Effect Of Radial Temperature Gradient Research Articles

Determining initial formation temperature considering radial temperature gradient and axial thermal conduction of the wellbore fluid

It is crucial to verify how to accurately determine the initial formation temperature by investigating the heat exchange of wellbore fluid. The heat transfer models of initial formation temperature were established considering the effect of radial temperature gradient and axial thermal conduction, which were solved using the implicit finite difference technique, and the calculated results from two temperature measurement methods, including the cable and measurement while drilling, were compared. Results reveal that fluid radial temperature gradient leads to a change of the initial formation temperature in the upper and lower sections of the wellbore of 0.03 °C and 0.32 °C, respectively, and the axial thermal conductivity of drilling fluid had little effect on the initial formation temperature. The identical initial formation temperature was calculated from both measurement methods after a long shut-in. Most relevant is that the model results matched actual field data better than other heat transfer models.

Convective heat transfer of turbulent decaying swirled flows in concentric annular pipes

The heat transfer characteristics of turbulent decaying swirled flows in concentric annular pipes is investigated numerically by means of CFD simulations using the OpenFOAM package. The simulations are performed for different Reynolds numbers and swirl angles at the duct inlet. By including cases with large temperature differences between the fluid and the wall, also the effects of radial temperature gradients on the velocity distribution are accounted for. A novel correlation, holding locally, is proposed and is presented in a form similar to the classical Sieder-Tate correlation, including an additional term to address the influence of the swirled flow. In a similar fashion, a correlation for the friction factor is given in the form of the Petukhov formula, yet with an additional swirl-related term. Also a formula assessing the swirl decay rate is presented. This allows global correlations to be extracted by solving the local ones over the pipe length in a system and integrating.

Effect of Radial Temperature Gradient on Stability of Hydromagnetic Couette Flow in Narrow-Gap Annulus with Constant Heat Flux at Outer Cylinder

In this paper, the stability of the Couette flow of a viscous incompressible and electrically conducting fluid between two electrically non-conducting concentric rotating cylinders is studied by taking into account the following conditions (i) a radial temperature gradient (ii) a constant heat flux at outer cylinder (iii) an axially applied constant magnetic field (iv) the inner cylinder rotating with the outer one stationary (v) co-rotating cylinders (vi) and counter-rotating cylinders. The approximate solution of the eigenvalue problem is obtained by using the Galerkin’s method, when the gap between the cylinders is narrow. The numerical values of the critical wave number and the critical Taylor number are computed from the obtained approximate expression. It is found that the numerical values of the critical wave number and the critical Taylor number obtained by taking three terms in the Galerkin method agree very well with earlier results obtained by the shooting method. The amplitude of the radial velocity and the cell-pattern are also shown on the graphs for different values of the ratio of the angular velocities. The effects of ratios of angular velocities, radial temperature gradient and magnetic field on the stability of flows are discussed. It is found that the effect of the magnetic field is to inhibit the onset of instability but the effect of heat flux on the outer cylinder is to increase the onset of instability. These effects are more when the cylinders are rotating in anti clockwise sense.

Effect of Radial Temperature Gradient on the Stability of Magnetohydrodynamic Dean Flow in an Annular Channel at High Magnetic Parameter

The effect of a radial temperature gradient on the stability of Dean flow of an electrically conducting fluid in an annular channel is investigated. A strong constant magnetic field is imposed in the axial direction. Finite-difference method is used to solve the eigenvalue problem. For given values of gap width d, between the cylinders, and magnetic parameter Q, electrically nonconducting (NC) walls are found to be more destabilizing than perfectly conducting (PC) walls when the temperature parameter N < 0. This trend persists even for small positive values of N but when N (>0) exceeds a critical value depending on Q, PC walls are slightly more destabilizing than NC walls. The critical value of the radii ratio η (0 < η < 1) beyond which the first unstable mode becomes nonaxisymmetric is determined for various values of N and Q.

Effect of radial temperature gradient on the stability of Taylor–Dean flow between two arbitrarily spaced concentric rotating cylinders

The effect of a radial temperature gradient on the stability of Taylor–Dean flow of an incompressible viscous fluid between two arbitrarily spaced concentric rotating circular cylinders driven by a constant azimuthal pressure gradient is studied. Here the ratio of representative pumping and rotation velocities β is varied from −6.1613 to 1.00 and both positive and negative values of the temperature gradient parameter N are considered, where N depends on the temperature differences T2−T1 between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem which is solved by using a classical Runge–Kutta scheme combined with a shooting technique, termed unit disturbance method. It is found that as the gap width between the cylinders increases, the critical Taylor number progressively increases for given values of β and N. It is also found that for given values of η (the ratio of the radii of inner and outer cylinders) and β, the flow becomes more and more unstable with increase in N(>0). In the present work, emphasis is given on the point as to whether the two neutral stability curves cross at some point for given value of N for which the flow is completely stable.

Investigation of lattice plane bending in large (0001)SiC crystals using high‐energy X‐ray technique

Bulk SiC crystals have been investigated using high-energy X-ray technique. The penetration depth of the high-energy X-rays was enough to perform the mapping of the whole crystal bulk in order to analyze the distribution of subgrain boundaries (SGB) and bending of the lattice planes. The full width at half maximum (FWHM) of the rocking curves reflects the structural quality of bulk SiC and correlates to the SGB density. The shift of θBragg when moving the sample in reference to the incident beam reflects the inclination of the lattice planes. A model, which emphasizes the effect of growth interface morphology on SGB density and lattice bending, is presented. The effect of radial temperature gradient on crystal quality is demonstrated presenting a way to reduce structural defects. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of Radial Temperature Gradient on the Stability of a Viscous Flow between Two Rotating Porous Cylinders with a Narrow Gap

The linear stability of viscous fluid flow between two rotating concentric porous cylinders at temperature θ 1 (of the inner cylinder) and θ 2 (of the outer cylinder) is studied in a narrow gap case. The numerical values of the critical wave number a c and the critical Taylor number T c are listed in a table for different values of μ (-0 only the inner cylinder rotating), μ (≷0, both cylinders co-rotating or counter-rotating) ratio of angular velocities Ω 2 /Ω 1 , and for different values of ±N, ±S where N is a radial temperature gradient parameter based on the temperature difference θ 2 - θ 1 >/ 0) or injection (<0) velocity. The effects of these parameters on the stability of flows are discussed.

Effect of radial temperature gradient on the stability of flow in a curved channel

The stability of the Dean problem in the presence of a radial temperature gradient is studied in the narrow-gap case. A finite-difference method is used to solve an eigenvalue problem, and critical values of the parameters A and a are given, where a is a wavenumber and A is a parameter determining the onset of instability. The parameter M , which depends upon T 2 − T 1), where T 1 is the temperature of the inner cylinder and T 2 is that of the outer cylinder, governs the onset of instability in such a way that an increase in (+ M ) tends to destabilize the flow, whereas an increase in (− M ) tends to stabilize the flow. The cells and the maximum value of the radial velocity perturbation are found to move towards a cylinder with lower temperature when M > 0.

The effect of radial temperature gradient and axial magnetic field on the stability of couette flow: The narrow gap problem

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under the following conditions: (i) the inner cylinder rotating with the outer cylinder stationary, (ii) corotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, (v) conducting and nonconducting walls, and (vi) the presence of a radial temperature gradient. Results for the critical wave number ac, and the critical Taylor number Tc, are presented. The variation of Tc is shown on graphs for both the conducting and nonconducting walls and for different values of ±μ (= Ω2/Ω1, where Ω2 is the angular velocity of the outer cylinder, and Ω1 is the angular velocity of the inner cylinder), the magnetic field parameter Q, which is the square of the Hartmann number and ± N (= Ra/Ta, where Ra is the Rayleigh number). The effects of ±μ, N and Q on the stability of flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, this being more so in the presence of conducting walls and a negative temperature gradient.

Effects of radial temperature gradient on the stability of a narrow-gap annulus flow

An eigenvalue problem of the stability of Couette flow between two concentric cylinders in relative motion in the presence of a positive ( T 2 > T 1) and a negative ( T 2 < T 1) radial temperature gradient is solved numerically, where T 1, T 2 are the temperatures of the inner and outer cylinders, respectively. The numerical values of the critical wave number a c and the critical Taylor number T c are calculated for ± μ (= Ω 2 Ω 1 , where Ω 2 is the angular speed of the outer cylinder and Ω 1 is the angular speed of the inner cylinder) and ± N (ratio of the Rayleigh and Taylor numbers). The radial eigenfunction and the cell patterns are shown graphically for different values of ± μ and ± N. It is observed that the flow is more stable in the presence of a negative temperature gradient for both ±μ. The stabilising effect is more promising when the two cylinders are counterrotating. The magnitude of a c also increases steeply in the presence of counterrotating cylinders and a negative radial temperature gradient ( T 2 < T 1).

Effects of radial temperature gradient on the stability of flow in a narrow-gap annulus with constant heat flux at the inner rotating cylinder

The stability of Couette flow of a viscous, imcompressible fluid between two concentric rotating cylinders in the presence of a radial temperature gradient due to constant heat flux at the inner cylinder is studied. Assuming the flow that takes place in a narrow gap, the eigenvalue problem is solved numerically. The critical values ofa (the wave number) andTa (the Taylor number) are listed in a table and these are also shown graphically in the case of the rotation of the cylinders in clockwise and counter-clockwise direction. It is observed that greater amount of heat flux has a stabilising effect.

Effect of radial temperature gradient on the Stability of flow in an annulus with constant Heat flux at the inner cylinder: wide-gap Problem

An exact numerical solution is given to the eigenvalue problem of stability of Couette flow in a wide-gap region bounded by two concentric cylinders in the presence of constant heat flux at the inner cylinder. Numerical values of a c (the critical wave number) and T c (the critical Taylor) are calculated for different values of ±μ(=Ω 2/Ω 1) and η (=R 1/R 2) where Ω 1, Ω 2 are the angular velocities of the inner and outer cylinders of radii R 1, R 2 respectively. It is observed that the presence of radial temperature gradient enhances the stability of the flow, and with a decrease in the gap-width, the flow becomes less stable. In the presence of counter-rotating flow, the flow becomes more stable due to the presence of a radial temperature gradient.

Effects of radial temperature gradient on the stability of flow of a viscous incompressible fluid between two rotating cylinders

Stability of the flow of a viscous incompressible fluid in a narrow gap between two concentric cylinders rotating in opposite directions is studied. Exact values of critical Taylor number for the first and second modes are derived by a numerical procedure and these are compared with the known results. It is observed that the value of the critical Taylor number T crit decreases with increasing the values of a parameter N (N = Ra T , Ra = Rayleigh number, T = Taylor number) , and the rate of decrease in the value of T crit is more when the two cylinders rotate in the opposite directions.

The Effect of Radial Temperature Gradients on Glass Fracture in Simulated High-Level Waste Canisters

AbstractThe Pacific Northwest Laboratory performed experiments on canisters of simulated high-level waste (HLW) glass to estimate the effects of radial temperature gradients on the degree of glass fracture in actual HLW canisters. Glass cracking may result in an increased amount of fine glass particles that are of concern in transportation and repository safety analyses. A test matrix was developed to examine the effect of air cooling, water quenching, and internal fins on canister cooling rates, radial temperature gradients, glass cracking levels, and particle size distributions. The data shows the reduction of radial temperature gradients to be important in reducing the amount of waste glass fracture. Cracking profiles show that internal carbon steel fins significantly decrease the degree of fracture. Different cooling rates only affect the amount of particles above a certain size. The amount of particles below that size depends on the interaction between the glass and canister.

Effects of radial temperature gradient on the stability of viscous row in an annulus with a rotating inner cylinder

The Taylor stability problem is solved for the case of narrow gap between a rotating inner cylinder and a stationary outer cylinder where the latter is at a higher temperature than the former. The predictions are based on a numerical procedure with less restrictive assumptions than those previously adopted and they confirm the destablizing effect of a radial temperature gradient.

Elecrtrophoretic thermal theory : I. Temperature gradients and their effects

The effects of radial temperature gradients in circular-section columns and central-peripheral gradients in rectangular and annular columns, and lateral temperature gradients in both, normal to the electric field, are considered, taking into account the synergistic effects of gradients of resistivity due to negative temperature coefficients of resistivity of electrolyte solutions. Longitudinal temperature gradients and their interaction with radial temperature gradients in the steady and unsteady states are discussed. Consequences for distortion of separand bands, and limitations on apparatus design and choice of conditions are stated. Two methods of unlimited preparative scale-up are explained.

The Effect of Radial Temperature Gradient on the Stability of a Viscous Flow Between Two Rotating Coaxial Cylinders

The Effect of Radial Temperature Gradient on the Stability of a Viscous Flow Between Two Rotating Coaxial Cylinders

The effect of radial temperature gradient on the formation of axial void in UO 2 fuel elements

The process of axial cavity formation in UO 2 rods of nuclear fuel was investigated by means of a nodal model of heat transfer incorporating a space dependent heat source and both temperature and irradiation dependent thermal conductivity. The radii of the cavity and of the reorganized crystal zone were reproduced through calculation by postulating a progressive recrystallization of the initially porous UO 2 commencing at 1700°C, and associated with differential sublimation and condensation of UO 2, within the microscopic pores under the action of a high temperature gradient. The calculational model was found sufficient to predict quantitatively the experimentally observed changes in UO 2, rods and leads to the conclusion that the axial cavity may form before the UO 2, melting temperature of 2876°C is reached at the center of the rod.