scholarly journals Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition – An exact solution

2014 ◽  
Vol 228 (15) ◽  
pp. 2778-2789 ◽  
Author(s):  
Nader Karimi ◽  
Yasser Mahmoudi ◽  
Kiumars Mazaheri
Keyword(s):  
Porous Material ◽  
Fluid Transport ◽  
Darcy Number ◽  
Equation Model ◽  
Temperature Fields ◽  
Thermal Conductivity Ratio ◽  
Fluid Temperature ◽  
Thermal Boundary Conditions ◽  
Constant Wall Heat Flux ◽  
Non Equilibrium

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

Local Thermal Equilibrium in Forced Convection Through Porous Media

2010 ◽  
Author(s):  
A. Nouri-Borujerdi
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Forced Convection ◽  
Thermal Equilibrium ◽  
Fluid Transport ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Equation Model ◽  
Temperature Fields ◽  
Local Thermal Equilibrium

Forced convection heat transfer through a channel filled with a porous medium is investigated using perturbation method. Two-energy equation model is utilized to represent the assumption of local thermal non-equilibrium which exists between the solid and fluid phases. The Brinkman-Forchheimer extension of the Darcy model is used to represent the fluid transport within the porous medium. Analytical solution is obtained for both fluid and solid temperature fields incorporating the effects of various pertinent parameters such as the Darcy number, the Biot number, the thermal conductivity and the pressure gradient. It is found that the Darcy number and the pressure gradient have significant effects on the local thermal equilibrium assumption.

Turbulent Heat and Momentum Transports in an Infinite Rod Array

1987 ◽  
Vol 109 (3) ◽  
pp. 599-605 ◽  
Author(s):  
An-Shik Yang ◽  
Ching-Chang Chieng
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Equation Model ◽  
Temperature Fields ◽  
Turbulent Heat ◽  
Fluid Temperature ◽  
Transfer Coefficients ◽  
Anisotropic Factor ◽  
Flow Through ◽  
Rod Array

An anisotropic factor is carefully selected from eleven distributions and adopted to the k–ε two-equation model of turbulence to obtain detailed velocity and temperature fields for steady-state, fully developed turbulent flow through infinite triangular/square rod array. The present study covers the ranges of pitch-to-diameter ratio from 1.123 to 1.5, and Reynolds number from 2.4 × 104 to 106. Velocity and wall shear stress are calculated and compared to experimental data. Normalized fluid temperature, friction factor, and heat transfer coefficient are also computed. The correlations of friction factor and heat transfer coefficients for flow inside circular pipe and flow through finite rod arrays are compared with the results for flow through infinite rod arrays.

scholarly journals The use of a solution of the inverse heat conduction problem to monitor thermal stresses

2019 ◽  
Vol 108 ◽  
pp. 01003
Author(s):  
Jan Taler ◽  
Piotr Dzierwa ◽  
Magdalena Jaremkiewicz ◽  
Dawid Taler ◽  
Karol Kaczmarski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Power Plants ◽  
Thermal Stresses ◽  
Thermal Power ◽  
Temperature Fields ◽  
Thick Wall ◽  
Fluid Temperature ◽  
Unsteady Temperature

Thick-wall components of the thermal power unit limit maximum heating and cooling rates during start-up or shut-down of the unit. A method of monitoring the thermal stresses in thick-walled components of thermal power plants is presented. The time variations of the local heat transfer coefficient on the inner surface of the pressure component are determined based on the measurement of the wall temperature at one or six points respectively for one- and three-dimensional unsteady temperature fields in the component. The temperature sensors are located close to the internal surface of the component. A technique for measuring the fastchanging fluid temperature was developed. Thermal stresses in pressure components with complicated shapes can be computed using FEM (Finite Element Method) based on experimentally estimated fluid temperature and heat transfer coefficient

Passive Heat Transfer in Porous Enclosures Using a Two-Energy Equation Model

2012 ◽  
Author(s):  
Marcelo J. S. deLemos ◽  
Paulo H. S. Carvalho
Keyword(s):  
Heat Transfer ◽  
Energy Equation ◽  
Equation Model ◽  
Thermal Conductivity Ratio ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Energy Models ◽  
Different Temperatures ◽  
Volume Method ◽  
Generalized Coordinate

This paper presents computations for natural convection within a porous cavity filled with a fluid saturated permeable medium. The finite volume method in a generalized coordinate system is applied. The walls are maintained at constant but different temperatures, while the horizontal walls are kept insulated. Governing equations are written in terms of primitive variables and are recast into a general form. Flow and heat transfer characteristics are investigated for two energy models and distinct solid-to-fluid thermal conductivity ratio.

scholarly journals Natural convection air flow in vertical upright-angled triangular cavities under realistic thermal boundary conditions

2016 ◽  
Vol 20 (5) ◽  
pp. 1407-1420 ◽  
Author(s):  
Jaime Sieres ◽  
Antonio Campo ◽  
José Martínez-Súarez
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Aperture Angle ◽  
Temperature Fields ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Horizontal Wall ◽  
Rayleigh Numbers

This paper presents an analytical and numerical computation of laminar natural convection in a collection of vertical upright-angled triangular cavities filled with air. The vertical wall is heated with a uniform heat flux; the inclined wall is cooled with a uniform temperature; while the upper horizontal wall is assumed thermally insulated. The defining aperture angle ? is located at the lower vertex between the vertical and inclined walls. The finite element method is implemented to perform the computational analysis of the conservation equations for three aperture angles ? (= 15?, 30? and 45?) and height-based modified Rayleigh numbers ranging from a low Ra = 0 (pure conduction) to a high 109. Numerical results are reported for the velocity and temperature fields as well as the Nusselt numbers at the heated vertical wall. The numerical computations are also focused on the determination of the value of the maximum or critical temperature along the hot vertical wall and its dependence with the modified Rayleigh number and the aperture angle.

Heatline and Massline Visualization of Hydromagnetic Double Diffusive Convective Flow of Nanofluid Within a Porous Trapezoidal Cavity

2021 ◽  
Vol 10 (2) ◽  
pp. 270-284
Author(s):  
Bikash C. Saha ◽  
T. R. Mahapatra ◽  
Dulal Pal
Keyword(s):  
Aspect Ratio ◽  
Convective Flow ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Temperature Fields ◽  
Computational Domain ◽  
Aspect Ratios ◽  
Numerical Predictions ◽  
Double Diffusive

Double diffusive convective flow of nanofluid within a porous trapezoidal cavity of various aspect ratios consisting of Al2O3 nanoparticle in the presence of applied magnetic field in the direction perpendicular to the parallel top and bottom walls is analysed. The side walls of the cavity are maintained at constant temperature and concentration while its horizontal walls are insulated and impermeable. The irregular physical domain of the problem is transformed to a regular unit square computational domain. The governing equations have been solved by second order of finite difference method (FDM). Based upon numerical predictions, the effects of pertinent parameters such as Rayleigh number, Darcy number, aspect ratio, solid volume fraction and inclination angle on the flow and temperature fields and the heat transfer performance of the enclosure are examined. It is found that the intensity of heat and mass transfer increases with the increase in the Darcy number and aspect ratio. It is also observed that as the solid volume fraction increases there is increase in the average Nusselt number but reverse effect is observed on the average Sherwood number.

Ohmic and viscous dissipation effects on micropolar non-Newtonian nanofluid Al2O3 flow through a non-Darcy porous media

2022 ◽  
pp. 1-13
Author(s):  
Nabil T. Eldabe ◽  
Mohamed Y. Abou zeid ◽  
Sami M. El Shabouri ◽  
Tarek N. Salama ◽  
Aya M. Ismael
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Numerical Solutions ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
High Concentration ◽  
Ohmic Dissipation ◽  
Similarity Transformations

Inclined uniform magnetic field and mixed convention effects on micropolar non-Newtonian nanofluid Al2O3 flow with heat transfer are studied. The heat source, both viscous and ohmic dissipation and temperature micropolarity properties are considered. We transformed our system of non-linear partial differential equations into ordinary equations by using suitable similarity transformations. These equations are solved by making use of Rung–Kutta–Merson method in a shooting and matching technique. The numerical solutions of the tangential velocity, microtation velocity, temperature and nanoparticle concentration are obtained as functions of the physical parameters of the problem. Moreover, we discussed the effects of these parameters on the numerical solutions and depicted graphically. It is obvious that these parameters control the fluid flow. It is noticed that the tangential velocity magnifies with an increase in the value of Darcy number. Meanwhile, the value of the tangential velocity reduces with the elevation in the value of the magnetic field parameter. On the other hand, the elevation in the value of Brownian motion parameter leads to a reduction in the value of fluid temperature. Furthermore, increasing in the value of heat source parameter makes an enhancement in the value of nanoparticles concentration. The current study has many accomplishments in several scientific areas like medical industry, medicine, and others. Therefore, it represents the depiction of gas or liquid motion over a surface. When particles are moving from areas of high concentration to areas of low concentration.

scholarly journals Applications of Cattaneo–Christov fluxes on modelling the boundary value problem of Prandtl fluid comprising variable properties

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Umar Nazir ◽  
Muhammad Sohail ◽  
Umair Ali ◽  
El-Sayed M. Sherif ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Magnetic Parameter ◽  
Fluid Model ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Coupled System ◽  
Temperature Fields ◽  
Fluid Temperature ◽  
Variable Properties ◽  
Cartesian Coordinate ◽  
And Diffusion

AbstractStretched flows have numerous applications in different industrial, biomedical and engineering processes. Current research is conducted to examine the flow phenomenon of Prandtl fluid model over a moveable surface. The phenomenon of mass and thermal transportation is based on generalized theory of Cattaneo–Christov which considers the involvement of relaxation times. In addition to these, variable characteristics of thermal conductivity and diffusion coefficient are considered as a function of temperature. The physical problem in Cartesian coordinate system is modeled via boundary layer theory which yields a coupled system of partial differential equations. Group scaling transportation is applied to model these PDEs system. The converted equations have been approximated via optimal homotopic scheme. The efficiency and validity of used approach has been shown by computing the error analysis and establishing a comparative study. It is noted that the enhancement in magnetic parameter plays a controlling role for velocity field and it augment the concentration and temperature fields. Furthermore, increase in thermal relaxation parameter and Prandtl number maintains the fluid temperature.

Heat and Mass Transfer of Temperature-Dependent Viscosity Models in a Pipe: Effects of Thermal Radiation and Heat Generation

2020 ◽  
Vol 75 (3) ◽  
pp. 225-239 ◽  
Author(s):  
Fayyaz Ahmad ◽  
Mubbashar Nazeer ◽  
Mubashara Saeed ◽  
Adila Saleem ◽  
Waqas Ali
Keyword(s):  
Thermal Radiation ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Physical Property ◽  
Solid Particles ◽  
Temperature Fields ◽  
Fluid Temperature ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Increasing Trends

AbstractIn this paper, a study of the flow of Eyring-Powell (EP) fluid in an infinite circular long pipe under the consideration of heat generation and thermal radiation is considered. It is assumed that the viscosity of the fluid is an exponential function of the temperature of the fluid. The flow of fluid depends on many variables, such as the physical property of each phase and shape of solid particles. To convert the given governing equations into dimensionless form, the dimensionless quantities have been used and the resultant boundary value problem is solved for the calculation of velocity and temperature fields. The analytical solutions of velocity and temperature are calculated with the help of the perturbation method. The effects of the fluidic parameters on velocity and temperature are discussed in detail. Finite difference method is employed to find the numerical solutions and compared with the analytical solution. The magnitude error in velocity and temperature is obtained in each case of the viscosity model and plotted against the radius of the pipe. Graphs are plotted to describe the influence of various parameter EP parameters, heat generation parameter and thermal radiation parameters against velocity and temperature profiles. The fluid temperature has decreasing and increasing trends with respect to radiation and heat generations parameters, respectively.

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