Heat Transfer in Fully-Developed, Laminar Flows of Dissipative Pseudoplastic and Dilatant Fluids in Circular Conduits

2020 ◽  
Author(s):  
Massimo Capobianchi ◽  
Richard Cangelosi ◽  
Patrick McGah
Keyword(s):  
Shear Rate ◽  
Flow Curve ◽  
Numerical Study ◽  
Constant Heat Flux ◽  
Laminar Flows ◽  
Rate Parameter ◽  
Constant Heat ◽  
Shear Rates ◽  
Nusselt Numbers ◽  
Entire Flow

Abstract This paper reports the results of a numerical study that determined the Nusselt number for hydrodynamically and thermally fully-developed, laminar, dissipative flows of pseudoplastic and dilatant fluids through circular conduits. Two boundary conditions were considered, constant heat flux and constant temperature. Constitutive equations were used that describe the entire flow curve, from the zero-shear rate through the infinite-shear rate Newtonian regions, so that computed Nusselt numbers are valid for whatever shear rates may exist in the flow field. Nusselt numbers are reported as a function of a dimensionless shear rate parameter that establishes the region of the flow curve where the system is operating, and are shown to be bound by the Newtonian and power law values. The conditions required for the system to perform at these asymptotic limits are quantified.

Observations of rapidly flowing granular-fluid materials

1985 ◽  
Vol 150 ◽  
pp. 357-380 ◽  
Author(s):  
Daniel M. Hanes ◽  
Douglas L. Inman
Keyword(s):  
Shear Rate ◽  
Granular Material ◽  
Volume Concentration ◽  
Yield Criterion ◽  
Internal Boundary ◽  
Similar Data ◽  
Shear Rates ◽  
Lower Shear ◽  
High Shear Rates ◽  
Entire Flow

The rapid shearing of a mixture of cohesionless glass spheres and air or water was studied in an annular, parallel-plate shear cell designed after Savage (1978). Two types of flow were observed. In the first type of flow the entire mass of the granular material was mobilized. At high shear rates the shear and normal stresses were found to be quadratically dependent upon the mean shear rate (at constant volume concentration), in general agreement with the observations of Bagnold (1954) and Savage & Sayed (1984), and the ‘kinetic’ theory of Jenkins & Savage (1983). The stresses were found to be weakly dependent on the volume concentration up to approximately 0.5, and strongly dependent above this concentration. For flows in which water was the interstitial fluid, the ratio of the shear stress to the normal stress was slightly higher (than in air), and the stresses at lower shear rates were found to be more nearly linearly related to the shear rate. It is suggested that these effects are contributed to by the viscous dampening of grain motions by the water. The second type of flow was distinguished by the existence of an internal boundary above which the granular material deformed rapidly, but below which the granular material remained rigidly locked in place. The thickness of the shearing layer was measured to be between 5 and 15 grain diameters. The stress ratio at the bottom of the shearing layer was found to be nearly constant, suggesting the internal boundary is a consequence of the immersed weight of the shearing grains, and may be described by a Coulomb yield criterion. A scaled concentration is proposed to compare similar data obtained using different-sized materials or different apparatus. An intercomparison of the two types of flow studied, along with a comparison between the present experiments and those of Bagnold (1954) and Savage & Sayed (1984), suggests that the nature of the boundaries can have a significant effect upon the dynamics of the entire flow.

Heat Transfer in Turbulent Pipe Flow With Optically Thin Radiation

1969 ◽  
Vol 91 (3) ◽  
pp. 330-335 ◽  
Author(s):  
C. S. Landram ◽  
R. Greif ◽  
I. S. Habib
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Constant Heat Flux ◽  
Turbulent Pipe Flow ◽  
Radiation Problem ◽  
Constant Heat ◽  
Nusselt Numbers ◽  
Fully Developed Turbulent Flow ◽  
Good Agreement

The problem considered is the determination of the heat transfer in fully developed turbulent flow of a radiating optically thin gas in a circular tube. The radiation problem is formulated in terms of the Planck mean and the modified Planck mean coefficients and the temperature profiles and Nusselt numbers have been determined. It is shown that the simple constant shear, constant heat flux formulation yields results that are in very good agreement with more complex calculations.

Developing Region Solution for High Reynolds Number Laminar Flows of Pseudoplastic and Dilatant Fluids in Circular Ducts

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Massimo Capobianchi ◽  
Patrick McGah
Keyword(s):  
Shear Rate ◽  
Pressure Drop ◽  
Power Law ◽  
Total Pressure ◽  
Correlation Equation ◽  
Laminar Flows ◽  
Graphical Form ◽  
Shear Rates ◽  
Total Pressure Drop ◽  
High Reynolds

This article reports the results of a numerical computation of the length and total pressure drop in the entrance region of a circular tube with laminar flows of pseudoplastic and dilatant fluids at high Reynolds numbers (i.e., approximately 400 or higher). The analysis utilizes equations for the apparent viscosity that span the entire shear rate regime, from the zero to the infinite shear rate Newtonian regions, including the power law and the two transition regions. Solutions are thus reported for all shear rates that may exist in the flow field, and a shear rate parameter is identified that quantifies the shear rate region where the system is operating. The entrance lengths and total pressure drops were found to be bound by the Newtonian and power law values, the former being approached when the system is operating in either the zero or the infinite shear rate Newtonian regions. The latter are approached when the shear rates are predominantly in the power law region but only if, in addition, the zero and infinite shear rate Newtonian viscosities differ sufficiently, by approximately four orders of magnitude or more. For all other cases, namely, when more modest differences in the limiting Newtonian viscosities exist, or when the system is operating in the low- or high-shear rate transition regions, then intermediate results are obtained. Entrance length and total pressure drop values are provided in both graphical form, and in tabular and correlation equation form, for convenient access.

Experimental Study of Heat Transfer in Pulsation Flow in a Rectangular Duct

2012 ◽  
Author(s):  
H. Shokouhmand ◽  
M. Safarifard ◽  
S. M. Emami
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Test Section ◽  
Maximum Velocity ◽  
Constant Heat Flux ◽  
Heat Transfer Characteristics ◽  
Constant Heat ◽  
Nusselt Numbers ◽  
Flow Through ◽  
Minimum Velocity

An experimental study was performed to investigate the heat transfer characteristics of the pulsation flow through a rectangular air duct with aspect ratio of 10. The test section was designed to have a constant heat flux. For pulsating flows, the surface temperatures, the temperature of air at the inlet and at the outlet of the test section, maximum velocity and minimum velocity of air in the test section and the frequencies of pulsation flow were measured and averaged local Nusselt numbers and averaged Nusselt numbers were calculated. The effect of pulsation amplitudes and pulsation frequencies on heat transfer were analyzed.

Natural Convection in a Rectangular Porous Cavity With Constant Heat Flux on One Vertical Wall

1984 ◽  
Vol 106 (1) ◽  
pp. 152-157 ◽  
Author(s):  
V. Prasad ◽  
F. A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Local Heat ◽  
Constant Heat Flux ◽  
Heated Wall ◽  
Width Ratio ◽  
Constant Heat ◽  
Nusselt Numbers

Numerical solutions for two-dimensional, steady, free convection are presented for a rectangular cavity with constant heat flux on one vertical wall, the other vertical wall being isothermally cooled. The horizontal walls are insulated. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers at the heated wall, and the local heat flux at the cooled wall. Flow patterns are observed to be quite different from those in the case of a cavity with both vertical walls at constant temperatures. Specifically, symmetry in the flow field is absent and any increase in applied heat flux is not accompanied by linearly proportional increase in the temperature on the heated wall. Also, for low Prandtl number, the heat transfer rate based upon the mean temperature difference is higher as compared to experimental results for the isothermal case. Heat transfer results, further, indicate that the average Nusselt number is correlated by a relation of the form Nu = constant Ra*mAn, where Ra* is the Rayleigh number and A the height-to-width ratio of the cavity.

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