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

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 Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

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