Flow and Heat Transfer in Ducts of Arbitrary Shape With Arbitrary Thermal Boundary Conditions

1966 ◽  
Vol 88 (4) ◽  
pp. 351-357 ◽  
Author(s):  
E. M. Sparrow ◽  
A. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Cross Section ◽  
Arbitrary Cross Section ◽  
Space Technology ◽  
Closed Form Solutions ◽  
Thermal Boundary Conditions ◽  
Flow And Heat Transfer ◽  
Temperature Distributions ◽  
Circular Segment

A computation-oriented method of analysis is presented for determining closed-form solutions for fully developed laminar flow and heat transfer in ducts of arbitrary cross section. The analytical method can accommodate both uniform and circumferentially varying thermal boundary conditions. The solutions provide information for local quantities such as the velocity and the temperature distributions as well as for overall quantities such as the friction factor and the Nusselt number. As an application of the method, solutions are presented for flow and for heat transfer in ducts of circular-segment cross section, a configuration that is of current interest in space technology.

A Variational Method for Fully Developed Laminar Heat Transfer in Ducts

1959 ◽  
Vol 81 (2) ◽  
pp. 157-164 ◽  
Author(s):  
E. M. Sparrow ◽  
R. Siegel
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Variational Method ◽  
Cross Section ◽  
Cross Sections ◽  
Axial Direction ◽  
Circular Sector ◽  
Thermal Boundary Conditions ◽  
Temperature Distributions ◽  
Good Agreement

A variational method is presented for determining fully developed velocity and temperature distributions for laminar flow in noncircular ducts. The heat addition to the fluid is taken to be uniform in the axial direction, but a variety of thermal boundary conditions are considered around the periphery of the duct cross section. Several illustrative examples are given, and comparisons are made which show good agreement with available exact solutions. These examples include ducts of rectangular and circular-sector cross sections.

Experimental Investigation of Heat Transfer Dependency on Conjugate and Convective Thermal Boundary Conditions in Pin Fin Channel

2015 ◽  
Author(s):  
Weihong Li ◽  
Zhongran Chi ◽  
Rui Kan ◽  
Jing Ren ◽  
Hongde Jiang
Keyword(s):  
Heat Transfer ◽  
Liquid Crystal ◽  
Boundary Conditions ◽  
Internal Wall ◽  
External Temperature ◽  
External Wall ◽  
Pin Fin ◽  
Thermal Boundary Conditions ◽  
Temperature Distributions ◽  
Pin Fin Arrays

The present work experimentally quantifies the effects of thermal boundary conditions, i.e., conjugate and convective boundary conditions, on heat transfer performance for the pin fin channel in trailing edge of gas turbine blade. The geometry of pin fin arrays is typical of x/D=y/D=2.5 and H/D=1. For conjugate case, model is constructed with a relatively high conductivity material so that the Biot number of the model matches engine condition. Uniform heat flux is imposed along the external wall of pin fin arrays and highly resolved temperature distributions of internal wall is obtained with steady liquid crystal, meanwhile external temperature is measured through thermocouples. For convective case, model is constructed with low thermal conductivity material to ensure the usage of transient liquid crystal to obtain heat transfer coefficients of the internal wall on the same configuration. Both the measurements are used as boundary conditions to conduct simulation of solid part of pin fin array. Internal and external wall non-dimensional temperature distributions, as well as isothermal lines distribution, of the two cases are compared, results indicate that it will produce large errors in temperature predictions without considering conjugate effect. Further analysis are made about the mechanism of thermal boundary conditions in determining wall temperature, which demonstrates the necessity of taking conjugate heat transfer effect in turbine cooling design.

scholarly journals Flow and heat transfer of three immiscible fluids in the presence of uniform magnetic field

2014 ◽  
Vol 18 (3) ◽  
pp. 1019-1028 ◽  
Author(s):  
Dragisa Nikodijevic ◽  
Zivojin Stamenkovic ◽  
Milos Jovanovic ◽  
Milos Kocic ◽  
Jelena Nikodijevic
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Conditions ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Immiscible Fluids ◽  
Heat Transfer Characteristics ◽  
Closed Form Solutions ◽  
Electrically Conducting ◽  
Flow And Heat Transfer

The magnetohydrodynamic flow of three immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied magnetic field has been investigated. All three fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and closed-form solutions are obtained in three fluid regions of the channel. Separate solutions with appropriate boundary conditions for each fluid have been obtained and these solutions have been matched at the interface using suitable boundary conditions. The analytical results for various values of the Hartmann number, the ratio of fluid heights and thermal conductivities have been presented graphically to show their effect on the flow and heat transfer characteristics.

Effect of Apex Angle on the Flow and Heat Transfer in Triangular Porous Ducts With Iso-Flux Boundary Conditions

2011 ◽  
Author(s):  
S. Negin Mortazavi ◽  
Fatemeh Hassanipour
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Boundary Conditions ◽  
Integral Method ◽  
Apex Angle ◽  
Triangular Channel ◽  
Flow And Heat Transfer ◽  
Temperature Distributions ◽  
Flux Boundary Conditions

This study presents an analysis of fully developed laminar flow in a porous triangular channel. The flow is assumed to have constant properties and the porous channel is an isotropic matrix. Very accurate analytical solutions are presented by Galerkin Integral method for iso-flux boundary conditions. In this paper, the effect of apex angle in the triangular channel is shown on the velocity and temperature distributions along with the friction factor fRe, and the Nusselt number NuH.

Eigensolutions for Coupled Thermoelastic Vibrations of Timoshenko Beams

1979 ◽  
Vol 46 (1) ◽  
pp. 169-174 ◽  
Author(s):  
R. C. Shieh
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Solution Procedure ◽  
Surface Heat ◽  
Timoshenko Beams ◽  
Thermal Boundary Conditions ◽  
Linear Thermoelasticity ◽  
Special Case

A general solution procedure, together with two special case solutions, for the free-vibration boundary-value problem of a circular or rectangular cross-section Timoshenko beam under general mechanical boundary conditions and the thermal boundary conditions that follow the Newton surface heat transfer law is presented within the context of coupled linear thermoelasticity.

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