scholarly journals Natural Convection MHD Effect on Heat Transfer in Vertical Cylinder

2020 ◽  
Vol 8 (5) ◽  
pp. 237-240
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Prandtl Number ◽  
Transfer Equation ◽  
Graphical Representation ◽  
Vertical Cylinder ◽  
Heat Transfer Equation ◽  
Dimensionless Variables ◽  
Dimensionless Heat

In this paper, natural convection MHD effect on Heat transfer in vertical cylinder is analyzed. Firstly heat transfer equation and convert it in dimensionless form by introducing dimensionless variables has considered. By use of finite Hankel and inverse Hankel transforms in dimensionless heat transfer equation, the values of temperature and Nusselt number is obtained. Finally, graphical representation is used to study the effect of Prandtl number pr on temperature and Nusselt number Nu. It is observed that the fluid at the center region of the cylinder is not heated for value of Prandtl number Pr greater than 1.7 for small values of t.

scholarly journals Natural Convection from Four Circular Cylinders in Across Arrangement within Horizontal Annular Space

2020 ◽  
Vol 14 (2) ◽  
pp. 98-102
Author(s):  
Houssem Laidoudi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Prandtl Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Initial Conditions ◽  
Fluid Motion ◽  
Circular Cylinders ◽  
Thermal Buoyancy

AbstractNumerical investigation is accomplished to study the roles of governing parameters of natural convection on the fluid motion and heat transfer rate of four heated circular cylinders placed inside a circular enclosure of cold surface. The cylinders are positioned in across arrangement. The representative results are obtained within the ranges of initial conditions as: Prandtl number (Pr = 7.1 to 1000) and Rayleigh number (Ra = 103 to 105). The average Nusselt number of each inner cylinder is computed. The effects of thermal buoyancy strength on the fluid motion and temperature are also illustrated. It was found that the heat transfer rate of cylinders depends significantly on the position inside the enclosure. Moreover, the role of Prandtl number on flow and thermal patterns is negligible. The values of Nusselt number are also given, which can be useful for some engineering applications.

Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure Due to Uniform and Nonuniform Bottom Heating

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
S. Roy ◽  
Tanmay Basak ◽  
Ch. Thirumalesha ◽  
Ch. Murali Krishna
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nusselt Number ◽  
Natural Convection ◽  
Prandtl Number ◽  
Average Nusselt Number ◽  
Bottom Wall ◽  
Nonuniform Heating ◽  
Triangular Enclosure ◽  
Prandtl Numbers

A penalty finite element analysis with biquadratic elements has been carried out to investigate natural convection flows within an isosceles triangular enclosure with an aspect ratio of 0.5. Two cases of thermal boundary conditions are considered with uniform and nonuniform heating of bottom wall. The numerical solution of the problem is illustrated for Rayleigh numbers (Ra), 103⩽Ra⩽105 and Prandtl numbers (Pr), 0.026⩽Pr⩽1000. In general, the intensity of circulation is found to be larger for nonuniform heating at a specific Pr and Ra. Multiple circulation cells are found to occur at the central and corner regimes of the bottom wall for a small Prandtl number regime (Pr=0.026−0.07). As a result, the oscillatory distribution of the local Nusselt number or heat transfer rate is seen. In contrast, the intensity of primary circulation is found to be stronger, and secondary circulation is completely absent for a high Prandtl number regime (Pr=0.7–1000). Based on overall heat transfer rates, it is found that the average Nusselt number for the bottom wall is 2 times that of the inclined wall, which is well, matched in two cases, verifying the thermal equilibrium of the system. The correlations are proposed for the average Nusselt number in terms of the Rayleigh number for a convection dominant region with higher Prandtl numbers (Pr=0.7 and 10).

Convective Flow in Annuli of Stationary and Rotating Horizontal Cylinders

1997 ◽  
Author(s):  
T. S. Lee
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Cooling System ◽  
Cylindrical Annulus ◽  
Receiver System ◽  
The Mean ◽  
Effects Of Rotation

Heat transfer and fluid flow processes in enclosed spaces have been extensively studied due to their importance in energy conversion, storage and transmission systems. Concentric and eccentric annular geometries are most commonly encountered in solar collector-receiver system, cooling system in nuclear reactors etc. For mixed flow in the annulus between concentric or eccentric cylinders in a rotating system, most work were performed for the cases of vertical cylindrical annulus. More recently, the effects of recirculation on the natural convection between the annular region in horizontal rotating cylinders have become a topic of interest to researchers. The applications of these studies include food processing and the interest in seeking improved methods for crystallographic perfection in industrial processes, above studies are for air with Pr≅1.0. However, other effects of rotation on heat transfer characteristics for low Prandtl number fluids are encountered in high power electric machines with heated shafts, such as a mercury slip ring assembly. For the present study, natural convection is driven by vertical temperature gradient and vertical gravity force. The interaction with the effect of rotation of the inner cylinder is expected to lead to complicated flows. Studies show that the mean Nusselt number increases with Rayleigh number. At a Prandtl number of order 1.0 with a fixed Rayleigh number, when the inner cylinder is made to rotate, the mean Nusselt number decreases through out the flow. At lower Prandtl number of the order 0.1 to 0.01, the mean Nusselt number remained fairly constant with respect to the rotational Reynolds number.

scholarly journals Natural convection of Newtonian fluids between two concentric cylinders of a special cross-sectional form

2020 ◽  
pp. 190-190
Author(s):  
Houssem Laidoudi ◽  
Mustapha Helmaoui ◽  
Mohamed Bouzit ◽  
Abdellah Ghenaim
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Inclination Angle ◽  
Average Nusselt Number ◽  
Outer Cylinder ◽  
Cross Sectional ◽  
The Mean

In this paper, we performed a numerical simulation of natural convection of Newtonian fluids between two cylinders of different cross-sectional form. The inner cylinder is supposed to be hot and the outer cylinder is assumed to be cold. The diameter of inner cylinder to the diameter of outer cylinder defines the radii ratio (RR= 2.5). The governing equations describing the physical behavior of fluid flow and heat transfer are solved using finite volume method. The effects of Prandtl number (Pr = 0.71 to 100), Rayleigh number (Ra = 103 to 105) and inclination angle of inner cylinder (? = 0? to 80?) on streamlines, isotherms and dimensionless velocity are presented and discussed. Also, the mean average Nusselt number of inner cylinder is plotted versus the governing parameters. All present simulations are considered in two-dimensions for steady laminar flow regime. The obtained results showed that the flow between cylinders is more stable for the inclination angle ? = 0?. Increase in Rayleigh number increases the heat transfer rate for all values of inclination angle. Furthermore, the effect of Prandtl number on the mean average Nusselt number becomes negligible when Pr is over the value 7.01. For example at Pr = 0.71 and Ra =105, increase in inclination from 0? to 40?decreases the average Nusselt number by 5.4%. A new correlation is also provided to describe the average Nusselt number as function of Pr and Ra at ? = 0?.

Analytical Solutions of Pennes Bio-Heat Transfer Equation With a Blood Vessel

1994 ◽  
Vol 116 (2) ◽  
pp. 208-212 ◽  
Author(s):  
H. W. Huang ◽  
C. L. Chan ◽  
R. B. Roemer
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Blood Vessel ◽  
Analytical Solutions ◽  
Transfer Equation ◽  
Heat Transfer Equation ◽  
Mean Temperature ◽  
Mixed Mean ◽  
Equilibrium Length

The heat transfer within a perfused tissue in the presence of a vessel is considered. The bio-heat transfer equation is used for the perfused tissue and a lumped capacitance analysis is used for the convection in the vessel with a constant Nusselt number. Analytical solutions are obtained for two cases: (i) the arterial temperature of the perfused blood in the bio-heat transfer equation is equal to the axially varying mixed mean temperature of the blood in the vessel and, (ii) that arterial temperature is assumed to be constant. Dimensionless equilibrium length and temperature expressions are obtained and presented.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

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