A Closed-Form Solution for Laminar Free Convection on a Vertical Plate with Prescribed Nonuniform, Wall Heat Flux

1959 ◽  
Vol 26 (12) ◽  
pp. 846-847 ◽  
Author(s):  
Richard P. Bobco
Keyword(s):  
Heat Flux ◽  
Free Convection ◽  
Closed Form ◽  
Vertical Plate ◽  
Closed Form Solution ◽  
Form Solution ◽  
Wall Heat Flux

Thermal and Fluid Dynamic Model for Capillary-Driven Heat Pipe With Closed-Form Solution

2017 ◽  
Author(s):  
Jesse Maxwell
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Closed Form ◽  
Heat Pipe ◽  
Closed Form Solution ◽  
Constant Heat Flux ◽  
Form Solution ◽  
Constant Heat ◽  
Micro Channels ◽  
Flow Through

A model is derived for the steady state performance of capillary-driven heat pipes on the basis treating fluid flow through miniature- and micro-channels and applied as bulk properties to a large aspect ratio quasi-one-dimensional two-phase system. Surface tension provides the driving force based on an equivalent bulk capillary radius while laminar flow through micro-channels and the vapor core are treated. Heat conduction is accounted for radially while isothermal advection is treated along the axis. A closed-form solution is derived for a steady state heat pipe with a constant heat flux boundary condition on the evaporator as well as a constant heat flux or a convective boundary condition along the condenser. Two solution methods are proposed, and the result is compared to empirical data for a copper-water heat pipe. The components of the closed-form solution are discussed as contributors to driving or frictional forces, and the existence of an optimal pore radius is demonstrated.

scholarly journals Closed-form solution of a thermocapillary free-film problem due to Pukhnachev

2015 ◽  
Vol 26 (5) ◽  
pp. 721-741 ◽  
Author(s):  
BRIAN R. DUFFY ◽  
MATTHIAS LANGER ◽  
STEPHEN K. WILSON
Keyword(s):  
Heat Flux ◽  
Closed Form ◽  
Closed Form Solution ◽  
Critical Value ◽  
Form Solution ◽  
Free Fluid ◽  
Parametric Solution ◽  
Free Film ◽  
Film Version ◽  
Flux Parameter

We consider the steady two-dimensional thin-film version of a problem concerning a weightless non-isothermal free fluid film subject to thermocapillarity, proposed and analysed by Pukhnachev and co-workers. Specifically, we extend and correct the paper by Karabut and Pukhnachev (J. Appl. Mech. Tech. Phys. 49, 568–579, 2008), in which the problem is solved numerically, and in which it is claimed that there exists a unique solution for any value of a prescribed heat-flux parameter in the model. We present a closed-form (parametric) solution of the problem, and from this show that, on the contrary, solutions exist only when the heat-flux parameter is less than a critical value found numerically by Karabut and Pukhnachev, and that when this condition is satisfied there are in fact two solutions, one of which recovers that obtained numerically by Karabut and Pukhnachev, the other being new.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
Sign in / Sign up

Export Citation Format

Share Document