rate Constitutive Theories for Non-Classical Thermofluids Based on Convected Time Derivatives of the Strain and Higher Order Rotation Rate Tensors Using Entropy Inequality

This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem. Using the generalization of the conjugate pairs in the entropy inequality, the ordered rate constitutive theory for Cauchy stress tensor considers convected time derivatives of the Green’s strain tensor (or Almansi strain tensor) of up to orders n ε as its argument tensors and the ordered rate constitutive theory for the Cauchy moment tensor considers convected time derivatives of the symmetric part of the rotation gradient tensor up to orders n Θ . While the convected time derivatives of the strain tensors are well known the convected time derivatives of higher orders of the symmetric part of the rotation gradient tensor need to be derived and are presented in this paper. Complete and general constitutive theories based on integrity using conjugate pairs in the entropy inequality and the generalization of the argument tensors of the constitutive variables and the representation theorem are derived and the material coefficients are established. It is shown that for the type of non-classical thermofluids considered in this paper the dissipation mechanism is an ordered rate mechanism due to convected time derivatives of the strain tensor as well as the convected time derivatives of the symmetric part of the rotation gradient tensor. The derivations of the constitutive theories presented in the paper is basis independent but can be made basis specific depending upon the choice of the specific basis for the constitutive variables and the argument tensors. Simplified linear theories are also presented as subset of the general constitutive theories and are compared with published works.

Recognition of the state in modern international law (on the example of Kosovo)

Problem setting. International science has long been discussing the mechanism of legal recognition of newly created states. And in general the need for the existence of such an international legal institution as the recognition of states. If until the twentieth century this institution was considered as a purely theoretical component of the science of public international law, then with the collapse of the Soviet Union, Yugoslavia, Czechoslovakia, more than twenty new statessubjects of international law were formed. The need for their recognition by the international community has actualized the interest in this institution in international law. However, since then, the mechanism and criteria for such recognition have not been unified. Therefore, for example, the situation with the recognition of Kosovo still remains quite ambiguous. Target of research. The purpose of this study is the trace genesis of the development of the institution of recognition of states in international law, provide a doctrinal definition and scientific criteria for the recognition of states. On the example of Kosovo to analyze the current state of privately defined states in terms of their powers in the international arena. Analysis of resent researches and publications. The following scientists were engaged in research of the specified question: L. V. Shpakovsky, V. V. Ishchenko, T. V. Tsymbrivsky, P. V. Otenko, Yu. P. Ignatiuk, I. Ye. Khmelyova, A. I. Grigorshin. This question has been studied among foreign researchers: E. A. Kholina, R. Karaev, D. A. Budko. Article’s main body. The article considers the main approaches to the institution of international recognition of states. Examples of criteria for such recognition are proposed by both international legal doctrine and international organizations in the process of their functioning and interaction with states. Declarative and constitutive theories of recognition of states are analyzed. It also examines the current state and status of Kosovo as a partially recognized state. Conclusions and prospects for the development. The problem of international recognition of the state is extremely important and needs to be resolved as soon as possible. That the very ability of recognized national institutions to respond quickly to the principles of society and geopolitical changes are the marketing dynamics of the development of the entire world community. In this regard, it is appropriate to systematize and harmonize the existing norms on the international definition of states and to carry out their further codification. Since most countries of the world still recognized Kosovo as a newly created state, in our opinion, such recognition is appropriate for all other countries. For other unrecognized territories, each case of recognition of new countries before the creation of a single codified act should be considered individually and not through the prism of the formation of Kosovo.