Computational Study of Convective Transport in a Coating Applicator for a Non-Newtonian Fluid

Convective transport in an optical fiber coating applicator and die system has been simulated for a non-Newtonian fluid. Low-density polyethylene (LDPE) is employed for the numerical analysis, though ultraviolet (UV) curable acrylates are more commonly used, because of a lack of property information for acrylates and similar behavior of these two materials. The equations governing fluid flow and heat transfer are transformed to obtain flow in a cylindrical domain. A numerical scheme similar to the SIMPLE algorithm is developed and employed with a nonuniform grid. Variable fluid properties are employed because of the strong dependence of these on the temperature. In contrast to the isothermal case, streamlines for the non-Newtonian fluid are found to be quite different for various fiber speeds. The temperature level in the applicator is much higher for the Newtonian case, due to the larger fluid viscosity and associated viscous dissipation. The shear near the fiber is found to be lower for the Newtonian fluid. As expected, the effects become larger with increasing fiber speed. A fairly high temperature rise is observed in the die, regardless of fiber speed. This study focuses on the computational modeling of non-Newtonian effects during the coating process, and several interesting and important features, as compared to the Newtonian case, are observed.     

Thermally dependent viscosity and non-Newtonian flow in a double-pipe helical heat exchanger

A double-pipe helical heat exchanger was numerically studied to determine the effects of thermally dependent viscosity and non-Newtonian flows on heat transfer and pressure drop for laminar flow. Thermally dependent viscosities were found to have very little effect on the Nusselt number correlations for Newtonian fluids; however significant effects on the pressure drop in the heat exchanger were predicted. Changing the flow rate in the annulus can significantly affect the pressure drop in the inner tube, since the average viscosity of the fluid in the inner tube would change due to the change in the average temperature.The effects of non-Newtonian power law fluids on the heat transfer and the pressure drop were determined for laminar flow in the inner tube and in the annulus. The Nusselt number was correlated with the Péclet number for heat transfer in the inner tube. For the annulus, the Nusselt number was found to correlate best with the Péclet number and the curvature ratio. Pressure drop data were compared by using ratios of the pressure drop of the non-Newtonian fluid to a Newtonian fluid at identical mass flow rates and consistency indices.     

Assessment of heat transfer in large parallel plates with a narrow gap maintained at a constant temperature

Investigations are conducted on electromagnetohydrodynamic (EMHD) flow and heat transfer in a third-grade fluid flowing through large parallel plates, which are maintained at constant temperatures. The impact of convective heat transmission is disregarded since the space between the plates is small. The influence of viscous dissipation is considered. Despite being addressed for Newtonian fluids, the conduction problem with the viscous dissipation effect is not examined in third-grade fluids for EMHD flow and heat transfer behavior. The least-square method is adopted to solve nondimensional, nonlinear momentum and energy conservation equations to get the dimensionless velocity, temperature distribution, and heat flux. Temperature and heat flux are investigated in relation to the third-grade fluid parameter, the Hartmann number, the electric field parameter, and the Brinkman number. The findings show a rise in the Brinkman number dramatically increases heat transfer from both walls, necessitating cooling of both plates. The heat flow from both walls increases as the parameters of third-grade fluid increases.     

Thermal characteristics of forced convection in combined pressure and shear-driven flow of a non-Newtonian third-grade fluid through parallel plates

Heat transfer in a non-Newtonian third-grade fluid, flowing under the action of pressure gradient and shear, through two parallel plates, is considered. The upper plate moves with a constant velocity. Constant wall heat fluxes are applied to the plates. Effect of viscous dissipation is included, which has a major role in heat transfer of non-Newtonian fluids. The governing equations are nonlinear and are solved semi-analytically by using the least-square method (LSM). Then, using the solution for velocity in the energy equation, the solution is obtained by a direct integration process. Further, approximate analytical solutions are obtained by the perturbation method, which validates the results generated by the LSM. The effects of the third-grade fluid parameter on the velocity and temperature and also on the physical quantity, such as Nusselt's number, are discussed. Further, viscous dissipation effects on the temperature distribution have been analyzed. Observations show that the movement of the upper plate results in a significant decrease in temperature near the upper plate. For the unit heat flux ratio, the temperature difference between the surface and fluid is more at the upper surface due to the enhanced convective heat transfer caused by the moving upper plate. Nusselt's number increases significantly with an increase in the heat flux ratio.     

Viscous dissipation and heat transfer in pulsatile flows of a yield-stress fluid

The convective heat transfer phenomenon due to viscous dissipation associated with the low Reynolds number pulsatile flow of a non-Newtonian inelastic fluid exhibiting a yield-stress (Bingham fluid) through a circular pipe is studied numerically. The problem is of interest in a number of industrial applications such as the processing of industrial slurries and plastic melts. The singularities due to the infinite value attained by the effective viscosity at zero rates of deformation is avoided by adopting a bi-viscosity model. The flow enhancement characteristic of the pulsatile flows of non-Newtonian fluids affects the associated heat transfer rates in the case of non-isothermal flows. The emphasis in this study is on investigating the effects of the fluid rheology, characterized by the yield number, as well as the frequency of the imposed pulsatile pressure gradient on the fluid flow and its heat transfer characteristics. The presented results reveal the instataneous as well as the time averaged characteristics of the flow and heat transfer phenomena.     

Conjugate forced convection-conduction plate fin in power law fluids

The heat transfer characteristics of laminar, forced convection flow for power law fluids from a vertical plate fin are studied analytically based on the conjugate convection and conduction theory. The resulting boundary layer equations of fluids are coupled with the one-dimensional heat conduction equation of fin through interfacial conditions. Numerical results for the local heat flux, local heat transfer coefficient, and temperature distribution along the fin surface and overall heat transfer rate under the effects of the conjugate convection-conduction parameter, generalized Prandtl number and fluid flow index are illustrated. The results obtained of the non-Newtonian power law fluid are found to have trends similar to those of the Newtonian fluids.     

Heat transfer in a second grade fluid through a porous medium from a permeable stretching sheet with non-uniform heat source/sink

In the present article an analysis is carried out to study the boundary layer flow and heat transfer characteristics of a second grade, non-Newtonian fluid through a porous medium. The stretching sheet is assumed to be permeable so that suction effects come into play. The effects of viscous dissipation, non-uniform heat source/sink on heat transfer are addressed. The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. Analytical solutions are obtained for the resulting boundary value problems. The effects of viscous dissipation and non-uniform heat source/sink, Prandtl number, Eckert number and suction/injection on heat transfer are shown in several plots for two different heating processes (CST and PST cases). Dimensionless surface temperature gradient is tabulated for various values of the governing the parameters.     

The analysis of conjugate problems of conduction and convection for non-Newtonian fluids past a flat plate

In this paper, the conjugate problems of laminar forced convection in non-Newtonian fluid flow and heat conduction inside a heated flat plate is studied. A conjugate parameter ζ is proposed to reflect the characteristics of the conjugate problems. The value of the conjugate parameter lies among 0 and 1 and the two limiting values correspond to the ordinary convection problem with boundary condition of constant wall heat flux (ζ = 0) and constant wall temperature (ζ = 1), respectively. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics, n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of conjugate problems and the whole regime of the non-Newtonian fluids. The effects of the conjugate parameter, the power-law viscosity index and the generalized Prandtl number on the temperature profiles, as well as on the local heat transfer rate are clearly illustrated.     

Laminar Flow and Heat Transfer to a Non-Newtonian Fluid in an Entrance Region of a Square Duct with Prescribed Constant Axial Wall Heat Flux

Abstract

Forced-convection heat transfer information as a function of the pertinent nondimensional numbers is obtained numerically for laminar incompressible non-Newtonian fluid flow in the entrance region of a square duct with simultaneously developing temperature and velocity profiles for constant axial wall heat flux with uniform peripheral wall temperature. The power-law model characterizes the non-Newtonian behavior.

Finite-difference representations are developed for the equations of the mathematical model, and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Results are presented for local and mean Nusselt numbers as functions of the Graetz number and the Prandtl number in the entrance region. Comparisons are made with previous analytical work for Newtonian fluids. The results show a strong effect of the Prandtl number on the Nusselt numbers with fully developed and uniform velocity profiles representing the lower and upper limits, respectively. The results provide a new insight into the true three-dimensional character of the pseudoplastlc fluid flow in the entrance region of a square duct and are accurate.     

Forced convection with viscous dissipation using a two-equation model in a channel filled by a porous medium

The effects of viscous dissipation on the temperature profiles for a fully developed forced convection flow between two parallel plates with a constant heat flux boundary condition are studied. A two-equation model that includes viscous dissipation in the fluid phase is solved analytically and exact solutions for the temperature fields are obtained. Based on the solutions, the effects of several parameters on the transverse temperature profiles and Nusselt number are studied. The solution reducing to two respective limiting situations of slug flow and clear fluid flow agrees with the literature. A comparison with a one-equation model is also presented.     

Free surface dynamics of MHD third-grade fluid model over a heated stretching sheet with variable fluid properties

A thorough investigation of MHD third-grade differential-type fluid flow over a heated stretching sheet is performed in this work. In particular, we analyze the film thinning process, when the thermal sensitive fluid parameters vary due to the effect of heat supplied to the stretching sheet. Starting with a two-dimensional (2D) free surface boundary value problem of non-Newtonian third-grade fluid, we present a systematic derivation of a 1D transient thin-film height equation using longwave analysis with respect to the small aspect ratio of the fluid domain. The derived model is used to study the impact of Newtonian and non-Newtonian parameters with variable fluid properties on the thin film height. The model is discretized using an upwind discretization in space and implicit time integration to guarantee first-order convergence. The model is analyzed thoroughly with the help of numeric computing software MATLAB. The existing findings for a Newtonian fluid are in excellent agreement with derived evidence. In comparison to Newtonian fluid, the study finds that the third-grade parameter causes thinning under different parametric restrictions. Simulations on the coupling effect explain that, the film thickness can be reduced with a high Marangoni number for highly viscous fluids. Also, since the effect of the conductivity parameter can be reduced at a low Prandtl number, the fluid shows a thinning effect. The film thinning rate, on the other hand, is reduced by the magnetic field.     

Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature: Part II. Annular ducts

The present paper, which is an extension of a previous study [O. Jambal, T. Shigechi, D. Ganbat, S. Momoki, Int. Commun. Heat Mass Transf. 32(9) (2005) 1165] on laminar heat transfer to non-Newtonian fluids in parallel plates and circular ducts, deals with concentric annular ducts subjected to a step change in wall temperature. A finite-difference scheme is applied to determine the velocity and temperature fields. Developing Nusselt numbers are graphically shown for various Brinkman numbers and Peclet numbers and the effects of viscous dissipation, fluid axial heat conduction, non-Newtonian behavior together with the radius ratio effect on heat transfer are discussed.     

Effects of dissipation and temperature-dependent viscosity on the performance of plate heat exchangers

The fluid temperature profiles in a multi-passage plate heat exchanger and its effectiveness were calculated with a model which includes dissipation, temperature-dependent viscosity and appropriate correlations for the Nusselt number and the friction coefficient. When the viscosity of the two fluids is low (e.g. water) the results are identical to the classic ε–NTU relations which are obtained by neglecting dissipation and by assuming that fluid properties and heat transfer coefficients are constant. But, when one of the fluids is very viscous (e.g. glycerol) the temperatures of both fluids are significantly higher while the effectiveness can be higher or lower than the value predicted by the classic relations. In particular, for cases with a very viscous hot fluid, the effectiveness may be even higher than unity.     

Performance of Microchannel Heat Sinks with Newtonian and Non-Newtonian Fluids

In this paper, the flow behavior and heat transfer performance of a microchannel heat sink is examined. Microchannel heat sink is a heat exchanger that is used to control the temperature of electronic devices with high heat flux capacity. A comprehensive thermal model for a microchannel should include a three-dimensional conduction analysis in the solid parts, followed by an extensive three-dimensional developing flow in the fluid region. The heat transfer analysis in the transition region of the fluid section is a crucial matter. Hydrodynamic and thermal entrance lengths are two important parameters, among others, which are studied in the solution. To examine the potential of using a non-Newtonian fluid, the power law model was used for both Newtonian and non-Newtonian fluids. The numerical solution of the problem was based on a finite difference approach using a control volume with staggered grid system. The SIMPLE algorithm was applied to the problem, and convection terms were estimated using QUICK method. A comparison of the Newtonian and non-Newtonian results showed that for shear thinning fluids, the pressure drop could reduce up to 45%, while for shear thickening fluids, it can increase up to 48%. The same comparison for the Nusselt number showed about a 160% increase with shear thinning fluids and a 43% decrease with shear thickening fluids. The thermal resistance at a Reynolds number of 50 will reduce approximately 25% with shear thinning fluids and will increase approximately 5% with shear thickening fluids. At higher values of the Reynolds number, the changes in the value of the thermal resistance are more pronounced.     

Heat transfer of a non-Newtonian fluid (Carbopol aqueous solution) in transitional pipe flow

An experimental study of the forced convection heat transfer for non-Newtonian fluid flow in a pipe is presented. We focus particularly on the transitional regime. A wall boundary heating condition of heat flux is imposed. The non-Newtonian fluid used is Carbopol (polyacrylic acid) aqueous solutions. Detailed rheology as well as the variation of the rheological parameters with temperature are reported. Newtonian and shear thinning fluids are also tested for comparative purposes. The characterization of the flow and the thermal convection is made via the pressure drop and the wall temperature measurements over a range of Reynolds number from laminar to turbulent regime. Our measurements show that the non-Newtonian character stabilizes the flow, i.e., the critical Reynolds number to transitional flow increases with shear thinning and yield stress. The heat transfer coefficients are given and compared with heat transfer laws for different regime flows. Details when the heat transfer coefficient loses rapidly its local dependence on the Reynolds number are analyzed.     

Solutal Dispersion and Viscous Dissipation Effects on Non‐Darcy Free Convection Over a Cone in Power‐Law Fluids

The effects of viscous dissipation and solutal dispersion on free convection about an isothermal vertical cone with a fixed apex half angle, pointing downwards in a power‐law fluid‐saturated non‐Darcy porous medium are analyzed. The governing partial differential equations are transformed into partial differential equations using non‐similarity transformation. The resulting equations are solved numerically using an accurate local non‐similarity method. The accuracy of the numerical results is validated by a quantitative comparison of the heat and mass transfer rates with previously published results for a special case and the results are found to be in good agreement. The effects of viscous dissipation, solutal dispersion, and/or buoyancy ratio on the velocity, temperature, and concentration field as well as on the heat and mass transfer rates are illustrated, by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 476–488, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21095     

Predicting turbulent friction factors of non-newtonian fluids in noncircular ducts

On the basis of limited experimental data it appears that the procedure developed by Jones for predicting turbulent friction factors for Newtonian fluids in rectangular and concentric annular ducts may be extended to purely viscous non-Newtonian fluid in noncircular ducts using the Reynolds number introduced by Kozicki.     

Forced convection of non-Newtonian fluids on a heated flat plate

Forced convective heat transfer due to a non-Newtonian fluid flowing past a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved by (numerically) marching downstream from the leading edge as is common for boundary layers involving Newtonian fluids. For shear-thinning and shear-thickening fluids, non-Newtonian effects are illustrated via velocity and temperature distributions, shear stresses, and heat transfer rates. The most significant effects occur near the leading edge, gradually tailing off far downstream where the variation of shear stresses becomes smaller.     

Slip-flow and heat transfer of gaseous flows in the entrance of a wavy microchannel

The present work investigates the developing fluid flow and heat transfer through a wavy microchannel with numerical methods. Governing equations including continuity, momentum and energy with the velocity slip and temperature jump conditions at the solid walls are discretized using the finite-volume method and solved by SIMPLE algorithm in curvilinear coordinate. The effects of creep flow and viscous dissipation are assumed. The numerical results are obtained for various Knudsen numbers. The results show that Knudsen number has declining effect on both the C_f.Re and Nusselt number on the undeveloped fluid flow. Significant viscous dissipation effects have been observed for large Knudsen number. Also, viscous dissipation causes a singular point in Nusselt profiles.     

Heat and mass transfer analysis of chemically reactive tangent hyperbolic fluid in a microchannel

This study addresses the fully developed magnetohydrodynamic flow of non-Newtonian fluid in a microchannel using tangent hyperbolic fluid model. The physical situation has been modeled by accessing boundary layer theory along with the physical aspects of thermophoresis and Brownian motion. The heat and mass transport phenomena are depicted through graphical interpretations. The modeled equations are nondimensionalized using dimensionless variables. The obtained corresponding equations are solved by employing Runge–Kutta–Fehlberg scheme accompanied with shooting technique. The fluctuations in distinct entities of physical connotations, like, the Nusselt number, friction factor and Sherwood number are explored in this examination. A notable reduction in the concentration field of the tangent hyperbolic fluid has been obtained for a larger chemical reaction parameter. The result shows that non-Newtonian fluids exhibit higher Nusselt number than Newtonian fluids. Furthermore, a significant enhancement in Nusselt number has been attained through a rise in the power-law index and thermophoresis aspect.