Simultaneous Wall and Fluid Axial Conduction in Laminar Pipe-Flow Heat Transfer

1980 ◽  
Vol 102 (1) ◽  
pp. 58-63 ◽  
Author(s):  
M. Faghri ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Pipe Flow ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Upstream Region ◽  
Heated Region ◽  
Axial Conduction ◽  
Conductance Parameter ◽  
Flow Heat ◽  
Laminar Pipe Flow

Consideration is given to a laminar pipe flow in which the upstream portion of the wall is externally insulated while the downstream portion of the wall is uniformly heated. An analysis of the problem is performed whose special feature is the accounting of axial conduction in both the tube wall and in the fluid. This conjugate heat transfer problem is governed by two dimensionless groups—a wall conductance parameter and the Peclet number, the latter being assigned values from 5 to 50. From numerical solutions, it was found that axial conduction in the wall can carry substantial amounts of heat upstream into the non directly heated portion of the tube. This results in a preheating of both the wall and the fluid in the upstream region, with the zone of preheating extending back as far as twenty radii. The preheating effect is carried downstream with the fluid, raising temperatures all along the tube. The local Nusselt number exhibits fully developed values in the upstream (non directly heated) region as well as in the downstream (directly heated) region. Of the two effects, wall axial conduction can readily overwhelm fluid axial conduction.

Some Boundary Layer-Porous Wall Coupling Effects in Laminar Flows With Surface Injection

1970 ◽  
Vol 92 (3) ◽  
pp. 257-266
Author(s):  
D. A. Nealy ◽  
P. W. McFadden
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Balance ◽  
Transfer Problem ◽  
Porous Wall ◽  
Laminar Flows ◽  
Stream Velocity ◽  
Axial Conduction ◽  
Boundary Layer Development ◽  
Layer Development

Using the integral form of the laminar boundary layer thermal energy equation, a method is developed which permits calculation of thermal boundary layer development under more general conditions than heretofore treated in the literature. The local Stanton number is expressed in terms of the thermal convection thickness which reflects the cumulative effects of variable free stream velocity, surface temperature, and injection rate on boundary layer development. The boundary layer calculation is combined with the wall heat transfer problem through a coolant heat balance which includes the effect of axial conduction in the wall. The highly coupled boundary layer and wall heat balance equations are solved simultaneously using relatively straightforward numerical integration techniques. Calculated results exhibit good agreement with existing analytical and experimental results. The present results indicate that nonisothermal wall and axial conduction effects significantly affect local heat transfer rates.

Heat Transfer in Cavities Having a Fixed Amount of Solid Material

2005 ◽  
Author(s):  
Edimilson J. Braga ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Continuum Model ◽  
Average Nusselt Number ◽  
Numerical Solutions ◽  
Solid Phase ◽  
Transfer Problem ◽  
Void Space ◽  
Fixed Amount ◽  
The Continuum

This work compares two different approaches for obtaining numerical solutions for laminar natural convection within a square cavity, which is filled by a fixed amount of a solid conducting material. The first model considered, namely, porous-continuum model, is based on the assumption that the solid and the fluid phases are seen as the same medium, over which volume-averaged transport equations apply. Secondly, a continuum model is considered to solve the momentum equations for the fluid phase that would resemble a conjugate heat transfer problem in both the solid and the void space. In the continuum model, the solid phase is composed of square obstacles, equally spaced within the cavity. In both models, governing equations are numerically solved using the finite volume method. The average Nusselt number at the hot wall, obtained from the porous-continuum model, for several Darcy numbers, are compared with those obtained with the second approach, namely the continuum model, with different number of obstacles. When comparing the two methodologies, this study shows that the average Nusselt number calculated for each approach for the same Ram differs between each other and that this discrepancy increases as the Darcy number decreases, in the porous-continuum model, or the number of blocks increases and their size decreases, in the continuum model. A correlation is suggested to modify the macroscopic thermal expansion coefficient in order to match the average Nusselt numbers calculated by the two models for Ram = const = 104 and Da ranging from 1.2060×10−4 to 1.

scholarly journals Heat transfer of coal water mixture under laminar pipe flow condition.

1987 ◽  
Vol 13 (6) ◽  
pp. 741-748 ◽  
Author(s):  
Yoshihiko Ninomiya ◽  
Toshiyuki Mori ◽  
Mitsuho Hirato
Keyword(s):  
Heat Transfer ◽  
Pipe Flow ◽  
Flow Condition ◽  
Water Mixture ◽  
Laminar Pipe Flow

scholarly journals Radiative MHD Sutterby Nanofluid Flow Past a Moving Sheet: Scaling Group Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1430
Author(s):  
Mohammed M. Fayyadh ◽  
Kohilavani Naganthran ◽  
Md Faisal Md Basir ◽  
Ishak Hashim ◽  
Rozaini Roslan
Keyword(s):  
Heat Transfer ◽  
Thermal Radiation ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Group Analysis ◽  
Shrinking Sheet ◽  
Nanofluid Flow ◽  
Stagnation Region ◽  
Flow And Heat Transfer ◽  
Scaling Group

The present theoretical work endeavors to solve the Sutterby nanofluid flow and heat transfer problem over a permeable moving sheet, together with the presence of thermal radiation and magnetohydrodynamics (MHD). The fluid flow and heat transfer features near the stagnation region are considered. A new form of similarity transformations is introduced through scaling group analysis to simplify the governing boundary layer equations, which then eases the computational process in the MATLAB bvp4c function. The variation in the values of the governing parameters yields two different numerical solutions. One of the solutions is stable and physically reliable, while the other solution is unstable and is associated with flow separation. An increased effect of the thermal radiation improves the rate of convective heat transfer past the permeable shrinking sheet.

Unsteady conjugated heat transfer in laminar pipe flow

1991 ◽  
Vol 34 (6) ◽  
pp. 1443-1450 ◽  
Author(s):  
S. Olek ◽  
E. Elias ◽  
E. Wacholder ◽  
S. Kaizerman
Keyword(s):  
Heat Transfer ◽  
Pipe Flow ◽  
Conjugated Heat Transfer ◽  
Laminar Pipe Flow

Note on heat transfer in laminar, fully developed pipe flow with axial conduction

1970 ◽  
Vol 21 (2) ◽  
pp. 266-269 ◽  
Author(s):  
Robert L. Ash ◽  
John H. Heinbockel
Keyword(s):  
Heat Transfer ◽  
Pipe Flow ◽  
Axial Conduction
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