Laminar Pipe Flow With Mass Transfer Cooling

1965 ◽  
Vol 87 (2) ◽  
pp. 252-258 ◽  
Author(s):  
Y. Peng ◽  
S. W. Yuan
Keyword(s):  
Temperature Distribution ◽  
Pipe Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Porous Wall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Coolant Injection ◽  
Laminar Pipe Flow ◽  
The Heat Transfer Coefficient

The effect of foreign coolant injection at the wall on the temperature distribution of a laminar flow of a fluid with variable transport and thermodynamic properties in a porous-wall pipe has been investigated. The velocity components, mass concentration, and temperature distribution were obtained by the solution of the Navier-Stokes equations, the diffusion equation, and the energy equation. A perturbation method was used to solve the first equations for small flows through the porous wall, and the eigenvalues in the latter two equations were calculated with the aid of the CDC 1604 computer. The results from this investigation depict the significant differences in both velocity distribution and temperature distribution between the present case of hydrogen coolant and the case of air coolant [1]. The results also show that the heat transfer coefficient at the wall in the present case is considerably smaller than the case of air-coolant injection.

Swirling Laminar Pipe Flow of Suspensions

1973 ◽  
Vol 40 (2) ◽  
pp. 331-336 ◽  
Author(s):  
S. K. Tung ◽  
S. L. Soo
Keyword(s):  
Pipe Flow ◽  
Stokes Equations ◽  
Fluid Phase ◽  
Navier Stokes ◽  
Swirl Ratio ◽  
Particulate Phase ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Flow Reynolds Number ◽  
Laminar Pipe Flow

Vortex pipe flow of suspensions with laminar motion in the fluid phase is treated. The pipe consists of two smoothly joined sections, one stationary and the other rotating with a constant angular velocity. The flow properties of the fluid phase are determined by solving the complete Navier-Stokes equations numerically. The governing parameters are the flow Reynolds number and swirl ratio. Subsequent numerical solution to the momentum equations governing the particulate phase provides for both particle velocity and concentration distributions.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

Numerical Simulation of the Cooling Process of Cubic Shells

2011 ◽  
Author(s):  
Manabu Okura ◽  
Kiyoaki Ono
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Temperature Fields ◽  
Numerical Code ◽  
Navier Stokes ◽  
Cooling Process ◽  
Air Velocity ◽  
Navier Stokes Equations ◽  
The Difference ◽  
The Heat Transfer Coefficient

In order to keep the environment in an air-conditioned room comfortable, it is important to anticipate the air velocity and temperature fields precisely. The numerical code, solving simultaneously the Navier-Stokes equations governing flow field inside and outside the room and the heat conduction equation applying to walls, are developed. The assumption that the heat transfer coefficient between the fluid and the surface of solids is not used. This code is applied to investigate the cooling process of a cubic shell. The computational results agree with the experimental results. We also investigated the same process of the cubic shells whose walls are internally or externally insulated. The difference of the amount of heat transfer will be discussed.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

The evolution of piston-driven pipe flow: thermal transpiration

2006 ◽  
Vol 463 (2079) ◽  
pp. 675-696
Author(s):  
A.M.J Davis
Keyword(s):  
Pipe Flow ◽  
State Transition ◽  
Stokes Equations ◽  
Solvability Condition ◽  
Navier Stokes ◽  
Entry And Exit ◽  
Flow Conditions ◽  
Additional Result ◽  
Navier Stokes Equations ◽  
Thermal Transpiration

The steady-state transition from and to the uniform entry and exit flow profiles is well described, at large aspect ratio, in terms of the stream function by the pipe eigenfunctions. But these latter are unsuited to oscillatory motion or the time evolution of the symmetric piston-driven pipe flow, for which an appropriate solution has a combination of a Fourier series along the finite pipe and a Fourier–Bessel series in the transverse direction. A non-uniqueness requires the identification of a solvability condition and care is needed in demonstrating its satisfaction. An additional result is that the solution must be constructed to satisfy the normal flow conditions identically. Application is made to thermal transpiration, recently explained by the revised Navier–Stokes equations and boundary conditions.

DYNAMIC BEHAVIOR OF A STEADY FLOW IN AN ANNULAR TUBE WITH POROUS WALLS AT DIFFERENT TEMPERATURES

2009 ◽  
Vol 19 (09) ◽  
pp. 2939-2951 ◽  
Author(s):  
JACQUES HONA ◽  
ELISABETH NGO NYOBE ◽  
ELKANA PEMHA
Keyword(s):  
Steady Flow ◽  
Shooting Method ◽  
Energy Equation ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Navier Stokes ◽  
Specific Mass ◽  
Navier Stokes Equations ◽  
Different Temperatures ◽  
Annular Tube

In this paper, the axisymmetric flow of a viscous fluid through a porous annular tube with walls kept at different temperatures is studied theoretically. The physical properties of the fluid remain constant, notably its specific mass, its dynamic viscosity and its thermal diffusivity. The nondimensional parameters which the solutions of the problem depend on are defined. A numerical integration using the shooting method is applied for solving the Navier–Stokes equations and the energy equation. Bifurcation diagrams are presented and enable to highlight significant properties of the flow. Some thermal behaviors corresponding to specific values of the parameters are performed. Asymmetric solutions of the steady flow are described and some results about velocity components are also analyzed.

Effect of Nanofluid Properties on Magnetohydrodynamic Pump (MHD)

2011 ◽  
Vol 403-408 ◽  
pp. 663-669 ◽  
Author(s):  
Azadeh Shahidian ◽  
Majid Ghassemi ◽  
Rafat Mohammadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Al2o3 Nanoparticles ◽  
Nacl Solution ◽  
Navier Stokes Equations ◽  
Side Walls

A Magnetohydrodynamic pump uses the Lorentz effect. It is based on the injection of an electric field into two electrodes located at facing side walls of a channel. The purpose of this study is to numerically investigate the effect of Nanofluid properties on the flow field as well as the temperature distribution in a MHD pump. To solve the non-linear governing differential equations, a finite difference based code is developed and utilized. The temperature and velocity are calculated by solving the energy and Navier-Stokes equations. Result shows that temperature stays almost constant with magnetic field. Furthermore velocity and temperature behaviours are similar for each period. However heat transfer inside the MHD pump varies with nanofluid (NaCl solution and Al2O3 nanoparticles) in comparison with the NaCl solution.

scholarly journals Direct Numerical Simulation of Liquid Flow in a Horizontal Microchannel

2005 ◽  
Author(s):  
Cenk Evren Ku¨krer ◽  
I˙lker Tarı
Keyword(s):  
Liquid Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Micro Channel ◽  
Governing Equations ◽  
Qualitative Comparison ◽  
Navier Stokes Equations ◽  
Axial Conduction ◽  
Micro Channels

Numerical Simulations of liquid flow in a micro-channel between two horizontal plates are performed. The channel is infinite in streamwise and spanwise directions and its height is taken as 3.1×10−4 m which falls within the dimension ranges of micro-channels. The Navier-Stokes equations with the addition of Brinkman number (Br) to the energy equation are used as the governing equations and a spectral methods based approach is applied to obtain the required accuracy to handle liquid flow in the micro-channel. It is known for micro-channels that Br combines the effects of conduction and viscous dissipation in liquids and is also a way of comparing the importance of later relative to former. A laminar flow of a liquid in a micro-channel shows different characteristics compared to a similar flow in a macro-channel. To observe the differences, three different cases are run over each of a range of Reynolds numbers: one with no axial conduction assumption that correspond to a case similar to macro-channel flow, another case with axial conduction included in the energy equation to simulate one of the main differences and lastly a case with inclusion of Br number in the governing equations. The results are compared with each other to see the effects of axial conduction and Br inclusion. A qualitative comparison is made with the previous results in literature.

Sign in / Sign up

Export Citation Format

Share Document