A Numerical Solution for Laminar-Flow Heat Transfer in Circular Tubes With Axial Conduction and Developing Thermal and Velocity Fields

1967 ◽  
Vol 89 (1) ◽  
pp. 11-16 ◽  
Author(s):  
R. K. McMordie ◽  
A. F. Emery
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Constant Heat Flux ◽  
Velocity Fields ◽  
Constant Heat ◽  
Axial Conduction ◽  
Circular Tubes ◽  
Flow Heat ◽  
Prandtl Numbers ◽  
Radial Convection

This paper describes a numerical calculation of the local Nusselt number for laminar flow in a tube with axial conduction, radial convection, and simultaneously developing thermal and velocity profiles. The results are given for a constant heat flux at the wall and Prandtl numbers from 0.005 to 0.03 with a Pr = 0.7 used to compare with Kays solution.

Entropy Generation Minimization of Fully Developed Internal Convective Flows With Constant Heat Flux

2003 ◽  
Author(s):  
Eric B. Ratts ◽  
Atul G. Raut
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Entropy Generation ◽  
Cross Sections ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Entropy Generation Minimization

This paper addresses the thermodynamic optimum of single-phase convective heat transfer in fully developed flow for uniform and constant heat flux. The optimal Reynolds number is obtained using the entropy generation minimization (EGM) method. Entropy generation due to viscous dissipation and heat transfer dissipation in the flow passage are summed, and then minimized with respect to Reynolds number based on hydraulic diameter. For fixed mass flow rate and fixed total heat transfer rate, and the assumption of uniform heat flux, an optimal Reynolds number for laminar as well as turbulent flow is obtained. In addition, the method quantifies the flow irreversibilities. It was shown that the ratio of heat transfer dissipation to viscous dissipation at minimum entropy generation was 5:1 for laminar flow and 29:9 for turbulent flow. For laminar flow, the study compared non-circular cross-sections to the circular cross-section. The optimal Reynolds number was determined for the following cross-sections: square, equilateral triangle, and rectangle with aspect ratios of two and eight. It was shown that the rectangle with the higher aspect ratio had the smallest optimal Reynolds number, the smallest entropy generation number, and the smallest flow length.

Laminar Slug Flow: Heat Transfer Characteristics With Constant Heat Flux Boundary

2009 ◽  
Author(s):  
P. A. Walsh ◽  
E. J. Walsh ◽  
Y. S. Muzychka
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Heat Transfer Performance ◽  
Constant Heat Flux ◽  
Transfer Performance ◽  
Segmented Flow ◽  
Constant Heat ◽  
Flux Boundary Condition ◽  
Flow Heat

The problem of elevated heat flux in modern electronics has led to the development of numerous liquid cooling devices which yield superior heat transfer coefficients over their air based counterparts. This study investigates the use of liquid/gas slug flows where a liquid coolant is segregated into discrete slugs, resulting in a segmented flow, and heat transfer rates are enhanced by an internal circulation within slugs. This circulation directs cooler fluid from the center of the slug towards the heated surface and elevates the temperature difference at the wall. An experimental facility is built to examine this problem in circular tube flow with a constant wall heat flux boundary condition. This was attained by Joule heating a thin walled stainless steel tube. Water was used as the coolant and air as the segregating phase. The flow rates of each were controlled using high precision syringe pumps and a slug producing mechanism was introduced for segmenting the flow into slugs of various lengths at any particular flow rate. Tube flows with Reynolds numbers in the range 10 to 1500 were examined ensuring a well ordered segmented flow throughout. Heat transfer performance was calculated by measuring the exterior temperature of the thin tube wall at various locations using an Infrared camera. Nusselt number results are presented for inverse Graetz numbers over four decades, which spans both the thermally developing and developed regions. The results show that Nu in the early thermally developing region are slightly inferior to single phase flows for heat transfer performance but become far superior at higher values of inverse Gr. Additionally, the slug length plays an important role in maximizing Nusselt number in the fully developed region as Nu plateaus at different levels for slugs of differing lengths. Overall, this paper provides a new body of experimental findings relating to segmented flow heat transfer in constant heat flux tubes without boiling. Put abstract text here.

Magnetohydrodynamic Effects Upon Heat Transfer for Laminar Flow Across a Flat Plate

1960 ◽  
Vol 82 (2) ◽  
pp. 87-93 ◽  
Author(s):  
R. D. Cess
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Free Stream ◽  
Frictional Heating ◽  
Convection Heat Transfer ◽  
Constant Heat Flux ◽  
Stream Velocity ◽  
Electrically Conducting ◽  
Prandtl Numbers

Forced-convection heat transfer for laminar flow of electrically conducting fluids across a flat plate is considered for a magnetic field of constant inductance acting normal to the free stream velocity and fixed relative to the plate. The boundary condition on the surface of the plate is taken to be either a constant temperature or constant heat flux, and solutions are presented for the following cases: (a) Fluids having a Prandtl number of unity for which both Joule heating and frictional heating are accounted for; (b) fluids having moderate and large Prandtl numbers for negligible Joule and frictional heating; and (c) fluids having low Prandtl numbers for negligible frictional heating.

Sign in / Sign up

Export Citation Format

Share Document