numerical methods in heat transfer pdf

... adaptive methods generally do not work if F(x, y) contains discontinuities.Because the error behaves erratically at the point of discontinuity, the program can get stuck in an infinite loop trying ... Runge–Kutta MethodsThis changes the analytical solution to y = εe 3x + e −x We now see that the term containing the errorε becomes dominant as x is increased. Because errors inherent in the numerical ... obtained by polyno-mial interpolation If no great precision is needed, linear interpolation will do Letting 1000+ t be the time of impact, we can write r (1000 + t) = R e Expanding r in a

Ngày tải lên: 07/08/2014, 04:20

... are independent because each contains a fundamental variable not contained in the other Conditions for bursting can be investigated by relating only two variables, the pi-terms, rather than interrelating ... dimensionless Following is an example of a well-designed experiment Example Using experimental techniques, find the equation for internal bursting pressure, P', for a thin-wall pipe Start by writing the ... (t/D) used to find the equation for bursting pressure P' in plain pipe Plain (or bare) pipe has smooth cylindrical surfaces with constant wall thickness — not corrugated or ribbed or reinforced Figure

Ngày tải lên: 05/05/2018, 09:27

... found by dividing the loaded surface area into infinitesimal areas and integrating to find the sum of their effects at some point at depth H See Figure 4-6 Newmark performed such an integration ... principles of soil stresses is essential to understanding the structural performance of buried pipes These principles are explained in standard texts on soil mechanics A few are reviewed in ... print The rectangular tire prints are subdivided as shown for establishing a common corner A' The effects of the left tire print and the right tire print are analyzed separately, then combined

Ngày tải lên: 05/05/2018, 09:27

... strain in a pipe ring if D/t = 20 and the ring is deflected from a circle into an ellipse with ring deflection of d = 10%? Neglect the ring compression strain Consider only flexural 5-7 Find ring ... pipe, are listed in industry manuals Trang 115-1 A thin-wall pipe is initially an ellipse with ring deflection, d What is the maximum moment in the ring due to rerounding? 5-2 Find the moment at ... loads are, in fact, distributed over a finite area Ring instability is the worst case of collapse analysis because instability is reduced by the interaction of ring stiffness and longitudinal stiffness

Ngày tải lên: 05/05/2018, 09:27

... soil is invariably loose agains t the ring at the interface In plastic pipes, stress relaxation results in further reduction of normal pressure of the soil against the pipe The stiffer the ring, ... etc In this chapter, performance limit is analyzed in terms of stress at the point of excessive deformation Hoop Stress Hoop stress due to internal pressure, P', in a thin-walled circular ring, ... fundamental principles of pipe mechanics However, analysis in greater depth is often essential In all cases, performance limit is deformation; i.e., rupture, wall crushing, wall buckling, ring deflection,

Ngày tải lên: 05/05/2018, 09:27

... pipes, the com-bination of ring compression stress and ring deformation stress may result in dimpling of corrugations, or plastic hinging But for buried pipes, dimpling and incipient hinging are not ... Or knowing allowable stress, maximum allowable changes in radii, or changes in middle ordinate from a cord can be used by inspectors for control of the pipe shape during installation Internal ... that within cord length L, a pipe is initially circular and ring compression stress in the pipe wall is Pr/A Now if the ring is deformed, the change in radius of curvature causes a change in Pr/A;

Ngày tải lên: 05/05/2018, 09:27

... soil-structure interaction The stiffness of the ring resists inversion Soil supports the ring by holding it in a stable (near circular) shape Soil resists inversion of the ring Two basic modes of ring instability ... either: wall crushing (ring compression) or inversion (ring deformation) Collapse due to longitudinal bending is not included in this analysis Bending deforms the pipe cross section into an ellipse ... elliptical ring showing approximate ring compression thrust in the walls due to pressure P ©2000 CRC Press LLC CHAPTER 10 RING STABILITY The performance limit of ring stability is instability Ring instability

Ngày tải lên: 05/05/2018, 09:27

... 2rsin α = 2rysin β Substituting the resulting ry = rsin α /sin β into Equation 11.4, critical pressure is, P = σfsin β/(r/t)sin α (11.8) Figure 11-7 (bottom) shows pressure P = f(α ) The inversion ... that may occur inside the liner The liner is flexible Initially, it fits snugly against the encasement But it may shrink, leaving an annular space between liner and encasement The liner is snug ... ring stiffness, EI/r3, and ring deflection, d It is assumed that pressure persists against the ring External Pressure at Inversion of Encased Rings The performance limit is inversion of the liner

Ngày tải lên: 05/05/2018, 09:27

... bedding.For Class B bedding, width of bedding is 0.6(OD) For Class C bedding, width of bedding is 0.5(OD) Variation of Lf in class A is based on the percent of area of reinforcing steel: Reinforced ... cracks form during curing or handling With tension reinforcement, rigid pipes serve well as pressure pipes Consider reinforced concrete pipes If performance limit is leakage, the reinforcing steel ... test pipe However, in reinforced concrete pipes, failure is often defined as the TEB load at which longitudinal cracks open to a width of 0.01 inch The 0.01-inch crack came about in the 1930s when

Ngày tải lên: 05/05/2018, 09:27

... minimum soil cover due to semi-infinite soil pressure P, showing the load "wedge" advancing against the ring and restraint "wedge" being lifted by the ring ©2000 CRC Press LLC where H" is in inches, ... W passing over a pipe buried in loose granular soil Figure 13-4 Flexible ring in the process of collapse under minimum dead load soil cover showing the load wedges advancing against the ring and ... for the maximum stress whenever stress (or strain) is of interest, as in the case of bonded linings Semi-infinite Surface Pressure For the semi-infinite uniform surface pressure of Figure 13-6,

Ngày tải lên: 05/05/2018, 09:27

... wound for shipping (or the minimum longitudinal radius for lowering continuous pipe into a trench)? If allowable strain is 2%, and pipe OD is 2 inches, from Equation 14.4, R = 50 inches If the ... 6Figure 14-3 Longitudinal stress (and strain) in tension and compression due to bending of the pipe into a longitudinal mean radius R Figure 14-4 Technique for measuring longitudinal inside radius of ... plastic hinge Strain is a better basis for analysis than stress In the following, both strain and stress are analyzed because yield stress is performance limit in some cases Due to beam bending,

Ngày tải lên: 05/05/2018, 09:27

... dt, and change in momentum is mass times change in velocity In the x-direction; Impulse = Fxdt Change in Momentum = (πD2/4)vdtρ(v-vcosθ) Equating impulse to the change in momentum in the x-direction, ... excavated without ripping or blasting On steep slopes, or in inaccessible areas, construction might require lowering personnel, platforms, and equipment down the pipeline by cables Rock pins are drilled ... because the change in velocity in the Qi direction is simply 2vsin(θ/2) Trang 4Figure 15-3 Pressure thrust-Qp at a bend (elbow) in a pipe due to internal pressure, P, showing the free-vector-diagram

Ngày tải lên: 05/05/2018, 09:27

... shifting of soil particles only tends to "shake-up" soil grains such that the soil volume tries to increase But the confined, saturated embedment cannot increase in volume Consequently, intergranular ... actually move the soil in against the pipe — including that hard-to-reach zone under the haunches — in order to achieve intimate contact between embedment and pipe 2 Jetting Soil density greater ... They can be injected into a lift of sidefill up to the spring line In order to fill holes left when jets are withdrawn, the stingers are vibrated A second lift up to the top is jetted in a similar

Ngày tải lên: 05/05/2018, 09:27

... during ring deflection as the soil wedge is thrust into the trench Trang 7provide the lateral support required to retain theflexible ring The ring deflects, thrusting out a soil wedge as indicated ... pertinent fundamental variables must be identified Ring stiffness is ignored because the ring is flexible In fact, at zero ring deflection, the ring stiffness has no effect anyway The remaining ... ring flexibility for plain pipes P = (8σf /3m2) for plain pipes (17.7) Based on plastic theory (plastic hinging), P = 24σf I/cD2 (17.8) P = 4σf /m2 for plain pipes (17.9) Vertical ring

Ngày tải lên: 05/05/2018, 09:27

... reduction in outflow areas from perfect gives a slight increase in flow velocities into the turbines This is desirable from the standpoint of turbine efficiency From guideline 2, the inside offset ... Nomenclature D = ID = inside diameter (nominal for steel) Di = inside diameter of inflow pipe (mainline) Do = inside diameter of outflow pipes (branch) t = wall thickness R = radius of bend in the pipe ... restraints by stiffener rings which can deform under Q-loads Therefore the analysis is statically indeterminate, depending upon the springconstants of the stiffener rings at A and B For atrue ring,

Ngày tải lên: 05/05/2018, 09:27

... been obtained, we combine all these partial maps (J s , resp. Υ s ) into single ones (J, resp. Υ) in the following way: 31 Heat Transfer for NDE: Landmine Detection Developments in Heat Transfer ... Landmines from Measured Infrared Images using Thermal Modeling of the Soil, PhD thesis, Universidad de Santiago de Compostela. 44 Developments in Heat Transfer Heat Transfer for NDE: Landmine ... the heat input increases. At maximum heat input (23A for every single channel) in this experiment, the equivalent weight heat transfer rate of non-uniform cross- Magneto Hydro-Dynamics and Heat...

Ngày tải lên: 19/06/2014, 10:20

... thermosyphon. 2.5.1 Surging (chugging) and geysering instability Surging and geysering occur mainly because of liquid superheat. Surging occurs when boiling is initiated in the evaporator, but ... drag-reducing solution stirred in a beaker Developments in Heat Transfer 328 (2) thermosyphon. A heat exchanger is a key component in the thermal systems used for transferring heat from ... Assuming heat transfer from a high temperature gas-cooled reactor to an industrial facility at 1223 K, the maximum single-phase heat transfer is given by the enthalpy gain from points A to B in...

Ngày tải lên: 19/06/2014, 10:20

... Research Methods in Public Administration AU5384_C002 Final Proof page 14 19.9.2007 4:33pm Compositor Name: BMani 14 Handbook of Research Methods in Public Administration 1 The Logic of Inquiry in ... Sage Publications. Harding, S. 1987. Introduction: Is there a feminist method? In Sandra Harding (ed.), Feminism and Methodology: Social Science Issues. Bloomington, Indiana: Indiana University Press. Kuhn, ... imprint of the Taylor & Francis Group, an informa business Boca Raton London New York Handbook of Research Methods in Public Administration Miller/Handbook of Research Methods in Public Administration...

Ngày tải lên: 15/03/2014, 05:20

... Cataloguing in Publication Data Otto, S. R. (Stephen Robert) An introduction to programming and numerical methods in MATLAB 1. MATLAB (Computer file) 2. Numerical analysis — Data processing I. ... solve problems (using just algebra and exploiting MATLAB as an advanced calculator). In Chapters 4 and 5 we meet some classical numerical methods, in the form of root finding and interpolation (and ... hexagram ddiamond It is also possible to control the line style. Instead of using a symbol, as in the previous command, we can draw the line using one of the following options: - solid : dotted dashdot -...

Ngày tải lên: 08/04/2014, 09:57