Laminar flow thermal transfer

J. E. Porter and R. Poulter, Electro-Thermal Convection Effects With Laminar Flow Heat Transfer in an Annulus, in Heat Transfer 1970, Proceedings of the 4th International Heat Transfer Conference, vol. 2, paper FC3.7, Elsevier, Amsterdam, 1970. 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

Essentially, except for once-through boilers, steam generation primarily involves two-phase nucleate boiling and convective boiling mechanisms (see Section 1.1). Any deposition at the heat transfer surfaces may disturb the thermal gradient resulting from the initial conduction of heat from the metal surface to the adjacent layer of slower and more laminar flow, inner-wall water and on to the higher velocity and more turbulent flow bulk water. 

Explain the concepts of momentum thickness" and displacement thickness for the boundary layer formed during flow over a plane surface. Develop a similar concept to displacement thickness in relation to heat flux across the surface for laminar flow and heat transfer by thermal conduction, for the case where the surface has a constant temperature and the thermal boundary layer is always thinner than the velocity boundary layer. Obtain an expression for this thermal thickness in terms of the thicknesses of the velocity and temperature boundary layers. 

Chapter 7 deals with the practical problems. It contains the results of the general hydrodynamical and thermal characteristics corresponding to laminar flows in micro-channels of different geometry. The overall correlations for drag and heat transfer coefficients in micro-channels at single- and two-phase flows, as well as data on physical properties of selected working fluids are presented. The correlation for boiling heat transfer is also considered. 

The problem of axial conduction in the wall was considered by Petukhov (1967). The parameter used to characterize the effect of axial conduction is P = (l - dyd k2/k ). The numerical calculations performed for q = const, and neglecting the wall thermal resistance in radial direction, showed that axial thermal conduction in the wall does not affect the Nusselt number Nuco. Davis and Gill (1970) considered the problem of axial conduction in the wall with reference to laminar flow between parallel plates with finite conductivity. It was found that the Peclet number, the ratio of thickness of the plates to their length are important dimensionless groups that determine the process of heat transfer. 

Below we consider a quasi-one-dimensional model of flow and heat transfer in a heated capillary, with hydrodynamic, thermal and capillarity effects. We estimate the influence of heat transfer on steady-state laminar flow in a heated capillary, on the shape of the interface surface and the velocity and temperature distribution along the capillary axis. 

Micro reactors permit high-throughput screening of process chemistries imder controlled conditions, unlike most conventional macroscopic systems [2], In addition, extraction of kinetic parameters from sensor data is possible, as heat and mass transfer can be fully characterized due to the laminar-flow condihons applied. More uniform thermal condihons can also be utilized. Further, reactor designs can be developed in this way that have specific research and development funchons. 

During recent years experimental work continued actively upon the macroscopic aspects of thermal transfer. Much work has been done with fluidized beds. Jakob (D5, J2) made some progress in an attempt to correlate the thermal transport to fluidized beds with transfer to plane surfaces. This contribution supplements work by Bartholomew (B3) and Wamsley (Wl) upon fluidized beds and by Schuler (S10) upon transport in fixed-bed reactors. The influence of thermal convection upon laminar boundary layers and their transition to turbulent boundary layers was considered by Merk and Prins (M5). Monaghan (M7) made available a useful approach to the estimation of thermal transport associated with the supersonic flow of a compressible fluid. Monaghan s approximation of Crocco s more general solution (C9) of the momentum and thermal transport in laminar compressible boundary flow permits a rather satisfactory evaluation of the transport from supersonic compressible flow without the need for a detailed iterative solution of the boundary transport for each specific situation. None of these references bears directly on the problem of turbulence in thermal transport and for that reason they have not been treated in detail. 

The large fluctuations in temperature and composition likely to be encountered in turbulence (B6) opens the possibility that the influence of these coupling effects may be even more pronounced than under the steady conditions rather close to equilibrium where Eq. (56) is strictly applicable. For this reason there exists the possibility that outside the laminar boundary layer the mutual interaction of material and thermal transfer upon the over-all transport behavior may be somewhat different from that indicated in Eq. (56). The foregoing thoughts are primarily suppositions but appear to be supported by some as yet unpublished experimental work on thermal diffusion in turbulent flow. Jeener and Thomaes (J3) have recently made some measurements on thermal diffusion in liquids. Drickamer and co-workers (G2, R4, R5, T2) studied such behavior in gases and in the critical region. 

Heat Transfer and Velocity Distribution in Hydrodynamically and Thermally Developed Laminar Flow in Conduits... 

The physical mechanism of heat transfer in turbulent flow is quite similar to that in laminar flow the primary difference is that one must deal with the eddy properties instead of the ordinary thermal conductivity and viscosity. The main difficulty in an analytical treatment is that these eddy properties vary across the boundary layer, and the specific variation can be determined only from experimental data. This is an important point. All analyses of turbulent... 

Die thermal conductivity k for use in the Nu relations above should be evaluated at the bulk mean fluid temperature, which is the arithmetic average of the mean fluid temperatures at the inlet and the exit of the tube. For laminar flow, the effect of suiface roughness on the friction factor and the heat transfer coefficient is negligible. 

The relative grosvth of the velocity and thermal boundary layers in laminar flow is governed by the Prandtl number, whereas tbe relative growth of the velocity and concentration boundary layers is governed by the Schmidt number. A Prandtl number of near unity (Pr 1) indicates that momentum and heat transfer by diffusion are comparable, and velocity and thermal boundary layers alniosi comcide with each other. A Schmidt number of near unity (Sc = 1) indicates that momentum and mass transfer by difftision are comparable, and velocity and concentration boundary layers almost coincide with each other. 

Tso and Mahulikar [46, 47] proposed the use of the Brinkman number to explain the unusual behaviors in heat transfer and flow in microchannels. A dimensional analysis was made by the Buckingham vr theorem. The parameters that influence heat transfer were determined by a survey of the available experimental data in the literature as thermal conductivity, density, specihc heat and viscosity of the fluid, channel dimension, flow velocity and temperature difference between the fluid and the wall. The analysis led to the Brinkman number. They also reported that viscous dissipation determines the physical limit to the channel size reduction, since it will cause an increase in fluid temperature with decreasing channel size. They explained the reduction in the Nusselt number with the increase in the Reynolds number for the laminar flow regime by investigating the effect... 

Toh et al. [45] investigated numerically three-dimensional fluid flow and heat transfer phenomena inside heated microchannels. The steady, laminar flow and heat transfer equations were solved using a finite-volume method. The numerical procedure was validated by comparing the predicted local thermal resistances with available experimental data. The friction factor was also predicted in this study. It was found that the heat input lowers the frictional losses, particularly at lower Reynolds numbers. Also, at lower Reynolds numbers the temperature of the water increases, leading to a decrease in the viscosity and hence smaller frictional losses. 

Consider steady-state heat transfer in thermally developing, hydrodynamically developed forced laminar flow inside a micro conduits (parallel plate micro channel or micro mbe) under following assumptions o The fluid is incompressible with constant physical properties, o The free heat convection is negligible, o The energy generation is negligible, o The entrance temperature is uniform, o The surface temperature is uniform. 

Consider periodic heat transfer in thermally developing, hydrodynamically developed forced laminar flow inside a parallel plate micro channel or micro tube under following assmnptions ... 

Aparecido, J., and Cotta, R. (1990) Thermally Developing Laminar Flow inside Rectangular Ducts, Int. J. Heat andMass Transfer. Vol. 33, pp. 341-347. 

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