Heat and Mass Transfer on the Unsteady Magnetohydrodynamic Flow Due to a Porous Rotating Disk Subject to a Uniform Outer Radial Flow

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Heat Transfer ◽  
Radial Flow ◽  
Magnetic Interaction ◽  
Rotating Disk ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Shear Stresses ◽  
Surface Shear ◽  
Entire Family ◽  
Integration Algorithm

An unsteady flow and heat transfer of an incompressible electrically conducting fluid over a porous rotating infinite disk impulsively set into motion are studied in the present paper. The disk finds itself subjected to a uniform normal magnetic field. The particular interest lies in searching for the effects of an imposed uniform outer radial flow far above the disk on the behavior of the physical flow. The governing Navier–Stokes and Maxwell equations of the hydromagnetic fluid, together with the energy equation, are converted into self-similar forms using suitable similarity transformations. A compact, unconditionally stable, and highly accurate implicit spectral numerical integration algorithm is then employed in order to resolve the transient behavior of the velocity and temperature fields. The time evolution and steady state case of some parameters of fundamental physical significance such as the surface shear stresses in the radial and tangential directions and the heat transfer rate are also fully examined for the entire family of magnetic interaction, radial flow, and suction/blowing parameters.

scholarly journals Series solutions for the flow in the vicinity of the equator of an MHD boundary-layer over a porous rotating sphere with heat transfer

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 527-537 ◽  
Author(s):  
Mohammad Rashidi ◽  
Navid Mehr
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Fields ◽  
Strength Parameter ◽  
Shear Stresses ◽  
Surface Shear ◽  
Rotating Sphere ◽  
Mhd Boundary Layer ◽  
Magnetic Strength ◽  
Blowing Parameter

In this paper, an analytical method (DTM-Pad?) is employed to solve the flow and heat transfer near the equator of an MHD boundary-layer over a porous rotating sphere. This method is used to give solutions of nonlinear ordinary differential equations with boundary conditions at infinity. The velocity components in all directions (meridional, rotational and radial) and temperature fields are derived. The obtained results are verified with the results of numerical solution. A very good agreement can be observed between them. The effect of involved parameters such as magnetic strength parameter, rotation number, suction/blowing parameter and Prandtl number on the all-different types of velocity components, temperature field and surface shear stresses in meridional and rotational directions, infinite radial velocity and rate of heat transfer is checked and discussed.

Development of Convective Heat Transfer Near Suddenly Heated, Vertically Aligned Horizontal Wires

1987 ◽  
Vol 109 (4) ◽  
pp. 912-918 ◽  
Author(s):  
J. R. Parsons ◽  
M. L. Arey
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Fluid Layer ◽  
Convective Motion ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Heat Sources ◽  
Transfer Coefficients ◽  
Vertically Aligned ◽  
The Wire

Experiments have been performed which describe the transient development of natural convective flow from both a single and two vertically aligned horizontal cylindrical heat sources. The temperature of the wire heat sources was monitored with a resistance bridge arrangement while the development of the flow field was observed optically with a Mach–Zehnder interferometer. Results for the single wire show that after an initial regime where the wire temperature follows pure conductive response to a motionless fluid, two types of fluid motion will begin. The first is characterized as a local buoyancy, wherein the heated fluid adjacent to the wire begins to rise. The second is the onset of global convective motion, this being governed by the thermal stability of the fluid layer immediately above the cylinder. The interaction of these two motions is dependent on the heating rate and relative heat capacities of the cylinder and fluid, and governs whether the temperature response will exceed the steady value during the transient (overshoot). The two heat source experiments show that the merging of the two developing temperature fields is hydrodynamically stabilizing and thermally insulating. For small spacing-to-diameter ratios, the development of convective motion is delayed and the heat transfer coefficients degraded by the proximity of another heat source. For larger spacings, the transient behavior approaches that of a single isolated cylinder.

Thermal Convection in an Infinite Porous Medium Induced by a Heated Sphere

1997 ◽  
Vol 119 (3) ◽  
pp. 647-650 ◽  
Author(s):  
R. Ganapathy
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Rayleigh Number ◽  
Free Convection ◽  
Wall Temperature ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Series Expansions ◽  
Medium Permeability ◽  
Velocity And Temperature Fields

This paper investigates the transient behavior of the free convection motion and heat transfer induced by a heated sphere with prescribed wall temperature embedded instantaneously in an infinite porous medium. Solutions for the velocity and temperature fields have been obtained in the form of series expansions in Rayleigh number which is based on the medium permeability and the temperature of the sphere. All discussions are based on the assumption that the flow is governed by Darcy's law and the thermal Rayleigh number is small.

scholarly journals Radiation Effect On Three Dimensional Vertical Channel Flow Through Porous Medium

2015 ◽  
Vol 20 (4) ◽  
pp. 817-833
Author(s):  
M. Guria
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Perturbation Technique ◽  
Vertical Channel ◽  
Temperature Fields ◽  
Shear Stresses ◽  
Radiation Parameter ◽  
Permeability Parameter ◽  
Primary Velocity

Abstract The flow of a viscous incompressible fluid through a vertical channel in the presence of radiation immersed in a porous medium has been studied. Approximate solutions have been obtained for the velocity and temperature fields, shear stresses and rate of heat transfer using the perturbation technique. It is found that the primary velocity decreases with an increase in the radiation parameter as well as the Prandtl number for cooling of the plate. It is also found that with an increase in the permeability parameter, the primary velocity increases for cooling of the plate. The magnitude of the secondary velocity decreases near the plate y = 0 and increases near the plate y = d with an increase in the permeability parameter. The temperature distribution decreases with an increase of the radiation parameter as wall as the Prandtl number for cooling of the plate. The shear stresses and the rate of heat transfer, which are of physical interest, are presented in the form of tables.

Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Viscous Fluid ◽  
Exact Solutions ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Incompressible Viscous Fluid ◽  
Temperature Fields ◽  
Partial Slip ◽  
Shear Stresses ◽  
Rotating Disk Flow

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

Heat Transfer From a Shrouded Rotating Disk to a Single Fluid Stream

1965 ◽  
Vol 87 (4) ◽  
pp. 485-492 ◽  
Author(s):  
J. W. Mitchell ◽  
D. E. Metzger
Keyword(s):  
Heat Transfer ◽  
Gas Turbines ◽  
Radial Flow ◽  
Rotating Disk ◽  
Test Facility ◽  
Algebraic Expression ◽  
Fluid Stream ◽  
Model Study ◽  
Transfer Behavior ◽  
Initial Results

This paper presents the initial results of a model study to determine the heat-transfer characteristics of radial-flow gas turbines. A test facility was constructed and several unconventional experimental techniques were developed for use in the facility. An idealized model consisting of a shrouded rotating disk with a single radially inward airflow was studied. The flow pattern and heat-transfer behavior were analytically and experimentally determined. The experimentally determined heat transfer is correlated by an algebraic expression over the range of nondimensional parameters characteristic of radial-flow gas-turbine operation.

Heat Transfer From a Shrouded Rotating Disk With Film Cooling

1966 ◽  
Vol 88 (1) ◽  
pp. 140-146 ◽  
Author(s):  
D. E. Metzger ◽  
J. W. Mitchell
Keyword(s):  
Heat Transfer ◽  
Film Cooling ◽  
Gas Turbines ◽  
Radial Flow ◽  
Rotating Disk ◽  
Operating Conditions ◽  
Main Stream ◽  
Cooling Method ◽  
Model Study ◽  
Transfer Behavior

A study of the cooling effect of secondary fluid injection on the heat transfer between a shrouded rotating disk and a radially inward main flow stream is presented. The investigation is intended as a model study of film-cooled, radial-flow gas turbines. The film-cooling method is reviewed, and the nondimensional parameters governing the heat transfer are obtained. Experimental results, covering the range of radial-flow, gas-turbine operating conditions, were obtained from a film-heated, rotating-disk facility. The heat-transfer behavior of the main stream only was determined separately, and the film-cooling results are presented as ratios of the heat transfer obtained with film cooling to the heat transfer obtained with only the single radial inflow.

A Numerical Model of the Flow and Heat Transfer in a Rotating Disk Chemical Vapor Deposition Reactor

1987 ◽  
Vol 109 (4) ◽  
pp. 928-935 ◽  
Author(s):  
G. Evans ◽  
R. Greif
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Chemical Vapor Deposition ◽  
Vapor Deposition ◽  
Finite Size ◽  
Chemical Vapor ◽  
Rotating Disk ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Flow And Heat Transfer

Steady, laminar, axisymmetric, and circumferentially uniform flow and heat transfer, including the effects of variable properties and buoyancy, have been modeled within a rotating disk chemical vapor deposition (CVD) reactor. The reactor is oriented vertically, with the hot, isothermal, spinning disk facing upward. The Navier–Stokes and energy equations have been solved for the carrier gas helium. The solutions have been obtained over a range of parameters, which is of importance in CVD applications. The primary parameters are the ratio of the disk temperature to the free stream temperature Tw/T∞, the disk Reynolds number Re = rd2ω/ν∞, a mixed convection parameter Gr/Re3/2 = g(ρ∞ − ρw)/(ρwωων∞), the dimensionless inlet velocity u∞/ων∞, and two geometric parameters ro/rd and L/rd. Results are obtained for the velocity and the temperature fields and for the heat flux at the surface of the rotating disk. Comparisons are made with the one-dimensional, variable-property (excluding buoyant effects), infinite rotating disk solutions of Pollard and Newman. Results are presented in terms of a local Nusselt number. The potential uniformity of CVD in this geometry can be inferred from the variation of the Nusselt number over the surface of the rotating disk. The effects of buoyancy and the finite size of the rotating disk within the cylindrical reactor are clearly evident in the present work.

Oscillatory Magnetothermal Convection of Non-Ferrous Fluid in a Vertical Cylindrical Enclosure With a Heated Rotating Disk at Bottom Center

2010 ◽  
Author(s):  
Masato Akamatsu ◽  
Mitsuo Higano
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Time Dependence ◽  
Transfer Rate ◽  
Magnetic Force ◽  
Rotating Disk ◽  
Temperature Fields ◽  
Magnetic Gradient ◽  
Velocity And Temperature Fields ◽  
Magnetic Center

The non-ferrous fluid is contained in a vertical cylindrical enclosure, which is cooled from both above and side isothermally. The lower end-plate has an isothermally heated disk in the center, while the outer part is thermally insulated. The magnetic gradient generated inside a bore space in a super-conducting magnet as a source of the magnetic force is replaced with that generated by the steady electric current circulating within a single circular electric coil. When the enclosure was installed inside a bore space with the magnetic gradient, our transient three-dimensional numerical computations for a non-ferrous fluid in the enclosure were showed the following numerical results. In the enclosure with the heated static disk at bottom center, when the heated static disk was fixed above the magnetic center, the magnetothermal convection with the symmetric velocity and temperature fields was induced by the magnetic force. The heat transfer rate of magnetothermal convection became larger than that of natural convection. On the other hand, when the heated static disk was fixed below the magnetic center, the magnetothermal convection with the asymmetric velocity and temperature fields was induced by the magnetic force. The heat transfer rate of magnetothermal convection became smaller than that of natural convection. These magnetothermal convections were independent of time. In the enclosure with the heated rotating disk at bottom center, when the heated rotating disk was fixed above the magnetic center, the symmetric magnetothermal convection without the time dependence was also computed. However, when the heated rotating disk was fixed below the magnetic center, the asymmetric magnetothermal convection with the time dependence was computed.

scholarly journals Unsteady MHD Mixed Convection Flow of Non-Newtonian Casson Hybrid Nanofluid in the Stagnation Zone of Sphere Spinning Impulsively

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 197
Author(s):  
Essam R. El-Zahar ◽  
Abd El Nasser Mahdy ◽  
Ahmed M. Rashad ◽  
Wafaa Saad ◽  
Laila F. Seddek
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Convection Flow ◽  
Published Data ◽  
Hybrid Nanofluid ◽  
Shear Stresses ◽  
Stagnation Zone ◽  
Mixed Convection Flow ◽  
Surface Shear

In the present analysis, an unsteady MHD mixed convection flow is scrutinized for a non-Newtonian Casson hybrid nanofluid in the stagnation zone of a rotating sphere, resulting from the impulsive motion of the angular velocity of the sphere and the velocity of the free stream. A set of linearized equations is derived from the governing ones, and these differential equations are solved numerically using the hybrid linearization–differential quadrature method. The surface shear stresses in the x- and y-directions and the surface heat transfer rate are improved due to the Casson βo, mixed convection α, rotation γ and magnetic field M parameters. In addition, as nanoparticles, the solid volume fraction (parameter ϕ) increases, and the surface shear stresses and the rate of heat transfer are raised. A comparison between earlier published data and the present numerical computations is presented for the limiting cases, which are noted to be in very good agreement.

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