Laminar forced convection to non-Newtonian fluids in ducts with prescribed wall heat flux

Heat transfer in laminar forced convection to non-Newtonian fluids in thermally developing flow inside circular tubes and parallel plate ducts with prescribed wall heat flux is solved exactly. The local and average Nusselt numbers are determined and accuracy of the existing approximate solutions is examined.     

Viscous non-newtonian forced convection heat transfer in semi-circular and equilateral triangular ducts: an experimental study

An experimental study was made of the steady developing laminar convective heat transfer to distilled water and viscous non-Newtonian fluids described by the power law model flowing in straight channels of uniform semi-circular and equilateral triangular cross-sections. Local axial Nusselt number distributions are presented for ducts with the horizontal bottom plane subjected to uniform heat flux while the rest of the channel is well-insulated. The measured Nusselt number distribution for Carbopol 934 solutions compared very well with the numerical predictions using the Galerkin finite element method to solve the governing conservation equations. The effect of Rayleigh number on the heat transfer is discussed. It is shown at high Rayleigh numbers the local Nusselt number shows local minima and maxima whose magnitude depends on the Rayleigh number.     

Numerical study of convective heat transfer to supercritical water in rectangular ducts

Numerical investigation has been performed to analyze forced convective heat transfer to supercritical water in horizontal rectangular ducts. Convective heat transfer near the critical region in the rectangular ducts is strongly influenced by large variations of thermodynamic and transport properties of supercritical fluid with gravity force, especially close to pseudocritical temperature. Fluid flow and heat transfer characteristics such as velocity, temperature, and local heat transfer coefficient with water properties distribution in the ducts are presented. Flow accelerates along the horizontal ducts because of decreased water density from heat transfer at the duct walls. Center of large flow recirculation in the duct section locates near the middle of vertical surface and additional secondary recirculation in clockwise direction appears with the increase of duct height. Local wall temperature severely varies along the inner surface of the duct section and its variation depends on aspect ratio of the duct. The heat transfer coefficient distributions along the ducts for various aspect ratios are compared with the proximity effect to the critical pressure.     

Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature: Part I: Parallel plates and circular ducts

Laminar heat transfer in parallel plates and circular ducts subject to uniform wall temperature is studied by taking into account both viscous dissipation and fluid axial heat conduction in an infinite region. Developing temperature fields are evaluated numerically by a finite-difference method for various Brinkman numbers (Br) and Peclet numbers (Pe). Nusselt numbers are presented graphically for Pe = 10 and Pe → ∞, and Br = 0, ± 0.5 and ± 1 for non-Newtonian fluids described by the power-law model with the flow index of n = 0.5, 1.0 and 1.5. It is shown that Nusselt number has a single fixed value independent of Br in the thermally developing region and its numerical value is equal to that at the fully developed region for non-zero Br, when the preheating of incoming fluid due to both viscous dissipation and fluid axial heat conduction is considered.     

Laminar mixed convection heat and mass transfer in vertical rectangular ducts with film evaporation and condensation

The investigation of mixed convection heat and mass transfer in vertical ducts with film evaporation and condensation has been numerically examined in detail. This work is primarily focused on the effect of film evaporation and condensation along the wetted wall with constant temperature and concentration on the heat and mass transfer in rectangular vertical ducts. The numerical results, including the distributions of dimensionless axial velocity, temperature and concentration distributions, Nusselt number as well as Sherwood number are presented for moist air mixture system with different wall temperatures and aspect ratios of the rectangular ducts. The results show that the latent heat transport with film evaporation and condensation augments tremendously the heat transfer rate. Better heat transfer enhancement related with film evaporation is found for a system with a higher wall temperature.     

Convective heat transfer in cross-corrugated triangular ducts under uniform heat flux boundary conditions

Cross-corrugated triangular ducts provide high heat mass transfer capabilities in membrane based air-to-air heat mass exchangers. The mixing effect would intensify the convective heat mass transfer coefficients on membrane surfaces. In this study, the fluid flow and convective heat transfer in a cross-corrugated triangular duct under uniform heat flux boundary condition is modeled and experimentally studied. A low Reynolds number k–ω (LKW) turbulence model is employed to account for the turbulence in the flow. Heat transfer experiments and high speed hot wire anemometry technology are used to validate the model. The transitional behavior of fluid flow in the duct is disclosed by velocity measurements and Fourier transforms. Correlations are provided for estimation of the pressure drop and the mean Nusselt numbers under uniform heat flux boundary conditions. The established correlations can be extended to estimate the convective mass transfer coefficients through heat mass analogy.     

Laminar flow and heat transfer in plate-fin triangular ducts in thermally developing entry region

Laminar forced flow and heat transfer in plate-fin isosceles triangular ducts encountered in compact heat exchangers is investigated. The flow is hydrodynamically fully developed, but developing thermally under uniform temperature conditions. Heat conduction in the fin of finite conductance and convection in the fluid are analyzed simultaneously as a conjugate problem. The study covers a wide range of apex angles from 30° to 120°, and fin conductance parameters from 0 to infinitely large. Nusselt numbers in the developing and fully developed regions for various apex angles and fin conductance parameters are obtained, which can be used in estimation of heat transfer characteristics in plate-fin compact heat exchangers with fins of various conductivities and thickness.     

Mixed convection heat transfer in horizontal rectangular ducts with radiation effects

The study of mixed convection heat transfer in horizontal ducts with radiation effects has been numerically examined in detail. This work is primarily focused on the interaction of the thermal radiation with mixed convection for a gray fluid in rectangular horizontal ducts. The vorticity–velocity method is employed to solve the three-dimensional Navier–Stokes equations and energy equation simultaneously. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The attention of the results is focused on the effects of thermal buoyancy and radiative transfer on the development of temperature, the friction factor and the Nusselt number. Results reveal that radiation effects have a considerable impact on the heat transfer and would reduce the thermal buoyancy effects. Besides, the development of temperature is accelerated by the radiation effects.     

Laminar heat transfer performance of power law fluids in coiled square tube with various configurations

This study addresses heat transfer performance of laminar non-Newtonian fluid flow in various configurations of coiled square tubes e.g., in-plane spiral ducts, helical spiral ducts and conical spiral ducts. The non-Newtonian fluid considered in this study is the aqueous solution of carboxymethyl cellulose (CMC) which is modeled as power-law fluid. Effects of tube geometries, power-law index (concentration of CMC) and other parameters are quantified and discussed to analyze flow behavior and heat transfer performance. Results are compared with those for a straight square tube of the same length as that used to form the coils. A Figure of Merit is defined to compare the heat transfer performance of different geometries with respect to the pumping power. The results suggest that CMC solution yields better heat transfer performance of about twice than that of water at Re ~ 1000. Among all considered designs, helical coil gives the best heat transfer performance; however, when the pumping power is considered, in-plane coil design performs the best in term of Figure of Merit.     

Mixed convection heat transfer enhancement through film evaporation in inclined square ducts

The investigation of mixed convection heat transfer enhancement through film evaporation in inclined square ducts has been numerically examined in detail. The main parameters discussed in this work include the inclined angle, the wetted wall temperature and the relative humidity of the moist air mixture. The numerical results of the local friction factor, Nusselt number and Sherwood number are presented for moist air mixture system. Attention was particular paid to the effects of latent heat transport on the heat transfer enhancement. Results show that the latent heat transport with film evaporation augments tremendously the heat transfer rate. The heat transfer rate can be enhanced to be 10 times of that without mass transfer, especially for a system with a lower temperature. Besides, better heat and mass transfer rates related with film evaporation are found for case with a higher wetted wall temperature. The increase in the relative humidity of moist air in the ambient causes the decrease in heat transfer enhancement.     

Entrance heat transfer in rectangular ducts with constant axial energy input

The study of heat transfer in the entrance region of ducts with different cross-sections is important in engineering practice. This paper considers laminar, hydrodynamically fully developed flow in the thermal entrance regions of rectangular passages, emphasizing heat transfer aspects. By having a prescribed heating or cooling rate and considering the wall temperature to depend on the axial coordinate alone, the temperature solution leads to an integral equation. Solution of this equation is found using an inverse technique to determine the temperature at the walls. For verification purposes, an asymptotic solution is developed which produces results that agree very well with those from the inverse analysis. The results include a correlation and computed values of the Nusselt number at entrance locations, for rectangular ducts with different aspect ratios.     

Mixed convection heat transfer in inclined rectangular ducts with radiation effects

A numerical study was carried out to investigate the radiation effect on the characteristics of the mixed convection fluid flow and heat transfer in inclined ducts. The three-dimensional Navier–Stokes equations and energy equation are solved simultaneously with the vorticity–velocity method. The integro-differential radiative transfer equation was solved by the discrete ordinates method. The effects of the thermal buoyancy and the radiative transfer on the distributions of the bulk fluid temperature, the friction factor and the Nusselt number are emphasized in detail. Results indicate that radiation effects have a considerable impact on the heat transfer and tend to reduce the thermal buoyancy effects. In addition, the development of the bulk fluid temperature is enhanced by the radiation effects.     

Heat transfer and friction coefficients in corrugated ducts confined by sinusoidal and arc curves

The thermally developing laminar forced-convection flow and heat transfer characteristics in corrugated ducts confined by sinusoidal and arc curves, which are often encountered in honeycomb desiccant wheels, are numerically investigated via the boundary-fitted coordinate system. The control volume-based finite difference technique is applied to obtain the solution utilizing the numerically generated boundary-fitted coordinates. According to this method, the complex domain in the physical plane is transformed into a regular square domain in the computational plane. Studied and graphically illustrated are the effects of aspect ratios and bending ratios of the ducts on the friction coefficients and heat transfer coefficients under uniform wall temperature (T) boundary conditions. For the special cases of corrugated ducts such as circular, square, and flat sinusoidal, the results are compared with some findings in the literature, and very good agreement is obtained. Furthermore, variations of the bulk temperature, Nusselt numbers, velocity, and temperature profiles in the entire thermal entry region are plotted.     

Numerical analysis of laminar heat transfer performance of in-plane spiral ducts with various cross-sections at fixed cross-section area

A numerical approach is carried out to investigate the heat transfer performance of in-plane spiral ducts with various cross sections – rectangular, square, triangular, trapezoidal, circular and half circular. Simulations were carried out at a constant inlet Reynolds number at fixed cross section area for both constant wall temperature and constant wall heat flux conditions. Results are compared to straight ducts of the same cross sections and at the same length as the coiled ducts. The effects of Reynolds number and Prandtl number are also discussed for various geometries. The results are presented and are aimed to determine the advantages, limitations and effects of in-plane spiral ducts of various cross sections on the flow and heat transfer characteristics when the cross section area is fixed.     

Natural convection heat and mass transfer from a vertical truncated cone in a porous medium saturated with a non-Newtonian fluid with variable wall temperature and concentration

This work presents a boundary-layer analysis about the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a porous medium saturated with non-Newtonian power-law fluids. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary-layer equations are solved by the cubic spline collocation method. Results for local Nusselt numbers are presented as functions of power-law indexes, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. The heat and mass transfer rates of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents. Moreover, an increase in the power-law index of fluids tends to decrease the heat and mass transfer from a vertical truncated cone in a porous medium saturated with non-Newtonian power-law fluids.     

Effects of viscous dissipation on forced convective heat transfer in a channel embedded in a power-law fluid saturated porous medium

The convective heat transfer analysis in a channel embedded in a power-law fluid saturated porous medium subject to uniform heat flux is presented and compared with a Newtonian fluid concerning the effects of viscous dissipation. Governing momentum and energy equations for non-Newtonian fluids which accounts for the viscous dissipation effects are solved numerically. The temperature profiles of the non-Newtonian fluids are found to relate closely to the velocity profiles. When viscous dissipation is taken account of, Nusselt numbers for non-Newtonian fluid are found to deviate more from Newtonian fluid with increasing Brinkman number for a certain range of the Darcy number.     

Three-dimensional computational analysis of gas and heat transport phenomena in ducts relevant for anode-supported solid oxide fuel cells

Various transport phenomena occurring in an anode duct of medium temperature solid oxide fuel cell (SOFC) have been simulated and analyzed by a fully three-dimensional calculation method. The considered composite duct consists of a thick porous layer, the gas flow duct and solid current interconnector. Unique fuel cell boundary and interfacial conditions, such as the combined thermal boundary conditions on solid walls, mass transfer associated with the electrochemical reaction and gas permeation across the interface, were applied in the analysis. Based on three characteristic ratios proposed in this study, gas flow and heat transfer were investigated and presented in terms of friction factors and Nusselt numbers. It was revealed that, among various parameters, the duct configuration and properties of the porous anode layer have significant effects on both gas flow and heat transfer of anode-supported SOFC ducts. The results from this study can be applied in fuel cell overall modeling methods, such as those considering unit/stack level modeling.     

Estimation of flow and heat transfer for the design of PV cooling ducts

A practical and convenient procedure is set out, for determining the flow and convective heat transfer in inclined cooling ducts, as used in PV installations. This covers the critical case of free convection, induced only by the buoyancy due to heat input into the duct, when temperatures are highest, those of forced convection induced by wind pressure differences between the duct ends, and the mixed-flow conditions when both influences occur together. The flow regime may be laminar or turbulent. Conditions usually fall in the entrance region of ducts, where temperature and velocity distributions are far from the fully-developed state, and wall friction and heat transfer are enhanced. The main object of the procedure is to generate the set of heat transfer coefficients for the duct walls, required for insertion into the overall thermal model of the PV installation and the underlying building. The effects of the major influences in this area are illustrated by generalised solutions, given in dimensionless forms, for a standard case chosen to approximate to many real situations: the parallel-plate duct with heat input from one side. This shows graphically how the operating conditions and the proportions of the duct affect the flow and heat transfer characteristics, directing attention to situations in which optimum duct designs may be sought.     

Further finite element analyses of fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts: Heat transfer predictions

Forced convection heat transfer to hydrodynamically and thermally fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts has been studied for the H1 and T thermal boundary conditions. The solutions for the velocity and temperature fields were obtained numerically using the finite element method with quartic triangular elements. From these solutions, very accurate Nusselt number values were determined. Computations were performed over a range of power-law indices and duct aspect ratios.     

Laminar flow of viscoelastic fluids in rectangular ducts with heat transfer: A finite element analysis

A numerical study on the laminar flow and heat transfer behavior of viscoelastic fluids in rectangular ducts is conducted using the finite element approach. A Criminale-Ericksen-Fibley relation is applied to describe the viscoelastic character of the fluid, and a hydrodynamically and thermally fully developed flow with the H1 thermal boundary condition is considered. The finite element procedure employed yields essentially mesh-independent predictions with a fairly moderate computational effort. Computed results are presented and discussed in terms of the secondary flow field, the temperature field, the friction factor and the Nusselt number. In particular it is shown that the presence of a secondary flow markedly alters the temperature field and results in a substantial heat transfer enhancement with all duct aspect ratios considered.