Steady laminar flow with suction or injection and heat transfer through porous pipe

Following the method due to Bhatnagar (P. L.) [Jour. Ind. Inst. Sic., 1968, 1, 50, 1], we have discussed in this paper the problem of suction and injection and that of heat transfer for a viscous, incompressible fluid through a porous pipe of uniform circular cross-section, the wall of the pipe being maintained at constant temperature. The method utilises some important properties of differential equations and some transformations that enable the solution of the two-point boundary value and eigenvalue problems without using trial and error method. In fact, each integration provides us with a solution for a suction parameter and a Reynolds number without imposing the conditions of smallness on them. Investigations on non-Newtonian fluids and on other bounding geometries will be published elsewhere.

Free convection heat transfer between vertical parallel plates

A new mathematical model for the solution of the problem of free convection heat transfer between vertical parallel flat isothermal plates under isothermal boundary conditions, has been presented. The set of boundary layer equations used in the model are transformed to nonlinear coupled differential equations by similarity type variables as obtained by Ostrach for vertical flat plates in an infinite fluid medium. By utilising a parameter ηw* to represent the outer boundary, the governing differential equations are solved numerically for parametric values of Pr = 0.733. 2 and 3, and ηw* = 0.1, 0.5, 1, 2, 3, 4, ... and 8.0. The velocity and temperature profiles are presented. Results indicate that ηw* can effectively classify the system into (1) thin layers where conduction predominates, (2) intermediate layers and (3) thick layers whose results can be predicted by the solutions for vertical flat plates in infinite fluid medium. Heat transfer correlations are presented for the 3 categories. Several experimental and analytical results available in the literature agree with the present correlations.

Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified "half-range" quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.

Correlation between terrestrial heat flow and thermal conductivity

The significant correlation coefficient between the terrestial heat flow and thermal conductivity computed from the continental heat flow data by Horai and Nur [1]2) may be explained as a natural consequence of terrestrial heat flow through a random medium. The theory predicts a value of 0.40 for the correlation coefficient. A simple statistical test shows that the majority of the computed coefficients belong to the statistical population whose mean is equal to the theoretical correlation coefficient. There are, however, a few observations of unsually high correlation coefficient which cannot be explained by the above hypothesis.

Agricultural expansion and climate change in the Taita Hills, Kenya: an assessment of potential environmental impacts

The indigenous cloud forests in the Taita Hills have suffered substantial degradation for several centuries due to agricultural expansion. Currently, only 1% of the original forested area remains preserved in this region. Furthermore, climate change imposes an imminent threat for local economy and environmental sustainability. In such circumstances, elaborating tools to conciliate socioeconomic growth and natural resources conservation is an enormous challenge. This dissertation tackles essential aspects for understanding the ongoing agricultural activities in the Taita Hills and their potential environmental consequences in the future. Initially, alternative methods were designed to improve our understanding of the ongoing agricultural activities. Namely, methods for agricultural survey planning and to estimate evapotranspiration were evaluated, taking into account a number of limitations regarding data and resources availability. Next, this dissertation evaluates how upcoming agricultural expansion, together with climate change, will affect the natural resources in the Taita Hills up to the year 2030. The driving forces of agricultural expansion in the region were identified as aiming to delineate future landscape scenarios and evaluate potential impacts from the soil and water conservation point of view. In order to investigate these issues and answer the research questions, this dissertation combined state of the art modelling tools with renowned statistical methods. The results indicate that, if current trends persist, agricultural areas will occupy roughly 60% of the study area by 2030. Although the simulated land use changes will certainly increase soil erosion figures, new croplands are likely to come up predominantly in the lowlands, which comprise areas with lower soil erosion potential. By 2030, rainfall erosivity is likely to increase during April and November due to climate change. Finally, this thesis addressed the potential impacts of agricultural expansion and climate changes on Irrigation Water Requirements (IWR), which is considered another major issue in the context of the relations between land use and climate. Although the simulations indicate that climate change will likely increase annual volumes of rainfall during the following decades, IWR will continue to increase due to agricultural expansion. By 2030, new cropland areas may cause an increase of approximately 40% in the annual volume of water necessary for irrigation.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Free convection heat transfer from vertical cylinders part II: Exponential surface temperature variation

Investigation on laminar free convection heat transfer from vertical cylinders and wires having a surface temperature variation of the form TW - T∞ = M emx are presented. As in Part I for power law surface temperature variation, the axisymmetric boundary layer equations of mass, momentum and energy are transformed to more convenient forms and solved numerically. The second approximation refines the results of the first upto a maximum of only 2%. Analysis of the results indicates that cylinders can be classified into the same three categories as in Part I, namely, short cylinders, long cylinders, and wires, heat transfer and fluid flow correlations being developed for each case.

Effect of vibration on heat transfer from a horizontal cylinder to a normal air stream

The effect of vibration on heat transfer from a horizontal copper cylinder, 0.344 in. in diameter and 6 in. long, was investigated. The cylinder was placed normal to an air stream and was sinusoidally vibrated in a direction perpendicular to the direction of the air stream. The flow velocity varied from 19 ft/s to 92 ft/s; the double amplitude of vibration from 0.75 cm to 3.2 cm, and the frequency of vibration from 200 to 2800 cycles/min. A transient technique was used to determine the heat transfer coefficients. The experimental data in the absence of vibration is expressed by NNu = 0.226 NRe0.6 in the range 2500 < NRe < 15 000. By imposing vibrational velocities as high as 20 per cent of the flow velocity, no appreciable change in the heat transfer coefficient was observed. An analysis using the resultant of the vibration and the flow velocity explains the observed phenomenon.

Estimation of the critical viscous sublayer in heat transfer problems

Imagining a disturbance made on a compressible boundary layer with the help of a heat source, the critical viscous sublayer, through which the skin friction at any point on a surface is connected with the heat transferred from a heated element embedded in it, has been estimated. Under similar conditions of external flow (Ray1)) the ratio of the critical viscous sublayer to the undisturbed boundary layer thickness is about one-tenth in the laminar case and one hundredth in the turbulent case. These results are similar to those (cf.1)) found in shock wave boundary layer interaction problems.

Lattice vibrations and specific heat of zinc blende

The dispersion relations, frequency distribution function and specific heat of zinc blende have been calculated using Houston's method on (1) A short range force (S. R.) model of the type employed in diamond by Smith and (2) A long range model assuming an effective charge Ze on the ions. Since the elastic constant data on ZnS are not in agreement with one another the following values were used in these calculations: {Mathematical expression}. As compared to the results on the S. R. model, the Coulomb force causes 1. A splitting of the optical branches at (000) and a larger dispersion of these branches; 2. A rise in the acoustic frequency branches the effect being predominant in a transverse acoustic branch along [110]; 3. A bridging of the gap of forbidden frequencies in the S. R. model; 4. A reduction of the moments of the frequency distribution function and 5. A flattening of the Θ- T curve. By plotting (Θ/Θ0) vs. T., the experimental data of Martin and Clusius and Harteck are found to be in perfect coincidence with the curve for the short range model. The values of the elastic constants deduced from the ratio Θ0 (Theor)/Θ0 (Expt) agree with those of Prince and Wooster. This is surprising as several lines of evidence indicate that the bond in zinc blende is partly covalent and partly ionic. The conclusion is inescapable that the effective charge in ZnS is a function of the wave vector {Mathematical expression}.

The heat kernel on AdS(3) and its applications

We derive the heat kernel for arbitrary tensor fields on S-3 and (Euclidean) AdS(3) using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS(3). We apply this to the calculation of the one loop partition function of N = 1 supergravity on AdS(3). We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.

Effect of copper addition on the fracture and fatigue crack growth behavior of solution heat-treated SUS 304H austenitic steel

Small additions of Cu to the SUS 304H, a high temperature austenitic stainless steel, enhance its high temperature strength and creep resistance. As Cu is known to cause embrittlement, the effect of Cu on room temperature mechanical properties that include fracture toughness and fatigue crack threshold of as-solutionized SUS 304H steel were investigated in this work. Experimental results show a linear reduction in yield and ultimate strengths with Cu addition of up to 5 wt.% while ductility drops markedly for 5 wt.% Cu alloy. However, the fracture toughness and the threshold stress intensity factor range for fatigue crack initiation were found to be nearly invariant with Cu addition. This is because the fracture in this alloy is controlled by the debonding from the matrix of chromium carbide precipitates, as evident from fractography. Cu, on the other hand, remains either in solution or as nano-precipitates and hence does not influence the fracture characteristics. It is concluded that small additions of Cu to 304H will not have adverse effects on its fracture and fatigue behavior. (C) 2010 Elsevier B.V. All rights reserved.

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.