The time reliant two part motion and thermal features of a finite domain particular quantity of matter in a permeable and impermeable space past an expanding space in touch with the impact of viscousness loss are analyzed. The target of the explo ration is to describe the features of finite domain particular quantity of matter and pores features in the existence of unchanged referencing temperature and concentra tion which fully disturb the movement lines, creates altering in the coldness/hotness processes and concentration species. Due to the importance of thermal conductivity and viscosity, the potentialities of particles driven and emission of rays of a MHD two directional finite domain particular quantity with hotness and matter delivery movement with the existence of viscousness loss lying on an expanding space are also analyzed in which the actual attention of the theme is to describe the elegant role of the dispersion changeable features like heating conduction and viscousness. The heating conduction relates in direct relation as a linear correspondence with energy manifesting the feature that describes the capability of a substance to change hot ness and the viscousness manifests to find to change in inverse relation as a linear mapping of energy manifesting that interior forces go to weakness at the peak of energy. Thermophoresis lies to describe the quantity of matter accumulation at the space of an expanding space while heating radiation lies, especially, on keeping peak position of energy. The impacts of Brownian movement and thermophoresis on a magnetohydrodynamic finite domain particular quantity of tiny matter movement accompanying Hall current and heating delivery past an expanding space exhibits that the Hall current yields the various effects associated with the flow of electric cur rent through thin film, studying two dimensions medium in three dimensions space. The zigzag movement generates direct solid-solid transfer of energy from one entity to the next entity, yielding an elevation in thermal conductivity. The exploration of intensified agent finite domain particular quantity with tiny particles dispersion CuO-H2O coated on an expanding body accompanying change of heat presents the interesting feature manifesting that the coating rate is a mapping of finite quantity of matter. In another study the joint convection in gravitational force prevailing non Newtonian tiny particles dispersion finite quantity of matter (Casson and Williamson) movement persisting the two things namely tiny particles and small organisms on a convectively hot space lying at right angle is attempted. The unique occupied tiny particles dispersion equations with extra informations are tackled to investigate the finite quantity of matter. The scenario views an analytical progress to the particular finite quantity of matter bioconvection resisting on physical system nominating for the tiny particles and the background dispersion, like zigzag movement and thermophore sis. The two dispersions keep almost the similar features for the reactions of the total active representative without the impact of one representative on the small organism saturation mapping in which the impact remains in converse. The basic governing ex pressions for the movement, energy, concentration and microorganism concentration utilized in the respective problems have been transformed to the peak different order coupled derivable statements accompanying physical informations by recalling the re quired similarity substitutions. The evaluation of the problems has been achieved via treating HAM (Homotopy Analysis Method). The heating and quantity of matter delivery features are endorsed to significant regime of the finite quantity of matter. In some problems results are checked comparatively with the practical work exist in the published papers manifesting a great precision in particular, in exploring impor tant industrial engineering quantities. The physical potentialities of finite quantity of matter representative and the remaining representatives are tested in curves and explained. The error due to h graphs and error due to h tables in some problems elucidate the authentication of the relevant problems.