Thermally Developing Heat Transfer With Nonlinear Viscoelastic and Newtonian Fluids With Pressure-Dependent Viscosity

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Dennis A. Siginer ◽  
F. Talay Akyildiz ◽  
Mhamed Boutaous
Keyword(s):  
Nusselt Number ◽  
Local Nusselt Number ◽  
Pressure Coefficient ◽  
Maxwell Fluid ◽  
Weissenberg Number ◽  
Newtonian Fluids ◽  
Bulk Temperature ◽  
Constant Wall Temperature ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity

A semi-analytical solution of the thermal entrance problem with constant wall temperature for channel flow of Maxwell type viscoelastic fluids and Newtonian fluids, both with pressure dependent viscosity, is derived. A Fourier–Gauss pseudo-spectral scheme is developed and used to solve the variable coefficient parabolic partial differential energy equation. The dependence of the Nusselt number and the bulk temperature on the pressure coefficient is investigated for the Newtonian case including viscous dissipation. These effects are found to be closely interactive. The effect of the Weissenberg number on the local Nusselt number is explored for the Maxwell fluid with pressure-dependent viscosity. Local Nusselt number decreases with increasing pressure coefficient for both fluids. The local Nusselt number Nu for Newtonian fluid with pressure-dependent viscosity is always greater than Nu related to the viscoelastic Maxwell fluid with pressure-dependent viscosity.

scholarly journals Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

Heat transfer analysis of ethylene glycol-based Casson nanofluid around a horizontal circular cylinder with MHD effect

2020 ◽  
Vol 234 (13) ◽  
pp. 2569-2580 ◽  
Author(s):  
Firas A Alwawi ◽  
Hamzeh T Alkasasbeh ◽  
AM Rashad ◽  
Ruwaidiah Idris
Keyword(s):  
Nusselt Number ◽  
Circular Cylinder ◽  
Ethylene Glycol ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Heat Transfer Analysis ◽  
Constant Wall Temperature ◽  
Local Skin ◽  
Casson Nanofluid ◽  
Horizontal Circular Cylinder

In this work, efforts were taken to investigate the free convection of ethylene glycol-based Casson nanofluid and it is affected by a magnetic field about a horizontal circular cylinder. Three different types of oxide nanoparticles were used along with constant wall temperature. Tiwari and Das's nanofluid model was used to investigate the MHD free convective flow of Casson nanofluid. The transformed governing PDEs were solved via the Keller box method. Numerical and graphical findings were acquired by using MATLAB software, in addition to studying and analyzing the influence of related parameters, on the velocity, temperature, local skin friction coefficient, and local Nusselt number. The results demonstrate that copper oxide ethylene glycol-based Casson nanofluid has the lowest local Nusselt number, velocity and, it has the highest temperature. Also, our results were in excellent agreement with prior published results.

Entrance and Temperature Dependent Viscosity Effects on Laminar Forced Convection in Straight Ducts With Uniform Wall Heat Flux

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Sections ◽  
Local Nusselt Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Effects Of Temperature ◽  
Dependent Viscosity ◽  
Fanning Friction Factor ◽  
Laminar Forced Convection

Abstract In this paper a parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously, i.e., hydro-dynamically and thermally, developing laminar flows of liquids in straight ducts of constant cross sections. Uniform heat flux boundary conditions are imposed on the heated walls of the ducts. Different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (rectangular and trapezoidal) ducts. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Pearson and Prandtl numbers. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions. Correlations are also provided for the local Nusselt number and the apparent Fanning friction factor in simultaneously developing flows in ducts of different cross sections.

The oil film in a closing gap

1962 ◽  
Vol 266 (1326) ◽  
pp. 312-328 ◽  
Keyword(s):  
High Pressure ◽  
Film Thickness ◽  
Pressure Coefficient ◽  
Lubricant Film ◽  
Polished Surface ◽  
Maximum Pressure ◽  
Pressure Dependent Viscosity ◽  
Special Cases ◽  
Dry Contact ◽  
Dependent Viscosity

This paper presents a solution to the elasto-hydrodynamic problem of normal approach of two cylindrical bodies separated by a lubricating film. Analytic solutions are found for the special cases of constant viscosity and rigid material and also for pressure-dependent viscosity. The more general case accounting for elastic deformation of the bodies with constant or pressure dependent viscosity was solved by using an iterative numerical process with the help of an electronic computer. It is found that a very high pressure may be developed in the lubricant film at a finite separation of the cylinders. As the film thickness is further reduced, the value of the maximum pressure decreases and as the film thickness approaches zero, the pressure distribution converges to the Hertzian dry contact form. For a given load applied to the cylinders, the value of the maximum pressure reached depends to a large extent upon the value of the parameter oc E , i.e. the product of the pressure coefficient of viscosity and the equivalent Young’s modulus of the elastic system. Also, once the pressure has reached a sufficiently high value it becomes extremely sensitive to an increase in load; a small increase in load will produce a large increase in maximum pressure. A number of experiments were performed in order to check some of the theoretical predictions made. In these experiments a loaded steel ball was allowed to approach the polished surface of various materials whose surfaces were covered by a lubricant film, and the plastic deformations produced in the surface were then measured. These tests showed clearly the influence of the lubricant in that in every case the depth of the impressions with lubricant was significantly larger than the corresponding ones produced under Hertzian, dry contact impacts. The experimental results indicate a correlation between maximum pressure and the value of ol E and its sensitivity to increase in load at high pressure as predicted by the theory.

Comparison Between Thermal Conductivity Models on Heat Transfer in Power-Law Non-Newtonian Fluids

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Botong Li ◽  
Liancun Zheng ◽  
Xinxin Zhang
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Power Law ◽  
Local Nusselt Number ◽  
Control Volume ◽  
Newtonian Fluids ◽  
Uniform Wall Temperature ◽  
Dependent Model ◽  
Conductivity Models

This paper endeavors to complete a numerical research on forced convection steady heat transfer in power-law non-Newtonian fluids in a circle duct. Incompressible, laminar fluids are to be studied with a uniform wall temperature. A hydrodynamic entrance length is neglected which allows establishing a fully developed flow. The energy equation is solved by using a LU decomposition coupled with control volume technique based on finite difference method. Four thermal conductivity models are adopted in this paper, that is, constant thermal conductivity model, linear thermal conductivity varying with temperature, thermal conductivity varying as a function of velocity gradient, and thermal conductivity varying as a function of temperature gradient. The results are compared with each other and the physical characteristics for values of parameters are also discussed in details. It is shown that the heat transfer behaviors are strongly depending on the power-law index in all models. Comparisons of temperature and local Nusselt number between models are made. It reveals the increasing values of thermal conductivity parameter result in increasing the local Nusselt number when the thermal conductivity is a linear one. Furthermore, there is obvious difference in the local Nusselt number between the constant model and the power-law velocity-dependent model, but Nusselt number varies little from the constant model to the power-law temperature-dependent model.

A Numerical Investigation on Nanofluid Laminar Mixed Convection in Confined Impinging Jets

2013 ◽  
Author(s):  
O. Manca ◽  
S. Nardini ◽  
D. Ricci ◽  
S. Tamburrino
Keyword(s):  
Nusselt Number ◽  
Numerical Investigation ◽  
Stream Function ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Convective Heat Transfer Coefficient ◽  
Temperature Fields ◽  
Bulk Temperature ◽  
Al2o3 Nanoparticles ◽  
Laminar Mixed Convection

In this paper a numerical investigation on confined impinging slot jets working with a mixture of water and Al2O3 nanoparticles is described. The flow is laminar and a constant temperature is applied on the target surface. A single-phase model approach has been adopted because the particle concentrations are low. Different geometric ratios and nanoparticle volume concentrations have been considered at different Richardson numbers in order to take into account also the buoyancy effects. The aim consists into study the behaviour of the system by means of average and local Nusselt number, convective heat transfer coefficient and required pumping power profiles, temperature fields and stream function contours. The dimensionless stream function contours showed that the intensity and size of the vortex structures depend on the confining effects, given by H/W ratio, Richardson number and particle concentrations. Furthermore, for increasing concentrations, nanofluids realize increasing fluid bulk temperature, as a result of the elevated thermal conductivity of mixtures. The local Nusselt number profiles show the highest values at the stagnation point and they depend on Richardson number and particle concentrations.

scholarly journals Non-Similar Solution for Magnetized Flow of Maxwell Nanofluid over an Exponentially Stretching Surface

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Raheela Razzaq ◽  
Umer Farooq ◽  
Jifeng Cui ◽  
Taseer Muhammad
Keyword(s):  
Nusselt Number ◽  
Brownian Motion ◽  
Skin Friction ◽  
Differential System ◽  
Local Nusselt Number ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Fluid Behavior ◽  
Exponentially Stretching ◽  
Physical Features

In this study, an analysis is made by studying more reliable nonsimilar magneto-hydrodynamics (MHD) flow of Maxwell fluid with nanomaterials. Nonsimilar transport is produced by extending of sheet with arbitrary velocity. Maxwell structure is marked to indicate the non-Newtonian fluid behavior. The leading nondimensional partial differential system (PDEs) is transmuted to a set of the nonlinear ordinary differential system (ODEs) through local nonsimilarity technique. The developing system is solved numerically using an implemented package known as bvp4c in MATLAB. The analysis discovers several physical features of thermal and velocity profiles. Remark the flow accelerated for greater Deborah and Hartman parameters. The influence of thermophoresis number on the thermal figure is minimal. The conducts of velocity, concentration, and thermal distribution and local Nusselt number and skin friction are illustrated graphically by taking distinct parameters. The consequences disclose that the local Nusselt number is an increasing function of Prandtl number; however, it is a decaying function for Brownian motion. The rise in skin friction is observed for increasing Brownian motion and Lewis numbers.

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