On the Nusselt Solution of a Nonisothermal Two-Fluid Inclined Film Flow

Nonisothermal viscous two-fluid flows occur in numerous kinds of coating devices. The corresponding mathematical models often represent two-dimensional free boundary value problems for the Navier-Stokes equations or their modifications. In the present paper we are concerned with a particular problem of coupled heat and mass transfer. Marangoni convection is incorporated, too. The solvability of a corresponding stationary problem is discussed. The obtained results generalize previous results for a similar isothermal problem

Design of Heat Transfer Surfaces in Agitated Vessels

The project on heat transfer surfaces in agitated vessels is based on the determination of the heat exchange area, which is necessary to abide by the process conditions as mixing quality and efficiency of heat transfer. The heat transfer area is determined from the overall heat transfer coefficient (U). The coefficient (U) represents the operation quality in heat transfers being a function of conduction and convection mechanisms. The determination of U is held from the Nusselt’s number, which is related to the dimensionless Reynolds and Prandtl’s, and from the fluid’s viscosity relation that is being agitated in the bulk temperature and the viscosity in the wall’s temperature of heat exchange. The aim of this chapter is to present a summary for the literature concerning heat transfer in agitated vessels (equipped with jackets, helical coils, spiral coils, and vertical tube baffles) and also the many parameters of Nusselt’s equation for these surfaces. It will present a numerical example for a project in an agitated vessel using vertical tube baffles and a 45° pitched blade turbine. Subsequently, the same procedure is held with a turbine radial impeller, in order to compare the heat transfer efficiencies

Laminar film condensation heat transfer on a vertical, non-isothermal, semi-infinite plate

This paper gives similarity transformations for laminar film condensation on a vertical flat plate with variable temperature distribution and finds analytical solutions for arbitrary Prandtl numbers and condensation rates. The work contrasts with Sparrow and Gregg's assertion that wall temperature variation does not permit similarity solutions. To resolve the long debatable issue regarding heat transfer of non-isothermal case, some useful formulas are obtained, including significant correlations for varying Prandtl numbers. Results are compared with the available experimental data

On a two-fluid inclined film flow with evaporation

This paper is concerned with a plane steady-state inclined film flow including evaporation effects. The motion is governed by a free boundary value problem for a coupled system of Navier–Stokes and Stefan equations. The flow domain is unbounded in two directions and it contains a geometrical perturbation on the inclined bottom. Existence and uniqueness of a suitable solution in weighted Sobolev spaces can be proved for small data (perturbation, inclination of the bottom) characterizing the problem

Non-isothermal flow of a thin film of fluid with temperature-dependent viscosity on a stationary horizontal cylinder

A comprehensive description is obtained of the two-dimensional steady gravity-driven flow with prescribed volume flux of a thin film of Newtonian fluid with temperature-dependent viscosity on a stationary horizontal cylinder. When the cylinder is uniformly hotter than the surrounding atmosphere (positive thermoviscosity), the effect of increasing the heat transfer to the surrounding atmosphere at the free surface is to increase the average viscosity and hence reduce the average velocity within the film, with the net effect that the film thickness (and hence the total fluid load on the cylinder) is increased to maintain the fixed volume flux of fluid. When the cylinder is uniformly colder than the surrounding atmosphere (negative thermoviscosity), the opposite occurs. Increasing the heat transfer at the free surface from weak to strong changes the film thickness everywhere (and hence the load, but not the temperature or the velocity) by a constant factor which depends only on the specific viscosity model considered. The effect of increasing the thermoviscosity is always to increase the film thickness and hence the load. In the limit of strong positive thermoviscosity, the velocity is small and uniform outside a narrow boundary layer near the cylinder leading to a large film thickness, while in the limit of strong negative thermoviscosity, the velocity increases from zero at the cylinder to a large value at the free surface leading to a small film thickness

Gravity-driven film flow down a uniformly heated smoothly corrugated rigid substrate

Gravity induced film flow over a rigid smoothly corrugated substrate heated uniformly from below, is explored. This is achieved by reducing the governing equations of motion and energy conservation to a manageable form within the mathematical framework of the well-known long-wave approximation; leading to an asymptotic model of reduced dimensionality. A key feature of the approach and to solving the problem of interest, is proof that the leading approximation of the temperature field inside the film must be nonlinear to accurately resolve the thermodynamics beyond the trivial case of ‘a flat film flowing down a planar uniformly heated incline.’ Superior predictions are obtained compared with earlier work and reinforced via a series of corresponding solutions to the full governing equations using a purpose written finite element analogue, enabling comparisons to be made between free-surface disturbance and temperature predictions, as well as the streamline pattern and temperature contours inside the film. In particular, the free-surface temperature is captured extremely well at moderate Prandtl numbers. The stability characteristics of the problem are examined using Floquet theory, with the interaction between the substrate topography and thermo-capillary instability modes investigated as a set of neutral stability curves. Although there are no relevant experimental data currently available for the heated film problem, recent existing predictions and experimental data concerning the behaviour of corresponding isothermal flow cases are taken as a reference point from which to explore the effect of both heating and cooling

Binary liquid film condensation from water-ammonia vapors mixture flowing downward along a parallel plate condenser

The ammonia-water film condensation is used as an efficient working fluid in industrial applications such as refrigeration, plate condenser and evaporator, absorber/generator heat exchange, air-conditioning, heat pumps and separation processes. The present work focuses on a numerical investigation of water-ammonia condensation on a falling binary liquid film inside a parallel plate condenser by mixed convection. The parallel plate condenser is composed by two parallel vertical plates. One of the plates is wetted by liquidfilm and cooled by the thermal flux cooling while the other plate is isothermal and dry. Parametric computations were performed to investigate the effects of the inlet parameters of gas, the properties of the binary liquid film as well as the thermal flux cooling on the combined mass and heat transfer and on the efficiency of the parallel plate condenser. The results show that an increase in the inlet vapor of ammonia as well as of vapor water enhances the efficiency of the parallel plate condenser. It is shown also that an enhancement of efficiency of the parallel plate condenser has been recorded when the thermal flux cooling and inlet liquid flow rate is elevated. Whereas the increase of the inlet liquid concentration of ammonia inhibits the efficiency of the parallel plate condenser