Viscous dissipation effect on heat transfer characteristics of rectangular microchannels under slip flow regime and H1 boundary conditions

Viscous dissipation effect on heat transfer characteristics of a rectangular microchannel is studied. Flow is governed by the Navier–Stokes equations with the slip flow and temperature jump boundary conditions. Integral transform technique is applied to derive the temperature distribution and Nusselt number. The velocity distribution is taken from literature. The solution method is verified for the case where viscous dissipation is neglected. It is found that, the viscous dissipation is negligible for gas flows in microchannels, since the contribution of this effect on Nu number is about 1%. However, this effect should be taken into account for much more viscous flows, such as liquid flows. Neglecting this effect for a flat microchannel with an aspect ratio of 0.1 for Br=0.04 underestimates the Nu number about 5%.     

THE SPACES OF CESARO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMB

As known,the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces.However,the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new(see [15]).The purpose of this paper is to introduce the new spaces f and f0 consisting of all sequences whose Cesa`ro transforms of order one are in the spaces f and f0,respectively.Also,in this paper,we show that f and f0 are linearly isomorphic to the spaces f and f0,respectively.The β-and γ-duals of the spaces f and f0 are computed.Furthermore,the classes(f:) and(:f) of infinite matrices are characterized for any given sequence space,and determined the necessary and sufficient conditions on a matrix A to satisfy BC-core(Ax) K-core(x),K-core(Ax) BC-core(x),BC-core(Ax) BC-core(x),BC-core(Ax) st-core(x) for all x ∈∞.