Erratum: ‘‘Self-similar expansion of dense matter due to heat transfer by nonlinear conduction’’ [Phys. Fluids 28, 232 (1985)]

1986 ◽  
Vol 29 (4) ◽  
pp. 1340 ◽  
Author(s):  
R. Pakula ◽  
R. Sigel
Keyword(s):  
Heat Transfer ◽  
Dense Matter ◽  
Nonlinear Conduction ◽  
Self Similar

scholarly journals Heat transfer enhancement in H2O suspended by aluminium alloy nanoparticles over a convective stretching surface

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402094234
Author(s):  
Adnan ◽  
Syed Zulfiqar Ali Zaidi ◽  
Umar Khan ◽  
Naveed Ahmed ◽  
Syed Tauseef Mohyud-Din ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Aluminium Alloy ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Magnetic Field Effects ◽  
Transfer Enhancement ◽  
Convective Condition ◽  
Self Similar ◽  
Increasing Trends

The purpose of this work is to investigate the heat transport on water suspended by aluminium alloy nanomaterials. The analysis is conducted by incorporating the influence of imposed magnetic field and viscous dissipation over convective surface. The self-similar version of the model is treated numerically and the results for the flow field are presented. It is perceived that the velocity of AA7072-H2O and AA7075-H2O declines for stronger magnetic field effects. Due to convective condition, the temperature rises abruptly. Moreover, increasing trends in the local heat transfer rate are examined for higher Biot effects.

Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration

2004 ◽  
Vol 126 (6) ◽  
pp. 997-1005 ◽  
Author(s):  
R. Saleh ◽  
A. B. Rahimi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Axial Velocity ◽  
Time Dependent ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Self Similar ◽  
Suction Rate ◽  
Axial Speed

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity and with uniform normal transpiration Uo are investigated. The impinging free stream is steady and with a constant strain rate k¯. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may move with constant speed, with exponentially increasing–decreasing axial velocity, with harmonically varying axial speed, or with accelerating–decelerating oscillatory axial speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semisimilar solutions of the unsteady Navier–Stokes and energy equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent axial velocity of the cylinder is a step-function, and a ramp function. All the solutions above are presented for Reynolds numbers, Re=ka¯2/2υ, ranging from 0.1 to 100 for different values of dimensionless transpiration rate, S=Uo/ka¯, where a is cylinder radius and υ is kinematic viscosity of the fluid. Absolute value of the shear-stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear- stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder moving with certain exponential axial velocity function at any particular value of Reynolds number and suction rate is axially stress-free. The heat transfer coefficient increases with the increasing suction rate, Reynolds number, Prandtl number, oscillation frequency and amplitude. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration. It is shown that a cylinder with certain type of exponential wall temperature exposed to a temperature difference has no heat transfer.

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

2006 ◽  
Vol 129 (1) ◽  
pp. 106-115 ◽  
Author(s):  
A. B. Rahimi ◽  
R. Saleh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Self Similar

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa2∕2υ, ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U0∕Γa, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

Lie Symmetry Analysis of Boundary Layer Stagnation-Point Flow and Heat Transfer of Non-Newtonian Power-Law Fluids Over a Nonlinearly Shrinking/Stretching Sheet with Thermal Radiation

2018 ◽  
Vol 19 (3-4) ◽  
pp. 415-426 ◽  
Author(s):  
G.C. Layek ◽  
Bidyut Mandal ◽  
Krishnendu Bhattacharyya ◽  
Astick Banerjee
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Power Law ◽  
Stretching Sheet ◽  
Symmetry Analysis ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Self Similar

AbstractA symmetry analysis of steady two-dimensional boundary layer stagnation-point flow and heat transfer of viscous incompressible non-Newtonian power-law fluids over a nonlinearly shrinking/stretching sheet with thermal radiation effect is presented. Lie group of continuous symmetry transformations is employed to the boundary layer flow and heat transfer equations, that gives scaling laws and self-similar equations for a special type of shrinking/stretching velocity ($c{x^{1/3}}$) and free-stream straining velocity ($a{x^{1/3}}$) along the axial direction to the sheet. The self-similar equations are solved numerically using very efficient shooting method. For the above nonlinear velocities, the unique self-similar solution is obtained for straining velocity being always less than the shrinking/stretching velocity for Newtonian and non-Newtonian power-law fluids. The thickness of velocity boundary layer becomes thinner with power-law index for shrinking as well as stretching sheet cases. Also, the thermal boundary layer thickness decreases with increasing values the Prandtl number and the radiation parameter.

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