An improved analytical solution on viscous dissipation effect in extended Stokes' second problem in microchannel with isothermal boundaries.

In this analytical study, the fluid motion within a microchannel is induced by the oscillation of one surface parallel to the other stationary surface, termed the extended Stokes' problem. The novelty and research gap are acquiring the thermal effect of such motion due to the viscous dissipation or fluid friction, subject to symmetric isothermal boundary conditions. The study may shed light on the role of viscous dissipation in temperature rise in the synovial fluid of an artificial hip joint, or in the fluid layer of a mechanical bearing. The full exact analytical temperature field, until now, has been unsolved, as it involves unsteady flow with manipulation of a complicated velocity field. The assumptions in the model are one-dimensional, incompressible, laminar, Newtonian flow with constant properties in a microchannel. Through the methodology of partial differential equation analysis, the temperature field is obtained in terms of Brinkman number, Prandtl number and a dimensionless angular frequency, and results are verified with a reported numerical solution, for specified range of the variables. Results complement recent approximate solutions which are valid only for the limited condition of the dimensionless angular frequency being less than or equal to unity, whereby suggesting a new Stokes number.

Impact of an effective Prandtl number model on the flow of nanofluids past an oblique stagnation point on a convective surface.

The stretched surface's convective heat transfer capability can be improved by using nanoparticles. There is a significant role of the Prandtl number in determining the thermal and momentum stretching layer surfaces. It is proposed in this study that an effective Prandtl number model be used to explore the two-dimensional oblique stagnation point flow of γ A l 2 O 3 - H 2 O and γ A l 2 O 3 - C 2 H 6 O 2 nanofluids moving over a convective stretching surface. The fluid in question is subjected to a thorough investigation. It is necessary to apply non-linear ordinary differential equations in order to connect the controlling partial differential equations with the boundary conditions. To solve these equations, an efficient and reliable numerical technique is used. Shooting Method with Runge Kutta-IV in Mathematica software. Visual representations of normal and tangential velocity and temperature as well as streamlines as a function of many physical parameters are shown. The results show that as the volume fraction of nanoparticles increases, the fluid flow f ( y ) , h ( y ) and velocity f ' ( y ) , h ' ( y ) all increase, whereas the flow f ( y ) and velocity f ' ( y ) both increase against the stretching ratio parameter, while the flow h ( y ) and velocity h ' ( y ) both decrease. When the volume percentage of nanoparticles and the Biot number are both increased, the temperature rises. However, when the stretching ratio parameter is increased, the temperature falls. Physical attributes like the local skin friction coefficient and the heat flow may be characterized in many ways. A nanofluid comprised of γ A l 2 O 3 - C 2 H 6 O 2 outperformed a γ A l 2 O 3 - H 2 O nanofluid in terms of heat transfer rate. The source of zero skin friction may be observed to move to the left or right depending on the balance of obliqueness and straining motion at point x s . The computed numerical results of the current research correspond well with those accessible in the literature for the limiting scenario.

Thermal-Fluid-Solid Coupling-Parametrical Numerical Analysis of Hot Turbine Nozzle Guide Vane.

The cooling technology of hot turbine components has been a subject of continuous improvement for decades. In high-pressure turbine blades, the regions most affected by the excessive corrosion are the leading and trailing edges. In addition, high Kt regions at the hot gas path are exposed to cracking due to the low and high cycle fatigue failure modes. Especially in the case of a nozzle guide vane, the ability to predict thermally driven loads is crucial to assess its life and robustness. The difficulties in measuring thermal properties in hot conditions considerably limit the number of experimental results available in the literature. One of the most popular test cases is a NASA C3X vane, but coolant temperature is not explicitly revealed in the test report. As a result of that, numerous scientific works validated against that vane are potentially inconsistent. To address that ambiguity, the presented work was performed on a fully structural and a very fine mesh assuming room inlet temperature on every cooling channel. Special attention was paid to the options of the k-ω SST (shear-stress transport) viscosity model, such as Viscous heating (VH), Curvature correction (CC), Production Kato-Launder (KT), and Production limiter (PL). The strongest impact was from the Viscous heating, as it increases local vane temperature by as much as 40 deg. The significance of turbulent Prandtl number impact was also investigated. The default option used in the commercial CFD code is set to 0.85. Presented study modifies that value using equations proposed by Wassel/Catton and Kays/Crawford. Additionally, the comparison between four, two, and one-equation viscosity models was performed.

Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids.

The Prandtl number is evaluated for the three-dimensional hard-sphere and one-component plasma fluids, from the dilute weakly coupled regime up to a dense strongly coupled regime near the fluid-solid phase transition. In both cases, numerical values of order unity are obtained. The Prandtl number increases on approaching the freezing point, where it reaches a quasi-universal value for simple dielectric fluids of about ≃1.7. Relations to two-dimensional fluids are briefly discussed.

Evaluation and improvement study of the Planetary Boundary-Layer schemes during a high PM2.5 episode in a core city of BTH region, China.

Accurate depictions of planetary boundary layer (PBL) processes are important for both meteorological and air quality simulations. This study examines the sensitivity of the model performance of the Weather Research Forecasting model coupled with Chemistry (WRF-Chem) to five different PBL schemes and further to different turbulence parameters for the simulation of a winter haze episode in Tianjin, a core city of the Beijing-Tianjin-Hebei (BTH) region in China. To provide a direct and comprehensive evaluation of the PBL schemes, measurements from multiple instruments are employed, including both meteorological and air quality quantities from near-surface observations, vertical sounding measurements and ceilometer data. Moreover, the vertical distribution of the turbulent exchange coefficient is derived from sounding measurements and is utilized to evaluate the PBL schemes. The results suggest that the Mellor-Yamada-Janjic (MYJ) scheme is generally statistically superior to the other schemes when comparing observations. However, considerable model discrepancies still exist during certain stages of this haze episode, which are found to be predominantly due to the deficiency of MYJ in distinguishing the intensity of turbulent mixing between different pollution stages. To improve the model performance, this study further tests the impact of different closure parameters on the simulation of winter haze episode. In the MYJ scheme, the closure parameters play a key role in the turbulent mixing within the PBL and therefore in haze simulations. Sensitivity experiments with different MYJ parameters confirm this diagnosis and suggest that a larger Prandtl number (Pr), rather than the default value in the MYJ formulation, may be more applicable for haze simulations under stable atmospheric conditions.

Effect of Prandtl Number on Mixed Convective Heat Transfer from a Porous Cylinder in the Steady Flow Regime.

The effect of the Prandtl number (Pr) on the flow and heat transfer from a porous circular cylinder with internal heat generation in the mixed convection regime is numerically investigated. The steady flow regime is considered over the ranges of the Reynolds number (Re), Darcy number (Da), and Richardson number (Ri), varying from 5 to 40, 10-6 to 10-2, and 0 to 2, respectively. The wake structure, the temperature distribution, and the heat transfer rate are discussed. Besides precipitating the growth of the recirculating wake, the Prandtl number is found to have a significant impact on the thermal characteristics. The concave isotherms, resembling a saddle-shaped structure, occur behind the cylinder at larger Pr, resulting in swells of the isotherms pairing off at the lateral sides. These swells are found to have a negative effect on heat transfer owing to a relatively smaller temperature gradient there. Then, the heat transfer rate in terms of the local Nusselt number (Nu) and enhancement ratio (Er) is calculated, which is closely related to Pr, Re, Da, and Ri. The local minimum heat transfer rate along the cylinder surface is found at the position where the swells of the isotherms form.

Theoretical and mathematical analysis of entropy generation in fluid flow subject to aluminum and ethylene glycol nanoparticles.

BACKGROUND: Here we have conducted a magnetohydrodynamic (MHD) flow of viscous material with alumina water and ethylene glycol over a stretched surface. The flow is discussed with and without effective Prandtl number. MHD liquid is considered. Electric field is absent. Effect of uniform magnetic field is taken in the vertical direction to the surface. Influence of thermal radiation as well as Joule heating are taken into account for both aluminum oxide-water and aluminum oxide-Ethylene glycol nanofluids. Velocity slip and melting heat effects are considered. METHODS: The nonlinear flow expressions are numerically solved via ND-solve technique (built-in-Shooting). RESULTS: The physical impacts of flow variables like mixed convection parameter, magnetic parameter, Reynold number, Eckert number, melting parameter and heat source/sink parameter are graphically discussed. Moreover, entropy generation (irreversibility) and Bejan number are discussed graphically through various flow variables. Physical quantities like skin friction coefficient and Sherwood and Nusselt numbers are numerically calculated and discussed through Tables. CONCLUSIONS: Impact of magnetic and slip parameters on the velocity field show decreasing behavior for both effective and without effective Prandtl number. Temperature field increases for both effective and without effective Prandtl number for higher values of magnetic and radiative parameters. Entropy number is an increasing function of Reynolds number while Bejan number shows opposite impact against Reynolds number. Moreover, heat transfer rate upsurges versus larger melting and radiative parameter.

Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-Bénard Convection at Various Prandtl Number.

Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for Pr=6,20,100 and 106 are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of Pr, the large scale circulation disappears with increasing Pr, and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing Pr. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate εθ already increasingly plays a dominant position in the thermal transport, εu can have no effect with increase of Pr. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing Pr. The energy spectrum significantly decreases with the increase of Pr. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing Pr, which is qualitatively consistent with the theoretical predictions.

On total turbulent energy and the passive and active role of buoyancy in turbulent momentum and mass transfer.

Measurements of turbulent fluctuations of horizontal and vertical components of velocity, salinity and suspended particulate matter are presented. Turbulent Prandtl numbers are found to increase with stratification and to become larger than 1. Consequently, the vertical turbulent mass transport is suppressed by buoyancy forces, before the turbulent kinetic energy (TKE) and vertical turbulent momentum exchange are inhibited. With increasing stratification, the buoyancy fluxes do not cease, instead they become countergradient. We find that buoyantly driven motions play an active role in the transfer of mass. This is in agreement with trends derived from Monin-Obukhov scaling. For positive Richardson flux numbers (Ri f ), the log velocity profile in the near-bed layer requires correction with a drag reduction. For negative Ri f , the log velocity profile should be corrected with a drag increase, with increasing |Ri f |. This highlights the active role played by buoyancy in momentum transfer and the production of TKE. However, the data do not appear to entirely follow Monin-Obukhov scaling. This is consistent with the notion that the turbulence field is not in equilibrium. The large stratification results in the decay of turbulence and countergradient buoyancy fluxes act to restore equilibrium in the energy budget. This implies that there is a finite adjustment timescale of the turbulence field to changes in velocity shear and density stratification. The energy transfers associated with the source and sink function of the buoyancy flux can be modeled with the concept of total turbulent energy.