Laminar convective heat transfer of non-Newtonian nanofluids with constant wall temperature

Nanofluids are obtained by dispersing homogeneously nanoparticles into a base fluid. Nanofluids often exhibit higher heat transfer rate in comparison with the base fluid. In the present study, forced convection heat transfer under laminar flow conditions was investigated experimentally for three types of non-Newtonian nanofluids in a circular tube with constant wall temperature. CMC solution was used as the base fluid and γ-Al₂O₃, TiO₂ and CuO nanoparticles were homogeneously dispersed to create nanodispersions of different concentrations. Nanofluids as well as the base fluid show shear thinning (pseudoplastic) rheological behavior. Results show that the presence of nanoparticles increases the convective heat transfer of the nanodispersions in comparison with the base fluid. The convective heat transfer enhancement is more significant when both the Peclet number and the nanoparticle concentration are increased. The increase in convective heat transfer is higher than the increase caused by the augmentation of the effective thermal conductivity.     

Experimental and numerical study of turbulent flow and heat transfer inside hexagonal duct

Flow and heat transfer characteristics in transition and turbulent regions are studied experimentally and numerically in a horizontal smooth regular hexagonal duct under constant wall temperature boundary condition covering a range of Reynolds number from 2.3 × 10³ to 52 × 10³. Two types of k-omega (standard and shear stress transport (SST)) and three types of k-ε (standard, renormalization (RNG), and realizable) turbulence model are employed for transition and turbulent regions, respectively. Both average and fully developed Darcy friction factor and Nusselt number are presented as a function of Reynolds number. It is seen that k-omega SST and k-ε realizable turbulence models gave the best agreement with the experimental data in transition and turbulent regions, respectively. All the experimental results are correlated within an accuracy of ±13 % and ±7 % for Nusselt number and Darcy friction factor, respectively. Results obtained in this study are compared with circular duct results using hydraulic diameter.     

Experimental and numerical investigation of transition to turbulent flow and heat transfer inside a horizontal smooth rectangular duct under uniform bottom surface temperature

In this study, steady-state turbulent forced flow and heat transfer in a horizontal smooth rectangular duct both experimentally and numerically investigated. The study was carried out in the transition to turbulence region where Reynolds numbers range from 2,323 to 9,899. Flow is hydrodynamically and thermally developing (simultaneously developing flow) under uniform bottom surface temperature condition. A commercial CFD program Ansys Fluent 12.1 with different turbulent models was used to carry out the numerical study. Based on the present experimental data and three-dimensional numerical solutions, new engineering correlations were presented for the heat transfer and friction coefficients in the form of $ {\text{Nu}} = {\text{C}}_{2} {\text{Re}}^{{{\text{n}}_{ 1} }} $ and $ {\text{f}} = {\text{C}}_{3} {\text{Re}}^{{{\text{n}}_{3} }} $ , respectively. The results have shown that as the Reynolds number increases heat transfer coefficient increases but Darcy friction factor decreases. It is seen that there is a good agreement between the present experimental and numerical results. Examination of heat and mass transfer in rectangular cross-sectioned duct for different duct aspect ratio (α) was also carried out in this study. Average Nusselt number and average Darcy friction factor were expressed with graphics and correlations for different duct aspect ratios.     

Combined radiative and convective heat transfer in a three-dimensional rectangular channel at different wall temperatures

 This paper deals with a numerical study of combined convective and radiative heat transfer in a three-dimensional rectangular duct with hydrodynamically and thermally developing laminar flow. The gas is assumed to be an incompressible, absorbing, emitting, isotropically scattering, gray medium. Isothermal, gray, diffuse boundary walls at different temperatures are assumed. The finite-volume method (FVM) is adopted to describe both convective and radiative heat transfer. The coupled continuity and momentum equations are solved by means of SIMPLER algorithm. Numerical results for the radiative flux show very good agreement with the available data. The effects of aspect ratio, optical thickness, scattering albedo and wall emissivity on the mean bulk temperature are also investigated. By splitting the heat flux into convective and radiative contributions, the relative importance of these components is assessed for a typical range of values of the parameters. Received on 9 February 1999     

Experimental study on axial wall heat conduction for convective heat transfer in stainless steel microtube

Distilled water and nitrogen gas used as the working fluids flow through the stainless steel microtube with inner diameter 168 μm outer diameter 406 μm. Using the Joule heating, the wall temperature field photos of the microtube is acquired by employing an IR camera and the temperature and the volume flow rate of the inlet and the outlet of microtube are measured. A correlation between the axial wall heat conduction and the convective heat transfer is obtained by theoretical analysis based on the experimental results. The investigative results clearly show that the axial heat conduction can reduce the convective heat transfer in the stainless steel microtube and the decrement may reach 2% compared to the convective heat transfer when the working fluid is nitrogen gas, however, the decrement can be neglected for distilled water as the working fluid.     

Turbulent flow and convective heat transfer in a wavy wall channel

This paper reports the numerical modeling of turbulent flow and convective heat transfer over a wavy wall using a two equations eddy viscosity turbulence model. The wall boundary conditions were applied by using a new zonal modeling strategy based on DNS data and combining the standard k– turbulence model in the outer core flow with a one equation model to resolve the near-wall region.It was found that the two-layer model is successful in capturing most of the important physical features of a turbulent flow over a wavy wall with reasonable amount of memory storage and computer time. The predicted results show the shortcomings of the standard law of the wall for predicting such type of flows and consequently suggest that direct integrations to the wall must be used instead. Moreover, Comparison of the predicted results of a wavy wall with that of a straight channel, indicates that the averaged Nusselt number increases until a critical value is reached where the amplitude wave is increased. However, this heat transfer enhancement is accompanied by an increase in the pressure drop.     

Transient free convective flow in a vertical channel with constant temperature and constant heat flux on walls

This note presents transient motion of a viscous and incompressible fluid in a vertical channel due to free convective currents occuring as a result of application of constant heat flux at one wall and constant temperature on other wall. The method of Laplace transform is used to solve the problem. The transient behaviour of flow on velocity and temperature fields are shown on the graphs.     

A new numerical scheme for convective dominated heat transfer in a porous medium with strong temperature gradients

A new numerical scheme, theimplicit correction scheme, has been developed for heat transfer in a porous medium with strong temperature gradients. The scheme includes diffusion, convection and transverse heat transfer processes. By using correction coefficients which are based on transverse heat transfer, the effects of convection enthalpy flow and diffusion are modified. Under suitable limiting conditions, the implicit correction scheme can be reduced to the central-difference, upwind, or power-law scheme. The correction scheme is shown to be especially useful in calculations of the thermal effectiveness of the regenerator in Stirling cycle refrigeration.     

Direct numerical simulation of turbulent heat transfer in a square duct with transverse ribs mounted on one wall

Turbulent heat transfer in a ribbed square duct of three different blockage ratios are investigated using direct numerical simulation (DNS). The results of ribbed duct cases are compared with those of a heated smooth duct flow. It is observed that owing to the existence of the ribs and confinement of the duct, organized secondary flows appear as large streamwise-elongated vortices, which intensely interact with the rib elements and four sidewalls and have profound influences on the transport of momentum and thermal energy. This study also shows that the drag and heat transfer coefficients are highly sensitive to the rib height. It is observed that as the rib height increases, the impinging effect of the flow on the windward face of the rib strengthens, leading to enhanced rates of turbulent mixing and heat transfer. The influence of sidewalls and rib height on the turbulence structures associated with temperature fluctuations are analyzed based on multiple tools such as vortex swirling strengths, temporal auto-correlations, spatial two-point cross-correlations, joint probability density functions (JPDF) between the temperature and velocity fluctuations, statistical moments of different orders, and temperature spectra.     

An improved numerical algorithm for solution of convective heat transfer problems on nonstaggered grid system

In this paper, a SIMPLE-like algorithm on co-located grid system has been developed. The ability to suppress the spurious pressure field is achieved via introducing the pressure difference between adjacent two grid points into the convection-diffusion finite difference scheme, and the interfacial velocity is obtained by simple linear interpolation. The differencing scheme, discretization of governing equations and solution procedure of the algorithm are described in detail. In order to check the validity of the algorithm, several test cases which have analytical or benchmark solutions are presented. Good agreements are obtained between the numerical and the corresponding analytical or benchmark solutions. The ability of the improved algorithm to suppress the spurious pressure field is demonstrated via a 3-D example. Received on 11 March 1997     

A numerical and experimental study of natural convective heat transfer from an inclined isothermal square cylinder with an exposed top surface

Natural convective heat transfer from an isothermal inclined cylinder with a square cross-section which have an exposed top surface and is, in general, inclined at an angle to the vertical has been numerically and experimentally studied. The cylinder is mounted on a flat adiabatic base plate, the cylinder being normal to the base plate. The numerical solution has been obtained by solving the dimensionless governing equations subject to the boundary conditions using the commercial cfd solver, FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. Results have only been obtained for Prandtl number of 0.7. Values of inclination angle between 0° and 180° and a wide range of Rayleigh number and the dimensionless cylinder width, W = w/h, have been considered. The effects of Dimensionless widths, Rayleigh numbers, and inclination angles on the mean Nusselt number for the entire cylinder and for the mean Nusselt numbers for the various surfaces that make up the cylinder have been examined. Empirical equations for the heat transfer rates from the entire cylinder have been derived.     

The effect of velocity distribution on forced convection laminar flow heat transfer in a pipe at constant wall temperature

In this paper, a theoretical study of heat transfer to a fluid of vanishing viscosity in laminar flow in a pipe is made. The constant wall temperature boundary condition is considered in order to facilitate comparison with other classical solutions. Using velocity profiles of simple geometrical shape, the dependence of the heat transfer on velocity distribution is illustrated. Because of the nature of the idealised flow and heat transfer models, the theoretical results are applicable to all axisymmetric flows. Accordingly, some account of the possible effects of swirl on heat transfer in real flows is given.

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Zusammenfassung Es handelt sich um eine theoretische Untersuchung des Wärmeübergangs in laminarer Rohrströmung bei verschwindender Viskosität. Zum Vergleich mit anderen klassischen Lösungen wurde konstante Wandtemperatur als Randbedingung vorgegeben. Unter Benutzung von Geschwindigkeitsprofilen einfacher Geometrie wurde deren Einfluß auf den Wärmeübergang ermittelt. Diese Ergebnisse sind wegen der gewählten Strömungs- und Wärmeübergangsmodelle auf alle achsensymmetrischen Strömungen anwendbar. Die mögliche Wirkung einer Wirbelströmung auf den Wärmeübergang wird diskutiert.

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Nomenclature =(k/c) Thermal diffusivity - C, C ₁, C₂, C₃, C_n Constants - c Specific heat at constant pressure - D=(2r_w) Diameter - k Thermal conductivity - M _n Root of Bessel Equation,J ₀(M_n)=0 - r Radius - T Temperature - u, Velocity, average velocity - x Axial distance - X, R Function ofx, (r) alone - _n (= 2M _n/r _w ² ) Eigen value - Dynamic viscosity - (=/) Kinematic viscosity - Density - (=(T-T _w)/(T₁-T_w)) Dimensionless temperature - (=(T–T _w)/(T ₁–T _w)) Nusselt number - Pe (=Re·Pr) Péclet number - Pr (= c/k) Prandtl number - Re(=2r_w·v) Reynolds number Suffixes b Bulk - 1 Inlet - w wall     

Experimental study on forced convective heat transfer of flowing gaseous solid suspension at high temperature

The results of an experimental study of the forced convective heat transfer to helium-graphite suspension at high temperatures up to 1173K are presented. Entering gas Reynolds number ranges from 1.0 x 10⁴ to 2.0 x 10⁴ and the particle loading ratio reaches about 4. The ratio of the Nusselt number of the suspension to that of gas alone increases considerably in a range of high loading ratios as the wall temperature increases. Subsequently, two kinds of turbulence promoters (200 and 400 mm pitch twisted tapes) are inserted in the flowing gaseous solid suspensions to make use of the large inertia forces of particles. The current results show that the local heat fluxes with use of the tapes increase significantly with the rise in the wall temperature owing to the radiative effect of the particulate phase.     

Experimental study on convective heat transfer of TiO2 nanofluids

In this study, nanofluids with different TiO₂ nanoparticle concentrations were synthesized and measured in different constant heat fluxes for their heat transfer behavior upon flowing through a vertical pipe. Addition of nanoparticles into the base fluid enhances the forced convective heat transfer coefficient. The results show that the enhancement of the convective heat transfer coefficient in the mixture consisting of ethylene glycol and distilled water is more than distilled water as a base fluid.     

Momentum and heat transfer in the entrance region of a parallel plate channel: developing laminar flow with constant wall temperature

A new integral method of solution is presented for developing laminar flow and heat transfer in the entrance region of a parallel plate channel with uniform surface temperature. Unlike earlier Karman-Pohlhausen analyses, the new analysis provides solutions which are free from jump discontinuities in the gradients of the velocity and temperature distributions throughout and at the end of the entrance region. The hydrodynamic and thermal results from the present analysis therefore join smoothly and asymptotically to their fully-developed values. The heat transfer results obtained are further found to agree well with previously published numerical solutions.Nomenclature a half width of the channel, m - D _h hydraulic diameter (=4a), m - h local heat transfer coefficient,W/(m²·K) - h _m mean heat transfer coefficient defined by Eq- (9),W/(m²·K) - k thermal conductivity, W/(m·K) - L _H axial length of the hydrodynamic entrance region, m - L _T axial length of the thermal entrance region, m - L _in,H axial length of the hydrodynamic inlet region, m - L _in,T axial length of the thermal inlet region, m - Nu _x local Nusselt number,hD _h /k, dimensionless - Nu _m mean Nusselt number defined by Eq. (9),h _mD_h/k, dimensionless - P pressure, N/m² - P _O pressure at the entrance, N/m² - Pr Prandtl number,c _p /k, dimensionless - Re Reynolds number, 4aU _o /v, dimensionless - T absolute temperature, K - T _b fluid bulk temperature, K - T _c centerline temperature, K - T _w wall temperature, K - U _c centerline velocity, m/s - U ₀ velocity of the fluid at entrance, m/s - U core velocity, m/s - u velocity component inx direction, m/s - v velocity component iny direction, m/s - x spatial coordinate, axial distance, m - y spacial coordinate measured from channel wall, m Greek Letters molecular thermal diffusivity, m²/s - hydrodynamic shape factor, dimensionless - _T thermal shape factor, dimensionless - hydrodynamic boundary layer thickness, m - * /a, dimensionless - _T thermal boundary layer thickness, m - * _{T T} /a, dimensionless - dimensionless distance,y/ ory/a - Pohlhausen's shape factor, dimensionless - dynamic viscosity coefficient, kg/(m·s) - v kinematic viscosity,/, m²/s - dimensionless axial distance,x/(a·Re) - _H dimensionless axial length of the hydrodynamic entrance region (=L _H /(a·Re)) - _T dimensionless axial length of the thermal entrance region (=L _T /(a·Re)) - _in,H dimensionless axial length of the hydrodynamic inlet region (=L _in,H/(a·Re)) - _in,T dimensionless axial length of the thermal inlet region (L _in,T /(a·Re)) - fluid density, kg/m³