Heat Transfer for Gaseous Flow in Microtubes With Viscous Heating

2000 ◽  
Author(s):  
Gokturk Tunc ◽  
Yildiz Bayazitoglu
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Jump ◽  
Integral Transform ◽  
Jump Condition ◽  
Viscous Heating ◽  
Brinkman Number ◽  
Viscous Effects ◽  
Knudsen Numbers ◽  
Integral Transform Technique

Abstract Convective heat transfer for steady state, laminar, hydrodynamically developed flow in microtubes with a boundary condition of constant temperature is solved by the integral transform technique. Temperature jump condition at the wall and viscous heating within the medium are included. For a given Brinkman number, at specified axial lengths, the viscous effects are presented for the developing range, reaching the fully developed Nusselt number. In previous studies without temperature jump condition at the wall, a 22% increase in the Nusselt number was found for Knudsen numbers ∈ [0,0.12]. In this work we have found that for the same range of Knudsen numbers, the Nusselt number decreases by 35.6%. In addition, as we increase the Prandtl number the temperature jump effect diminishes.

Slip-Flow and Conjugate Heat Transfer in Rectangular Microchannels

2008 ◽  
Author(s):  
H. D. Madhawa Hettiarachchi ◽  
Mihajlo Golubovic ◽  
William M. Worek ◽  
W. J. Minkowycz
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Conjugate Heat Transfer ◽  
Temperature Jump ◽  
Slip Flow ◽  
Numerical Code ◽  
Published Data ◽  
Rectangular Microchannels ◽  
Knudsen Numbers

Slip-flow and conjugate heat transfer in rectangular microchannels are studied numerically for thermally developing laminar flow subjected to constant wall temperature (T) and constant wall heat flux (H2) boundary conditions. A three-dimensional numerical code based on finite volume method is developed to solve the coupled energy equations in the wall and fluid regions together with temperature jump at the wall-fluid boundary. A modified convection-diffusion coefficient at the wall-fluid interface is defined to incorporate the temperature-jump boundary condition. The numerical code is validated by comparing the present results with the published data. The effect of rarefaction and wall conduction on the heat transfer in the entrance region is analyzed in detail. Results show that the wall conduction has a considerable influence on the developing Nusselt number along the channel for the H2 boundary condition, particularly at low Knudsen numbers. In the case of the T thermal boundary condition, negligible influence of wall conduction on the Nusselt number is observed for all Knudsen numbers considered.

scholarly journals A Non-Newtonian Magnetohydrodynamics (MHD) Nanofluid Flow and Heat Transfer with Nonlinear Slip and Temperature Jump

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1199 ◽  
Author(s):  
Jing Zhu ◽  
Yaxin Xu ◽  
Xiang Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Jump ◽  
Thin Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Slip Condition ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Flow And Heat Transfer

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches 10 − 6 from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

Influence of Fluid-Dynamics on Heat Transfer in a Pre-Swirl Rotating-Disc System

2004 ◽  
Author(s):  
Gary D. Lock ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Gas Turbines ◽  
Fluid Dynamic ◽  
Impinging Jets ◽  
Coolant Flow ◽  
Viscous Effects ◽  
Rotating Disc ◽  
Scaled Model ◽  
Flow Rates

Modern gas turbines are cooled using air diverted from the compressor. In a “direct-transfer” pre-swirl system, this cooling air flows axially across the wheel-space from stationary pre-swirl nozzles to receiver holes located in the rotating turbine disc. The distribution of the local Nusselt number, Nu, on the rotating disc is governed by three non-dimensional fluid-dynamic parameters: pre-swirl ratio, βp, rotational Reynolds number, Reφ, and turbulent flow parameter, λT. This paper describes heat transfer measurements obtained from a scaled model of a gas turbine rotor-stator cavity, where the flow structure is representative of that found in the engine. The experiments reveal that Nu on the rotating disc is axisymmetric except in the region of the receiver holes, where significant two-dimensional variations have been measured. At the higher coolant flow rates studied, there is a peak in heat transfer at the radius of the pre-swirl nozzles, associated with the impinging jets from the pre-swirl nozzles. At lower coolant flow rates, the heat transfer is dominated by viscous effects. The Nusselt number is observed to increase as either Reφ or λT increases.

scholarly journals A variational iteration method integral transform technique for handling heat transfer problems

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 55-61 ◽  
Author(s):  
Yuejin Zhou ◽  
Shun Pang ◽  
Guo Chong ◽  
Xiaojun Yang ◽  
Xiaoding Xu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Iteration Method ◽  
Integral Transform ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Excess Temperature ◽  
Variational Iteration ◽  
Transfer Equations ◽  
Transfer Problems ◽  
Integral Transform Technique

In this paper, we consider the heat transfer equations at the low excess temperature. The variational iteration method integral transform technique is used to find the approximate solutions for the problems. The used method is accurate and efficient.

Influence of Fluid Dynamics on Heat Transfer in a Preswirl Rotating-Disk System

2004 ◽  
Vol 127 (4) ◽  
pp. 791-797 ◽  
Author(s):  
Gary D. Lock ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Gas Turbines ◽  
Fluid Dynamic ◽  
Rotating Disk ◽  
Impinging Jets ◽  
Coolant Flow ◽  
Viscous Effects ◽  
Scaled Model ◽  
Flow Rates

Modern gas turbines are cooled using air diverted from the compressor. In a “direct-transfer” preswirl system, this cooling air flows axially across the wheel space from stationary preswirl nozzles to receiver holes located in the rotating turbine disk. The distribution of the local Nusselt number Nu on the rotating disk is governed by three nondimensional fluid-dynamic parameters: preswirl ratio βp, rotational Reynolds number Reϕ, and turbulent flow parameter λT. This paper describes heat transfer measurements obtained from a scaled model of a gas turbine rotor-stator cavity, where the flow structure is representative of that found in the engine. The experiments reveal that Nu on the rotating disk is axisymmetric except in the region of the receiver holes, where significant two-dimensional variations have been measured. At the higher coolant flow rates studied, there is a peak in heat transfer at the radius of the preswirl nozzles associated with the impinging jets from the preswirl nozzles. At lower coolant flow rates, the heat transfer is dominated by viscous effects. The Nusselt number is observed to increase as either Reϕ or λT increases.

Heat Transfer Measurements Using Liquid Crystal in a Pre-Swirl Rotating-Disc System

2003 ◽  
Author(s):  
Gary D. Lock ◽  
Youyou Yan ◽  
Paul J. Newton ◽  
Michael Wilson ◽  
J. Michael Owen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Liquid Crystal ◽  
Gas Turbines ◽  
Fluid Dynamic ◽  
Turbine Blades ◽  
Impinging Jets ◽  
Viscous Effects ◽  
Rotating Disc ◽  
Flow Rates

Pre-swirl nozzles are often used in gas turbines to deliver the cooling air to the turbine blades through receiver holes in a rotating disc. The distribution of the local Nusselt number, Nu, on the rotating disc is governed by three non-dimensional fluid-dynamic parameters: pre-swirl ratio, βp, rotational Reynolds number, Reφ, and turbulent flow parameter, λT. A scaled model of a gas turbine rotor-stator cavity, based on the geometry of current engine designs, has been used to create appropriate flow conditions. This paper describes how thermochromic liquid crystal (TLC), in conjunction with a stroboscopic light and digital camera, is used in a transient experiment to obtain contour maps of Nu on the rotating disc. The thermal boundary conditions for the transient technique are such that an exponential-series solution to Fourier’s one-dimensional conduction equation is necessary. A method to assess the uncertainty in the measurements is discussed and these uncertainties are quantified. The experiments reveal that Nu on the rotating disc is axisymmetric except in the region of the receiver holes, where significant two-dimensional variations have been measured. At the higher coolant flow rates studied, there is a peak in heat transfer at the radius of the pre-swirl nozzles. The heat transfer is governed by two flow regimes: one dominated by inertial effects associated with the impinging jets from the pre-swirl nozzles, and another dominated by viscous effects at lower flow rates. The Nusselt number is observed to increase as either Reφ or λT increases.

scholarly journals New temperature jump boundary condition in high-speed rarefied gas flow simulations

2017 ◽  
Vol 39 (2) ◽  
pp. 165-176
Author(s):  
Nam Tuan Phuong Le ◽  
Ngoc Anh Vu ◽  
Le Tan Loc ◽  
Tran Ngoc Thoai
Keyword(s):  
High Speed ◽  
Gas Flow ◽  
Sliding Friction ◽  
Temperature Jump ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Jump Condition ◽  
Rarefied Gas Flow ◽  
Flow Simulations ◽  
Knudsen Numbers

The effect of the sliding friction has been important in calculating the heat flux of gas flow from the surface since there is some slip over the surface. There has not been any the temperature jump condition including the sliding friction part so far. In this paper, we will propose a new temperature jump condition that includes the sliding friction. Our new temperature jump condition will be evaluated for NACA0012 micro-airfoil in high-speed rarefied gas flow simulations using the CFD method, which solves the Navier-Stokes equations within the OpenFOAM framework with working gas as air. The airfoil case is simulated with various Knudsen numbers from 0.026 to 0.26, and the angles-of-attack (AOAs) from 0-deg to 20-deg. The surface gas temperatures predicting by our new temperature jump condition give good agreements with the DSMC data, especially the NACA0012 micro-airfoil cases with the high Knudsen numbers, Kn = 0.1, and Kn = 0.26 with AOA = 20-deg. for the lower surface.

scholarly journals HEAT TRANSFER STUDY IN SLUG FLOW ON ELLIPTICAL DUCTS CROSS SECTIONS BY GENERALIZED INTEGRAL TRANSFORM TECHNIQUE

2005 ◽  
Vol 4 (2) ◽  
pp. 154
Author(s):  
C. R. M. Maia ◽  
R. A. V. Ramos ◽  
M. F. Pelegrini ◽  
T. A. Alves
Keyword(s):  
Heat Transfer ◽  
Cross Sections ◽  
Slug Flow ◽  
Integral Transform ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Elliptical Section ◽  
Thermal Entrance ◽  
Integral Transform Technique ◽  
Transfer Study

This work shows the calculation of heat transfer parameters for slug flow in the thermal entrance region of elliptical section tubes submitted to a second kind boundary condition. The main difficulty in the application of the boundary conditions in problems with this kind of geometry has been removed by using a suitable coordinate change. The generalized integral transform technique (GITT) has been used to obtain the solution of the energy equation. The mixture temperature and the local and average Nusselt numbers have been calculated for several aspect ratios and the results have been compared with those found in the literature.

scholarly journals LBM Analysis of Micro-Convection in MHD Nanofluid Flow

2017 ◽  
Vol 63 (7-8) ◽  
pp. 426 ◽  
Author(s):  
Arjun Kozhikkatil Sunil ◽  
Rakesh Kumar
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Temperature Jump ◽  
Volume Fraction ◽  
Slip Coefficient

The lattice Boltzmann-Bhatnagar-Gross-Krook method was used to simulate Al2O3-water nanofluid to find the effects of Reynolds, Rayleigh and Hartmann numbers, slip coefficient, nanoparticle volume fraction and axial distance on forced convection heat transfer in MATLAB. The ranges of studied Reynolds number, Rayleigh number, magnetic field strength, nanoparticle volume concentration and slip coefficient include 200 ≤ Re ≤ 4000; 103 ≤ Ra ≤ 106; 0 ≤ Ha 90; 0 ≤ φ ≤ 2%; 0.005 ≤ B ≤ 0.02, respectively. The results show that increasing Reynolds number and nanoparticle volume fractions improve heat transfer in the 2D microtube under laminar, turbulent, slip and temperature jump boundary conditions. Decreasing the values of slip coefficient decreases the temperature jump and enhances the Nusselt number. A critical value for the Rayleigh number (105) and magnetic field strength (Ha 10) exists, at which the impacts of the solid volume fraction and slip coefficient effects are the most pronounced. The pressure drop shows a similar type of enhancement in magnitude, as observed in the case of the Nusselt number. However, application of nanofluids for low Reynolds numbers is more beneficial, and the effect of volume fractions are more pronounced in comparison to slip coefficient, though the effects are marginal.

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