Viscous dissipation effects on natural convection from a vertical plate with uniform surface heat flux placed in a thermally stratified media

In the present study we investigate the effect of viscous dissipation on natural convection from a vertical plate placed in a thermally stratified environment. The reduced equations are integrated by employing the implicit finite difference scheme of Keller box method and obtained the effect of heat due to viscous dissipation on the local skin friction and local Nusselt number at various stratification levels, for fluids having Prandtl numbers of 10, 50, and 100. Solutions are also obtained using the perturbation technique for small values of viscous dissipation parameters $\xi$ and compared to the finite difference solutions for 0 · $\xi$ · 1. Effect of viscous dissipation and temperature stratification are also shown on the velocity and temperature distributions in the boundary layer region.

Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media

We present here a numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium. The governing equations of mass, momentum, energy and species are non-dimensionalized. These equations have been solved by using an implicit finite difference method and local non-similarity method. The results show many interesting aspects of complex interaction of the two buoyant mechanisms that have been shown in both the tabular as well as graphical form.

Natural convection from a vertical plate embedded in a stratified medium with uniform heat source

Natural convection flow from an isothermal vertical plate with uniform heat source embedded in a stratified medium has been discussed in this paper. The resulting momentum and energy equations of boundary layer approximation are made non-similar by introducing the usual non-similarity transformations. Numerical solutions of these equations are obtained by an implicit finite difference method for a wide range of the stratification parameter, X. The solutions are also obtained for different values of pertinent parameters, namely, the Prandtl number, Pr and the heat generation or absorption parameter, λ and are expressed in terms of the local skin-friction and local heat transfer, which are shown in the graphical form. Effect of heat generation or absorption on the streamlines and isotherms are also shown graphically for different values of λ.

"The Stratified Record upon Which We Set Our Feet" : The Spatial Turn and the Multilayering of History, Geography, and Geology

In Thomas Mann’s tetralogy of the 1930s and 1940s, Joseph and His Brothers, the narrator declares history is not only “that which has happened and that which goes on happening in time,” but it is also “the stratified record upon which we set our feet, the ground beneath us.” By opening up history to its spatial, geographical, and geological dimensions Mann both predicts and encapsulates the twentieth-century’s “spatial turn,” a critical shift that divested geography of its largely passive role as history’s “stage” and brought to the fore intersections between the humanities and the earth sciences. In this paper, I draw out the relationships between history, narrative, geography, and geology revealed by this spatial turn and the questions these pose for thinking about the disciplinary relationship between geography and the humanities. As Mann’s statement exemplifies, the spatial turn itself has often been captured most strikingly in fiction, and I would argue nowhere more so than in Graham Swift’s Waterland (1983) and Anne Michaels’s Fugitive Pieces (1996), both of which present space, place, and landscape as having a palpable influence on history and memory. The geographical/geological line that runs through both Waterland and Fugitive Pieces continues through Tim Robinson’s non-fictional, two-volume “topographical” history Stones of Aran. Robinson’s Stones of Aran—which is not history, not geography, and not literature, and yet is all three—constructs an imaginative geography that renders inseparable geography, geology, history, memory, and the act of writing.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.