On Combined Free and Forced Convection in Channels

1960 ◽  
Vol 82 (3) ◽  
pp. 233-238 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Forced Convection ◽  
Rectangular Channel ◽  
Complex Function ◽  
Vertical Channel ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Free And Forced Convection ◽  
Energy Equations ◽  
Helmholtz Wave Equation ◽  
Transfer Problems

The heat-transfer problems of combined free and forced convection by a fully developed laminar flow in a vertical channel of constant axial wall temperature gradient with or without heat generations are approached by a new method. By introducing a complex function which is directly related to the velocity and temperature fields, the coupled momentum and energy equations are readily combinable to a Helmholtz wave equation in the complex domain. This greatly reduces the complexities of the problems. For illustrations, the cases of flows between parallel plates and in a rectangular channel are treated. It shows that this method is more direct and powerful than those of previous investigations.

Optimization of Parallel, Horizontal, and Laminar Forced Air-Cooled Heat Generating Boards

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
M. O. Özdemir ◽  
H. Yüncü
Keyword(s):  
Forced Convection ◽  
Heat Dissipation ◽  
Rectangular Channel ◽  
Numerical Procedure ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Constant Property ◽  
Maximum Heat ◽  
Maximum Heat Transfer ◽  
Optimal Spacing

The objective of this study is to predict numerically the optimal spacing between parallel heat generating boards. The isothermal boards are stacked in a fixed volume of electronic package enclosed by insulated lateral walls, and they are cooled by laminar forced convection of air with prescribed pressure drop. In the numerical procedure, governing equations for the solution of forced convection of constant property incompressible flow through one rectangular channel are solved. Resulting flow and temperature fields in each rectangular channel yield the optimal board-to-board spacing by which maximum heat dissipation rate from the package to the air is achieved. Next, generalized correlations for the determination of the maximum heat transfer rate from the package and optimal spacing between boards are derived in terms of prescribed pressure difference, board length, and density and kinematic viscosity of air. Finally, corresponding correlations are compared with the available two-dimensional studies in literature for infinite parallel plates.

Unsteady Laminar Pulsating Flow in a Saturated Porous Microchannel in the Presence of Electrical Double-Layer Effects

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Muhammad Dilawar Khan Niazi ◽  
Hang Xu
Keyword(s):  
Angular Velocity ◽  
Forced Convection ◽  
Double Layer ◽  
Analytical Solutions ◽  
Electrical Double Layer ◽  
Darcy Number ◽  
Pulsating Flow ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Periodic Pressure

Abstract The forced convection of a pulsating flow in a saturated porous parallel-plates microchannel driven by a periodic pressure in the presence of an electrical double layer is investigated. Such configuration is very important but seldom considered in literature. Analytical solutions for electrical, momentum, and temperature fields are obtained by means of a substitution approach. The results show that the flow fields depend highly on the electro-osmotic parameter κ, the angular velocity parameter Ω, as well as the Darcy number Da.

Optimal Spacings for Mixed Convection

2004 ◽  
Vol 126 (6) ◽  
pp. 956-962 ◽  
Author(s):  
T. Bello-Ochende ◽  
A. Bejan
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Mixed Convection ◽  
Forced Convection ◽  
Geometry Optimization ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Dimensionless Groups ◽  
Drop Number ◽  
Single Formula

This paper completes the description of geometry optimization in stacks of parallel plates that generate heat. The spacing between plates, or the number of plates in a fixed volume, has been maximized in two limits: pure natural convection and pure forced convection. In this paper, the in-between regime of mixed convection is modeled numerically. After simulating the flow and temperature fields in configurations with a variety of spacings, this paper reports the optimal spacings and the dimensionless groups that govern them (Rayleigh number, pressure drop number, mixed convection ratio). It shows that the numerical results match the results in the limits of natural convection and forced convection. The paper constructs a correlation that bridges the gap between the two limits, and provides a single formula for optimal spacings covering the entire domain, from natural convection to forced convection.

scholarly journals A Pore-Scale Investigation of the Transient Response of Forced Convection in Porous Media to Inlet Ramp Inputs

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Rabeeah Habib ◽  
Bijan Yadollahi ◽  
Nader Karimi
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Forced Convection ◽  
Transient Response ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Pore Scale ◽  
Staggered Arrangement ◽  
Energy Equations ◽  
Convection In Porous Media

Abstract This paper investigates the transient response of forced convection of heat in a reticulated porous medium through taking a pore-scale approach. The thermal system is subject to a ramp disturbance superimposed on the entrance flow temperature/velocity. The developed model consisted of ten cylindrical obstacles aligned in a staggered arrangement with set isothermal boundary conditions. A few types of fluids, along with different values of porosity and Reynolds number, are considered. Assuming a laminar flow, the unsteady Navier Stokes and energy equations are solved numerically. The temporally developing flow and temperature fields as well as the surface-averaged Nusselt numbers are used to explore the transient response of the system. Also, a response lag ratio (RLR) is defined to further characterize the transient response of the system. The results reveal that an increase in amplitude increases the RLR. Nonetheless, an increase in ramp duration decreases the RLR, particularly for high-density fluids. Interestingly, it is found that the Reynolds number has almost negligible effects upon RLR. This study clearly reflects the importance of conducting pore-scale analyses for understanding the transient response of heat convection in porous media.

Effects of Important Parameters on the Transition from Forced to Mixed Convection Flow in a Square Cavity

2021 ◽  
Vol 406 ◽  
pp. 36-52
Author(s):  
Sofiane Boulkroune ◽  
Omar Kholai ◽  
Brahim Mahfoud
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Forced Convection ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Convection Flow ◽  
Square Cavity ◽  
Left Wall ◽  
Energy Equations

Combined free and forced convection in a square cavity filled with a viscous fluid characterized by a small Prandtl number is studied numerically. The left wall is moving with a constant velocity v and is maintained at a local cold temperature Tc, while the right wall is fixed and maintained at a local hot temperature Th (Tc <Th). The top and bottom walls of the cavity is assumed to be adiabatic. The governing Navier-Stokes, and energy equations along with appropriate boundary conditions are solved using the finite-volume method. The flow and temperature fields are presented by stream function and isotherms, respectively. The effects of important parameters such as Reynolds number, Prandtl number, and Grashof number on the transition from forced convection to mixed convection are investigated. Results indicate that increasing Reynolds number results to fluid acceleration and, thus, to flow transition. Results also show that Grashof and Prandtl's numbers influenced the conditions for the transition to the mixed convection regime.

On Unsteady Heat Transfer of Combined Free and Forced Convection in Circular Tubes

1963 ◽  
Vol 30 (2) ◽  
pp. 257-262 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Wall Temperature ◽  
Time Variation ◽  
Circular Tube ◽  
Unsteady Heat Transfer ◽  
Transient Problem ◽  
Axial Temperature ◽  
Free And Forced Convection ◽  
Transfer Problems

The unsteady heat-transfer problems of combined free and forced convection of a fully developed laminar flow of a heat-generating fluid in a circular tube with constant axial temperature gradient at the wall are investigated. The general solution with arbitrary time-dependent pressure gradient, heat generation, and wall temperature is established by the application of the “generalized Duhamel’s theorem.” Two specific cases are then studied. The results indicate that this type of transient problem has a time-variation of an oscillatory type with decaying amplitude. This time-variation is different from that of forced convection or of combined free and forced convection with constant axial wall temperature.

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