Theoretical Analysis of High Prandtl Number Heat Transfer in Non-Isothermal Pipe Flow

2005 ◽  
Author(s):  
Huajun Chen ◽  
Yitung Chen ◽  
Hsuan-Tsung Hsieh ◽  
Taide Tan
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Prandtl Number ◽  
Pipe Flow ◽  
Fourier Expansion ◽  
Mathematical Expressions ◽  
High Prandtl Number ◽  
Turbulent Wall

Based on Fourier expansion, an analytical solution is developed for the high Prandtl number heat transfer in both fully developed laminar and turbulent non-isothermal pipe flow. Both of the mathematical expressions of the temperature distribution and the local Nusselt number have been obtained. A parametric study illustrates the characteristics of high Prandtl number heat transfer in non-isothermal pipe flow in detailed. The solutions obtained can be used for the numerical construction of the solution to the more general problems of heat transfer in the developed turbulent wall-bounded shear flows.

Heat Transfer in Pipe Flow

2008 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Laminar Flow ◽  
Pipe Flow ◽  
Simple Procedure ◽  
Internal Flow ◽  
Uniform Heat Flux ◽  
Flux Boundary Conditions

A simple procedure using spreadsheets is presented where the temperature distribution for laminar flow in a circular pipe is determined from the entrance of the pipe up to the fully developed region is calculated numerically. The results are then used to show the different features of internal flow like constancy of Nusselt number. The solution is presented for both isothermal and uniform heat flux boundary conditions and are then compared with available correlations.

scholarly journals Effect of Prandtl number on heat transfer characteristics in an axisymmetric sudden expansion: A numerical study

2007 ◽  
Vol 11 (4) ◽  
pp. 171-178
Author(s):  
Khalid Alammar
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Study ◽  
Sudden Expansion ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Simulated Effect

Using the standard k-e turbulence model, an incompressible, axisymmetric turbulent flow with a sudden expansion was simulated. Effect of Prandtl number on heat transfer characteristics downstream of the expansion was investigated. The simulation revealed circulation downstream of the expansion. A secondary circulation (corner eddy) was also predicted. Reattachment was predicted at approximately 10 step heights. Corresponding to Prandtl number of 7.0, a peak Nusselt number 13 times the fully-developed value was predicted. The ratio of peak to fully-developed Nusselt number was shown to decrease with decreasing Prandtl number. Location of maximum Nusselt number was insensitive to Prandtl number.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

Effect of Wall Conduction on Combined Free and Forced Laminar Convection in Horizontal Rectangular Channels

1987 ◽  
Vol 109 (4) ◽  
pp. 936-942 ◽  
Author(s):  
G. J. Hwang ◽  
F. C. Chou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Numerical Study ◽  
Fully Developed Flow ◽  
Rectangular Channels ◽  
Laminar Convection

This paper presents a numerical study of the effect of peripheral wall conduction on combined free and forced laminar convection in hydrodynamically and thermally fully developed flow in horizontal rectangular channels with uniform heat input axially, In addition to the Prandtl number, the Grashof number Gr+, and the aspect ratio γ, a parameter Kp indicating the significance of wall conduction plays an important role in heat transfer. A finite-difference method utilizing a power-law scheme is employed to solve the system of governing partial differential equations coupled with the equation for wall conduction. The numerical solution covers the parameters: Pr = 7.2 and 0.73, γ = 0.5, 1, and 2, Kp = 10−4–104, and Gr+ = 0–1.37×105. The flow patterns and isotherms, the wall temperature distribution, the friction factor, and the Nusselt number are presented. The results show a significant effect of the conduction parameter Kp.

Heat Transfer Enhancement in Pipe Flow Problems of a Magnetic Fluid

2007 ◽  
Author(s):  
P. N. Kaloni ◽  
F. Lin ◽  
G. W. Rankin
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Internal Rotation ◽  
Magnetic Fluid ◽  
Pipe Flow ◽  
Magnetic Particles ◽  
Transfer Enhancement ◽  
Cylindrical Pipe ◽  
Flow Problems ◽  
Dissipation Term

Analytical solutions are presented for the temperature distribution and heat transfer coefficient in the forced convection of a magnetic fluid in cylindrical pipe flow. The theory of a ferro-fluid with internal rotation of magnetic particles is employed. Effects of the conventional dissipation term along with the dissipation reflecting the effect of internal rotation are considered and discussed. By computing the Nusselt number in various cases, the influence that different parameters have on the flow are revealed.

Effect of Rarefaction, Dissipation, and Accommodation Coefficients on Heat Transfer in Microcylindrical Couette Flow

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Latif M. Jiji
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Couette Flow ◽  
Knudsen Number ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Rotating Shaft ◽  
Number Range ◽  
Accommodation Coefficients

This paper examines the effects of rarefaction, dissipation, curvature, and accommodation coefficients on flow and heat transfer characteristics in rotating microdevices. The problem is modeled as a cylindrical Couette flow with a rotating shaft and stationary housing. The housing is maintained at uniform temperature while the rotating shaft is insulated. Thus, heat transfer is due to viscous dissipation only. An analytic solution is obtained for the temperature distribution in the gas filled concentric clearance between the rotating shaft and its stationary housing. The solution is valid in the slip flow and temperature jump domain defined by the Knudsen number range of 0.001<Kn<0.1. The important effect of the momentum accommodation coefficient on velocity reversal and its impact on heat transfer is determined. The Nusselt number was found to depend on four parameters: the momentum accommodation coefficient of the stationary surface σuo, Knudsen number Kn, ratio of housing to shaft radius ro∕ri, and the dimensionless group [γ∕(γ+1)](2σto−1)∕(σtoPr). Results indicate that curvature, Knudsen number, and the accommodation coefficients have significant effects on temperature distribution, heat transfer, and Nusselt number.

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