Laminar fully developed flow and heat transfer of Robertson–Stiff fluids in a rectangular duct

2005 ◽  
Vol 83 (2) ◽  
pp. 165-182 ◽  
Author(s):  
M E Sayed-Ahmed ◽  
A S El-Yazal
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Heat Flux ◽  
Physical Parameters ◽  
Rectangular Duct ◽  
Constant Wall Temperature ◽  
Fully Developed Flow ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Constant Wall Heat Flux

The laminar fully developed flow and heat transfer through a rectangular duct of a viscous incompressible Robertson–Stiff fluid is investigated. Robertson–Stiff fluids are time independent non-Newtonian materials possessing a yield value. The governing momentum and energy equations are solved numerically using finite-difference approximations. We consider two cases of thermal boundary conditions: H1 the "circumferentially constant wall temperature and axially constant wall heat flux" and H2 the "circumferentially and axially constant wall heat flux". The velocity, temperature, the average friction factor and Nusselt numbers for the two cases are computed for various values of the physical parameters. The present results have been compared with the known solutions for Newtonian and power-law fluids and are found to be in good agreement.PACS Nos.: 47.50.+d, 47.15.–x

The effect of Hall current on magnetohydrodynamic flow and heat transfer forBingham fluids in a rectangular duct

2005 ◽  
Vol 83 (6) ◽  
pp. 637-651 ◽  
Author(s):  
Mohamed Eissa Sayed-Ahmed ◽  
Hazem Ali Attia
Keyword(s):  
Heat Transfer ◽  
Magnetohydrodynamic Flow ◽  
Rectangular Duct ◽  
Constant Wall Temperature ◽  
Electrically Conducting ◽  
Finite Difference Approximations ◽  
Thermal Boundary Conditions ◽  
Flow And Heat Transfer ◽  
Constant Wall Heat Flux ◽  
Energy Equations

Laminar fully developed magnetohydrodynamic flow and heat transfer through a rectangular duct are investigated for the case of a viscous incompressible electrically conducting Bingham fluid. A constant pressure gradient and an external uniform magnetic field are applied. The Hall effect is taken into consideration. As thermal boundary conditions, constant wall heat flux is assumed axially and constant wall temperature is assumed peripherally, while the apparent viscosity is assumed to vary with the temperature. The governing momentum and energy equations are solved numerically with finite-difference approximations. The velocity, the temperature, the average friction factor, and the Nusselt number are computed for various values of the physical parameters.PACS Nos.: 44.05.te, 44.10.ti, 44.15.+a, 44.20.+b, 44.35.+c, 47.11.tj

scholarly journals Axisymmetric stagnation-point flow and heat transfer of nanofluid impinging on a cylinder with constant wall heat flux

2019 ◽  
Vol 23 (5 Part B) ◽  
pp. 3153-3164 ◽  
Author(s):  
Hamid Mohammadiun ◽  
Vahid Amerian ◽  
Mohammad Mohammadiun ◽  
Iman Khazaee ◽  
Mohsen Darabi ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Field ◽  
Stagnation Point ◽  
Base Fluid ◽  
Fluid Velocity ◽  
Wall Heat Flux ◽  
Flow And Heat Transfer ◽  
Constant Wall Heat Flux ◽  
Fluid Velocity Field

The steady-state, viscous flow and heat transfer of nanofluid in the vicinity of an axisymmetric stagnation point of a stationary cylinder with constant wall heat flux is investigated. The impinging free-stream is steady and with a constant strain rate, k ?. Exact solution of the Navier-Stokes equations and energy equation are derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced in this research. The general self-similar solution is obtained when the wall heat flux of the cylinder is constant. All the previous solutions are presented for Reynolds number Re = k ?a2/2n f ranging from 0.1 to 1000, selected values of heat flux and selected values of particle fractions where a is cylinder radius and n f is kinematic viscosity of the base fluid. For all Reynolds numbers, as the particle fraction increases, the depth of diffusion of the fluid velocity field in radial direction, the depth of the diffusion of the fluid velocity field in z-direction, shear-stresses and pressure function decreases. However, the depth of diffusion of the thermal boundary-layer increases. It is clear by adding nanoparticles to the base fluid there is a significant enhancement in Nusselt number and heat transfer.

Taylor-Heat Flux Effect on Fluid Flow and Heat Transfer in a Curved Rectangular Duct with Rotation

2021 ◽  
Vol 7 (4) ◽  
Author(s):  
Ratan Kumar Chanda ◽  
Mohammad Sanjeed Hasan ◽  
Md. Mahmud Alam ◽  
Rabindra Nath Mondal
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fluid Flow ◽  
Rectangular Duct ◽  
Flow And Heat Transfer

A New Nusselt Number for Complicated Configurations

2013 ◽  
Author(s):  
Tom I-Ping Shih ◽  
Srisudarshan Krishna Sathyanarayanan
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Local Heat ◽  
Negative Slope ◽  
Test Problems ◽  
Rectangular Duct ◽  
Circular Duct ◽  
Flow And Heat Transfer ◽  
Local Heat Flux

Convective heat transfer over surfaces is generally presented in the form of the heat-transfer coefficient (h) or its nondimensional form, the Nusselt number (Nu). Both require the specification of the free-stream temperature (Too) or the bulk (Tb) temperature, which are clearly defined only for simple configurations. For complicated configurations with flow separation and multiple temperature streams, the physical significance of Too and Tb becomes unclear. In addition, their use could cause the local h to approach positive or negative infinity if Too or Tb is nearly the same as the local wall temperature (Twall). In this paper, a new Nusselt number, referred to as the SCS number, is proposed, that provides information on the local heat flux but does not use h and hence by-passes the need to define Too or Tb. CFD analysis based on steady RANS with the shear-stress transport model is used to compare and contrast the SCS number with Nu for two test problems: (1) compressible flow and heat transfer in a straight duct with a circular cross section and (2) compressible flow and heat transfer in a high-aspect ratio rectangular duct with a staggered array of pin fins. Parameters examined include: Reynolds number at the duct inlet (3,000 to 15,000 for the circular duct and 15,000 and 150,000 for the rectangular duct), wall temperature (Twall = 373 K to 1473 K for the circular duct and 313 K and 1,173 K for the rectangular duct), and distance from of the inlet of the duct (up to 100D for the circular duct and up to 156D for the rectangular duct). For the circular duct, Nu was found to decrease rapidly from the duct inlet until reaching a minimum and then to rise until reaching a nearly constant value in the “fully” developed region if the wall is heating the gas. If the wall is cooling the gas, then Nu has a constant positive slope in the “fully” developed region. The location of the minimum in Nu and where Nu becomes nearly constant in value or in slope are strong functions of Twall. For the SCS number, the decrease from the duct inlet is monotonic with a negative slope, whether the wall is heating or cooling the gas. Also, different SCS curves for different Twall approach each other as the distance from the inlet increases. For the rectangular duct, Nu tends to oscillate about a constant value in the pin-fin region, whereas SCS tends to oscillate about a line with a negative slope. For both test problems, the variation of SCS is not more complicated than Nu, but SCS yields the local heat flux without need for Tb, a parameter that is hard to define and measure for complicated problems.

Heat-Transfer Effects on the Developing Laminar Flow Inside Vertical Tubes

1966 ◽  
Vol 88 (2) ◽  
pp. 214-222 ◽  
Author(s):  
W. T. Lawrence ◽  
J. C. Chato
Keyword(s):  
Heat Flux ◽  
Transition Process ◽  
Constant Heat Flux ◽  
Wall Heat Flux ◽  
Axial Position ◽  
Fluid Viscosity ◽  
Constant Heat ◽  
Constant Wall Temperature ◽  
Constant Wall Heat Flux ◽  
Vertical Tubes

A numerical method was developed for the calculation of entrance flows in vertical tubes for the cases of upflow or downflow and constant wall heat flux or constant wall temperature. The solutions were in excellent agreement with experimental data obtained with water flowing upward in a vertical heated tube. The results show that both the density and the viscosity have to be treated as nonlinear functions of temperature. Consequently, for the constant heat flux condition, the velocity and temperature profiles constantly change and never reach “fully developed” states. The transition to turbulent flow was also studied. The experimental measurements demonstrated that the transition process depends on the developing velocity profiles. For the constant heat flux case, transition will always occur at some axial position. For a given entrance condition, the distance to transition is fixed by the fluid flow rate and the wall heat flux. For the experimental results, a tentative transition criterion was obtained, which depends only on the velocity profile shape, fluid viscosity, and the entrance Reynolds number.

A Historical Misperception on Calculating the Average Convection Coefficient in Tubes With Constant Wall Heat Flux

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Ted D. Bennett
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Exact Solutions ◽  
Wall Heat Flux ◽  
First Principle ◽  
Convection Coefficient ◽  
Parallel Plates ◽  
Historical Approach ◽  
First Principle Calculations ◽  
Constant Wall Heat Flux

The historical approach to averaging the convection coefficient in tubes of constant wall heat flux leads to quantitative errors in short tubes as high as 12.5% for convection into fully developed flows and 33.3% for convection into hydrodynamically developing flows. This mistake can be found in teaching texts and monographs on heat transfer, as well as in major handbooks. Using the correctly defined relationship between local and average convection coefficients, eight new correlations are presented for fully developed and developing flows in round tubes and between parallel plates for the constant wall heat flux condition. These new correlations are within 2% of exact solutions for fully developed flows and within 6% of first principle calculations for hydrodynamically developing flows.

Effect of Wall Electrical Conductance on Magnetohydrodynamic Heat Transfer in a Channel

1963 ◽  
Vol 85 (4) ◽  
pp. 371-377 ◽  
Author(s):  
J. T. Yen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Electrical Conductance ◽  
Wall Heat Flux ◽  
Constant Wall Heat Flux

Effect of wall electrical conductance on laminar fully developed magnetohydrodynamic heat transfer in a channel with constant wall heat flux and exact magnetohydrodynamic boundary conditions are investigated. For channels with insulated walls, viscous dissipation is more important than joule heating for all Ec and M. For sufficiently large wall conductance, viscous dissipation is dominated by joule heating for all Ec, if M is large enough; both are in turn dominated by wall heat flux if Ec is large enough for all M. These and other conclusions are discussed in this paper.

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