Heat Transfer From a Wedge to Fluids at Any Prandtl Number Using the Asymptotic Model

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Correlation Method ◽  
Independent Parameter ◽  
Asymptotic Model ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Wedge Flow ◽  
First Case ◽  
Proposed Model

Heat transfer from a wedge to fluids at any Prandtl number can be predicted using the asymptotic model. In the asymptotic model, the dependent parameter Nux/Rex1/2 has two asymptotes. The first asymptote is Nux/Rex1/2Pr→0 that corresponds to very small value of the independent parameter Pr. The second asymptote is Nux/Rex1/2Pr→∞, that corresponds to very large value of the independent parameter Pr. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. The solution has two general cases. The first case is β ≠ −0.198838. The second case is the special case of separated wedge flow (β = −0.198838) where the surface shear stress is zero, but the heat transfer rate is not zero. The reason for this division is Nux/Rex1/2 ∼ Pr1/3 for Pr ⪢ 1 in the first case while Nux/Rex1/2 ∼ Pr1/4 for Pr ⪢ 1 in the second case. In the first case, there are only two common examples of the wedge flow in practice. The first common example is the flow over a flat plate at zero incidence with constant external velocity, known as Blasius flow and corresponds to β = 0. The second common example is the two-dimensional stagnation flow, known as Hiemenez flow and corresponds to β = 1 (wedge half-angle 90 deg). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model for both isothermal wedges and uniform-flux wedges can be determined.

Heat Transfer From a Wedge to Fluids at Any Prandtl Number Using the Asymptotic Model

2010 ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Correlation Method ◽  
Independent Parameter ◽  
Asymptotic Model ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Wedge Flow ◽  
First Case ◽  
Proposed Model

Heat transfer from a wedge to fluids at any Prandtl number can be predicted using the asymptotic model. In the asymptotic model, the dependent parameter Nux/Rex1/2 has two asymptotes. The first asymptote is Nux/Rex1/2Pr→0 that corresponds to very small value of the independent parameter Pr. The second asymptote is Nux/Rex1/2Pr→∞ that corresponds to very large value of the independent parameter Pr. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. The solution has two general cases. The first case is β ≠ −0.198838. The second case is the special case of separated wedge flow (β = −0.198838) where the surface shear stress is zero, but the heat transfer rate is not zero. The reason for this division is Nux/Rex1/2 ∼ Pr1/3 for Pr ≫ 1 in the first case while Nux/Rex1/2 ∼ Pr1/4 for Pr ≫ 1 in the second case. In the first case, there are only two common examples of the wedge flow in practice. The first common example is the flow over a flat plate at zero incidence with constant external velocity, known as Blasius flow and corresponds to β = 0. The second common example is the two-dimensional stagnation flow, known as Hiemenez flow and corresponds to β = 1 (wedge half-angle 90°). Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model for both isothermal wedges and uniform-flux wedges can be determined.

Heat Transfer From a Rotating Disk to Fluids for a Wide Range of Prandtl Numbers Using the Asymptotic Model

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
M. M. Awad
Keyword(s):  
Heat Transfer ◽  
Correlation Method ◽  
Rotating Disk ◽  
Compact Model ◽  
Asymptotic Model ◽  
Simple Method ◽  
Nusselt Numbers ◽  
Proposed Model ◽  
Wide Range ◽  
Prandtl Numbers

A simple method for calculating heat transfer from a rotating disk to fluids for a wide range of Prandtl numbers using asymptotic analysis is presented. Nusselt numbers for a heated rotating disk for different Prandtl numbers is expressed in terms of the asymptotic Nusselt numbers corresponding to a very small value of Prandtl numbers and Nusselt numbers corresponding to a very large value of Prandtl numbers. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model can be determined at Prandtl numbers corresponding to the intersection of the two asymptotes.

Numerical Analysis on Nanofluid Forced Convection in Ducts With Triangular Cross Sections

2011 ◽  
Author(s):  
O. Manca ◽  
S. Nardini ◽  
D. Ricci ◽  
S. Tamburrino
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Forced Convection ◽  
Cross Sections ◽  
Fluid Dynamic ◽  
Pure Water ◽  
Convection Flow ◽  
Uniform Heat Flux ◽  
Surface Shear Stress ◽  
Surface Shear

Heat transfer of fluids is very important to many industrial heating or cooling equipments. Convective heat transfer can be enhanced passively by changing flow geometry, boundary conditions or by enhancing the thermal conductivity of the working fluids. An innovative way of improving the fluid thermal conductivity is to introduce suspended small solid nanoparticles in the base fluids. In this paper a numerical investigation on laminar forced convection flow of a water–Al2O3 nanofluid in a duct having an equilateral triangular cross section is performed. The hydraulic diameter is set equal to 1.0×10−2 m. A constant and uniform heat flux on the external surfaces has been applied and the single-phase model approach has been employed. The analysis has been run in steady state regime for a nanoparticle size equal to 38 nm, considering different volume particle concentrations. The CFD code Fluent has been employed in order to solve the tri-dimensional numerical model. Results are presented in terms of temperature and velocity distributions, surface shear stress and heat transfer convective coefficient, Nusselt number and required pumping power profiles. Comparison with results related to the fluid dynamic and thermal behaviors in pure water are carried out in order to evaluate the enhancement due to the presence of nanoparticles in terms of volumetric concentration.

The Effects of Localized Blade Endwall Suction on Secondary Flows and Heat Transfer

2010 ◽  
Author(s):  
Rebecca Hollis ◽  
Jeffrey P. Bons
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
High Surface ◽  
Surface Heat ◽  
Secondary Flows ◽  
Surface Shear Stress ◽  
Mean Velocity ◽  
Surface Shear ◽  
Surface Heat Transfer ◽  
High Heat Transfer

Two methods of flow control were designed to mitigate the effects of the horseshoe vortex structure (HV) at an airfoil/endwall junction. An experimental study was conducted to quantify the effects of localized boundary layer removal on surface heat transfer in a low-speed wind tunnel. A transient infrared technique was used to measure the convective heat transfer values along the surface surrounding the juncture. Particle image velocimetry was used to collect the time-mean velocity vectors of the flow field across three planes of interest. Boundary layer suction was applied through a thin slot cut into the leading edge of the airfoil at two locations. The first, referred to as Method 1, was directly along the endwall, the second, Method 2, was located at a height ∼1/3 of the approaching boundary layer height. Five suction rates were tested; 0%, 6.5%, 11%, 15% and 20% of the approaching boundary layer mass flow was removed at a constant rate. Both methods reduced the effects of the HV with increasing suction on the symmetry, 0.5-D and 1-D planes. Method 2 yielded a greater reduction in surface heat transfer but Method 1 outperformed Method 2 aerodynamically by completely removing the HV structure when 11% suction was applied. This method however produced other adverse effects such as high surface shear stress and localized areas of high heat transfer near the slot edges at high suction rates.

scholarly journals The new analytical study for boundary-layer slip flow and heat transfer of nanofluid over a stretching sheet

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 289-301 ◽  
Author(s):  
Fazle Mabood ◽  
Waqar Khan ◽  
Muhammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Prandtl Number ◽  
Stretching Sheet ◽  
Lewis Number ◽  
Partial Slip ◽  
Surface Shear Stress ◽  
Slip Parameter ◽  
Slip Factor

In this article, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary layer decreases and thermal boundary layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.

scholarly journals Heat Transfer Enhancement Within a Turbine Blade Cooling Passage Using Ribs and Combinations of Ribs With Film Cooling Holes

1994 ◽  
Author(s):  
J. R. Shen ◽  
Z. Wang ◽  
P. T. Ireland ◽  
T. V. Jones ◽  
A. R. Byerley
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystals ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Scale Model ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Cooling Passage ◽  
Film Cooling Holes

A transient heat transfer method which uses liquid crystals has been applied to a scale model of a turbine rotor blade passage. Detailed contours of local heat transfer coefficient are presented for the passage in which the heat transfer to one wall was enhanced firstly by ribs and then with ribs combined with holes. The hole geometry and experimental dimensionless flow rates were representative of those occurring at the entrance to engine film cooling holes. The results for the ribbed passage are compared to established correlations for developed flow. Qualitative surface shear stress distributions were determined with liquid crystals. The complex distributions of heat transfer coefficient are discussed in the light of the interpreted flow field.

Heat Transfer Enhancement Within a Turbine Blade Cooling Passage Using Ribs and Combinations of Ribs With Film Cooling Holes

1996 ◽  
Vol 118 (3) ◽  
pp. 428-434 ◽  
Author(s):  
J. R. Shen ◽  
Z. Wang ◽  
P. T. Ireland ◽  
T. V. Jones ◽  
A. R. Byerley
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Crystals ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Scale Model ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Cooling Passage ◽  
Film Cooling Holes

A transient heat transfer method using liquid crystals has been applied to a scale model of a turbine rotor blade passage. Detailed contours of local heat transfer coefficient are presented for the passage in which the heat transfer to one wall was enhanced first by ribs and then with ribs combined with holes. The hole geometry and experimental dimensionless flow rates were representative of those occurring at the entrance to engine film cooling holes. The results for the ribbed passage are compared to established correlations for developed flow. Qualitative surface shear stress distributions were determined with liquid crystals. The complex distributions of heat transfer coefficient are discussed in light of the interpreted flow field.

Mixed Boundary Layer Skin Friction and Heat Transfer With Abrupt Transition

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
M. Q. Brewster
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Skin Friction ◽  
Mixed Boundary ◽  
Classical Problem ◽  
Heat Fluxes ◽  
Surface Shear Stress ◽  
Concentrated Mass ◽  
Surface Shear ◽  
Abrupt Transition

In the form that is commonly published in introductory textbooks, the classical problem of skin friction and heat transfer for a mixed laminar–turbulent boundary-layer flow on a flat-plate with an abrupt transition is nonconservative in mass, momentum, and energy. By forcing continuity in momentum and enthalpy thicknesses, the textbook problem takes on the appearance of conserving momentum and energy. But, by doing so while retaining a turbulent virtual origin at the plate's leading edge, the textbook example omits necessary jumps in these quantities and violates conservation of mass, momentum, and energy in the flow. Here we modify this classical problem to satisfy conservation principles through the introduction of either concentrated mass/momentum/energy fluxes, at the top of the boundary layer and/or concentrated surface shear stress/heat fluxes at the bottom. Out of this simple analysis comes the intriguing idea of an entrainment flux or inflow at the top of the boundary layer over the transition region.

Heat Transfer and Flow Characteristics of an Engine Representative Impingement Cooling System

2000 ◽  
Vol 123 (1) ◽  
pp. 154-160 ◽  
Author(s):  
Changmin Son ◽  
David Gillespie ◽  
Peter Ireland ◽  
Geoffrey M. Dailey
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Large Scale ◽  
Cooling System ◽  
Scale Model ◽  
Temperature Sensitive ◽  
Surface Shear Stress ◽  
Transfer Coefficients ◽  
Surface Shear ◽  
Impingement Cooling

A study of a large-scale model of an engine representative impingement cooling system has been performed. A series of tests were carried out to characterize the behavior of the system fully. These included cold flow diagnostic tests to determine the pressure loss and the static pressure distribution, and flow visualization to assess surface shear. The surface shear stress pattern provided by multiple stripes of colored paint applied to the target surface yielded important information on the near-wall flow features far from the jet axis. The row solved flow and pressure distributions are compared to industry standard predictions. Heat transfer tests using the transient liquid crystal technique were also conducted using coatings comprised of a mixture of three thermochromic liquid crystals. Analysis of the thermochromic liquid crystal data was enhanced by recent developments in image processing. In addition, an energy balance analysis of signals from fast-response thermocouples for air temperature measurement was applied to verify the levels of heat transfer coefficients on surfaces not coated with the temperature-sensitive liquid crystal.

scholarly journals Heat transfer analysis in the time-dependent axisymmetric stagnation point flow over a lubricated surface

2018 ◽  
Vol 22 (6 Part A) ◽  
pp. 2483-2492 ◽  
Author(s):  
Khalid Mahmood ◽  
Muhammad Sajid ◽  
Nasir Ali ◽  
Tariq Javed
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Dependent ◽  
Surface Shear Stress ◽  
Partial Differential ◽  
Surface Shear ◽  
Flow And Heat Transfer

In this paper time-dependent, 2-D, axisymmetric flow and heat transfer of a viscous incompressible fluid impinging orthogonally on a disc is examined. The disc is lubricated with a thin layer of power-law fluid of variable thickness. It is assumed that surface temperature of the disc is time-dependent. Continuity of velocity and shear stress at the interface layer between the fluid and the lubricant has been imposed to obtain the solution of the governing partial differential equations. The set of partial differential equations is reduced into ordinary differential equations by suitable transformations and are solved numerically by using Keller-Box method. Solutions are presented in the form of graphs and tables in order to examine the influence of pertinent parameters on the flow and heat transfer characteristics. An increase in lubrication results in the reduction of surface shear stress and consequently viscous boundary layer becomes thin. However, the thermal boundary layer thickness increases by increasing lubrication. It is further observed that surface shear stress and heat transfer rate at the wall enhance due to unsteadiness. The results for the steady case are deduced from the present solutions and are found in good agreement with the existing results in the literature.

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