Conjugate Nusselt Numbers for Simultaneously Developing Flow Through Rectangular Ducts

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Georgios Karamanis ◽  
Marc Hodes
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Extended Surface ◽  
Side Walls ◽  
Extended Surfaces ◽  
Prandtl Numbers

We consider conjugate forced-convection heat transfer in a rectangular duct. Heat is exchanged through the isothermal base of the duct, i.e., the area comprised of the wetted portion of its base and the roots of its two side walls, which are extended surfaces within which conduction is three-dimensional. The opposite side of the duct is covered by an adiabatic shroud, and the external faces of the side walls are adiabatic. The flow is steady, laminar, and simultaneously developing, and the fluid and extended surfaces have constant thermophysical properties. Prescribed are the width of the wetted portion of the base, the length of the duct, and the thickness of the extended surfaces, all three of them nondimensionalized by the hydraulic diameter of the duct, and, additionally, the Reynolds number of the flow, the Prandtl number of the fluid, and the fluid-to-extended surface thermal conductivity ratio. Our conjugate Nusselt number results provide the local one along the extended surfaces, the local transversely averaged one over the isothermal base of the duct, the average of the latter in the streamwise direction as a function of distance from the inlet of the domain, and the average one over the whole area of the isothermal base. The results show that for prescribed thermal conductivity ratio and Reynolds and Prandtl numbers, there exists an optimal combination of the dimensionless width of the wetted portion of the base, duct length, and extended surface thickness that maximize the heat transfer per unit area from the isothermal base.

scholarly journals Effect of an inserted porous layer on heat and fluid flow in a vertical channel with mixed convection

2015 ◽  
Vol 19 (3) ◽  
pp. 1005-1016 ◽  
Author(s):  
Hasan Celik ◽  
Moghtada Mobedi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Pressure Drop ◽  
Mixed Convection ◽  
Porous Layer ◽  
Convection Heat Transfer ◽  
Vertical Channel ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Transfer Condition

Temperature and velocity fields in a vertical channel partially filled with porous medium under mixed convection heat transfer condition are obtained. The heat transfer equation and equation of motion for clear and porous layer regions are written and solved analytically. The nondimensionalization of the governing equations yields two Grashof numbers as Grc and Grd for clear and porous sections where Grd=Da.Grc. The dimensionless governing parameters for the problem are Grc (or Grd), Da, thermal conductivity ratio (i.e., K) and thickness of porous layer. The temperature and velocity profiles for different values of Grc, Da, K and thickness of porous layer are plotted and their changes with the governing parameters are discussed. Moreover, the variation of pressure drop with the governing parameters is investigated. The decrease of porous layer thickness or thermal conductivity ratio increases the possibility of the downward flows. Thermal conductivity ratio plays important role on pressure drop, particularly for the channels with high values of Grc/Re.

Conjugate Heat Transfer Using Liquid Metals and Alloys for Enclosures With Solid Conducting Blocks

2010 ◽  
Vol 2 (1) ◽  
Author(s):  
M. McGarry ◽  
C. Bonilla ◽  
I. Metzger
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Conjugate Heat Transfer ◽  
Liquid Metals ◽  
Thermal Conductivity Ratio ◽  
Temperature Sensitive ◽  
Conductivity Ratio ◽  
Prandtl Numbers

A validated computational model was created to simulate the heat transfer from a heated surface using liquid metals and alloys during conjugate heat transfer. This model explores the effect of the Rayleigh number, Prandtl number, thermal conductivity ratio, and aspect ratio on the Nusselt number along the hot surface. The data will show how to keep the temperature sensitive components along the hot wall cool by maximizing the amount of heat removed from the hot wall. The data show three distinct regions that occur as a function of the Rayleigh number for a fixed k∗ and d∗. The data also show that the thermal conductivity ratio between the fluid and the solid conducting block has little effect on the Nusselt number at a fixed Rayleigh number. However, when examining the effect of the aspect ratio on the Nusselt number, two distinct regions can be seen. The results demonstrate that in order to keep the temperature sensitive components cool along the hot wall, one would want to have large Rayleigh and Prandtl numbers. The easiest way to achieve large Rayleigh numbers is by increasing the height of the enclosure. Large Prandtl numbers can be achieved by choosing a fluid that is highly conductive. In addition, the choice of material for the center solid conducting block does not impact the amount of heat removed from the hot wall. However, increased cooling can be achieved by decreasing the spacing between the hot and the cold wall.

scholarly journals Thermal study of fluid flow inside an annular pipe filled with porous media under local thermal non-equilibrium condition

2019 ◽  
Vol 13 (2) ◽  
pp. 4880-4897
Author(s):  
Abdelkrim Bouaffane ◽  
Kamel Talbi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Biot Number ◽  
Convection Heat Transfer ◽  
Radius Ratio ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Convection Heat ◽  
Local Difference ◽  
Annular Pipe

The present work involves the thermal numerical simulation of fluid flow inside an annular pipe completely filled porous material. The mathematical model of the energy transport is based on the Local Thermal Non-Equilibrium (LTNE) between the fluid and the solid phases. The governing equations are discretized by the finite volume method. SIMPLE algorithm has been used to solve the set of algebraic discretized coupled equations. This work is divided in two parts. In the first part, the effect of the pertinent dimensionless parameters which govern the study such as Biot number (Bi), solid-fluid thermal conductivity ratio (Rc) and radius ratio (Rr) on the LTNE intensity are analyzed by calculating: the local difference of temperature (LDT), the maximum of the local difference of temperature (LDTmax) and the average of LDT. The results show that the increase of Biot number and the solid-fluid thermal conductivity ratio, and the decrease of radius ratio reduce the LTNE intensity. The intensity of the LTNE in the developing region is greater than that of the fully developed region. In the second part, the convection heat transfer enhancement is studied, the results illustrate that the increase of Biot number and the solid-fluid thermal conductivity ratio, and the decrease of radius ratio represent good factors to ameliorate the rate of the convection heat transfer between the fluid and the inner wall.

Effects of a centered conducting body on natural convection of non-Newtonian fluid in a square enclosure with time-periodic temperature distribution

2020 ◽  
Author(s):  
Peixin Ye ◽  
Dinggen Li ◽  
Zihao Yu ◽  
Haifeng Zhang
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Capacity ◽  
Transient Heat Transfer ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Transfer Ratio ◽  
Periodic Temperature ◽  
Power Law Index ◽  
Time Periodic

In this paper, a modified lattice Boltzmann model that incorporates the effect of heat capacity is adopted to study the effects of a centered conducting body on natural convection of non-Newtonian fluid in a square cavity with time-periodic temperature distribution. The effects of power-law index, Rayleigh number, heat capacity ratio, thermal conductivity ratio, body size, temperature pulsating period and the temperature pulsating amplitude on fluid flow and heat transfer are analyzed in detail. The results showed that the increase of Rayleigh number and thermal conductivity ratio as well as the decrease of power-law index can strengthen both transient and global heat transfer, while the increase of heat capacitance of fluid to the solid wall can only enhance the transient heat transfer, and has little effect on the overall heat transfer. Further, the increase of body size will reduce both the transient heat transfer ratio and the overall heat transfer ratio. In addition, the decrease of temperature pulsating period can enhance the transient heat transfer, but it will slightly weaken the overall heat transfer. Finally, the results show that both the transient and the overall heat transfer ratio are increased with the increase of temperature pulsating amplitude.

Upward and downward conjugate mixed convection heat transfer in a partially porous cavity

2016 ◽  
Vol 26 (1) ◽  
pp. 159-188 ◽  
Author(s):  
Abderrahim Bourouis ◽  
Abdeslam Omara ◽  
Said Abboudi
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mixed Convection ◽  
Transfer Rate ◽  
Vertical Wall ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Content Type ◽  
Moving Wall ◽  
The Right

Purpose – The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer. The effect of the relevant parameters: Richardson number (Ri=0.1, 1, 10) and thermal conductivity ratio (Rk=0.1, 1, 10, 100) are investigated. Design/methodology/approach – The studied system is a two dimensional lid-driven enclosure with thick vertical porous layer. The left vertical wall of the enclosure is allowed to move in its own plane at a constant velocity. The enclosure is heated from the right vertical wall isothermally. The left and the right vertical walls are isothermal but temperature of the outside of the right vertical wall is higher than that of the left vertical wall. Horizontal walls are insulated. The governing equations are solved by finite volume method and the SIMPLE algorithm. Findings – From the finding results, it is observed that: for the two studied cases, heat transfer rate along the hot wall is a decreasing function of thermal conductivity ratio irrespective of Richardson numbers contrary to the heat transfer rate along the fluid-porous layer interface which is an increasing function of thermal conductivity ratio. At forced convection dominant regime, the difference between heat transfer rate for upward and downward moving wall is insensitive to the thermal conductivity ratio. For downward moving wall, average Nusselt number is higher than that of upward moving wall. Practical implications – Some applications: building applications, furnace design, nuclear reactors, air solar collectors. Originality/value – From the bibliographic work and the authors’ knowledge, the conjugate mixed convection in lid-driven partially porous enclosures has not yet been investigated which motivates the present work that represent a continuation of the preceding investigations.

Conjugate heat transfer in porous triangular enclosures with thick bottom wall

2009 ◽  
Vol 19 (5) ◽  
pp. 650-664 ◽  
Author(s):  
Yasin Varol ◽  
Hakan F. Oztop ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Natural Convection ◽  
Conjugate Heat Transfer ◽  
Bottom Wall ◽  
Thick Wall ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Governing Equations ◽  
Content Type

PurposeThe purpose of this paper is to study the conjugate heat transfer via natural convection and conduction in a triangular enclosure filled with a porous medium.Design/methodology/approachDarcy flow model was used to write governing equations with Boussinesq approximation. The transformed governing equations are solved numerically using a finite difference technique. It is assumed that the enclosure consists of a conducting bottom wall of finite thickness, an adiabatic (insulated) vertical wall and a cooled inclined wall.FindingsFlow patterns, temperature and heat transfer were presented at different dimensionless thickness of the bottom wall, h, from 0.05 to 0.3, different thermal conductivity ratio between solid material and fluid, k, from 0.44 to 283 and Rayleigh numbers, Ra, from 100 to 1000. It is found that both thermal conductivity ratio and thickness of the bottom wall can be used as control parameters for heat transport and flow field.Originality/valueIt is believed that this is the first paper on conduction‐natural convection in porous media filled triangular enclosures with thick wall. In the last years, most of the researchers focused on regular geometries such as rectangular or square cavity bounded by thick wall.

Using Porous Fins for Heat Transfer Enhancement

2000 ◽  
Vol 123 (4) ◽  
pp. 790-795 ◽  
Author(s):  
S. Kiwan ◽  
M. A. Al-Nimr
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Performance ◽  
Thermal Conductivity Ratio ◽  
Operating Parameters ◽  
Conductivity Ratio ◽  
Transfer Enhancement ◽  
Porous Fin ◽  
Novel Method ◽  
Porous Fins

This work introduces a novel method that enhances the heat transfer from a given surface by using porous fins. The thermal performance of porous fins is estimated and compared with that of the conventional solid fins. It is found that using porous fin of porosity ε may enhance the performance of an equal size conventional solid fin and, as a result, save 100 ε percent of the fin material. The effect of different design and operating parameters on the porous fin thermal performance is investigated. Examples of these parameters are Ra number, Da number, and thermal conductivity ratio. It is found that more enhancement in the porous fin performance may be achieved as Ra increases especially at large Da numbers. Also, it is found that there is an optimum limit for the thermal conductivity ratio beyond which there is no further improvement in the fin performance.

scholarly journals Effect of Al2O3/water nanofluid on Conjugate Free Convection in a Baffle Attached Square Enclosure

Mechanika ◽  
2020 ◽  
Vol 26 (2) ◽  
pp. 126-133
Author(s):  
Thansekhar M.Rathinam
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Rayleigh Number ◽  
Free Convection ◽  
Conjugate Heat Transfer ◽  
Volume Fraction ◽  
Numerical Study ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Square Enclosure

A numerical study of conjugate free convection heat transfer of Al2O3/water nanofluid inside a differentially heated square enclosure with a baffle attached to its hot wall has been carried out. A detailed parametric study has been carried out to analyze the effect of Rayleigh number (104 < Ra < 106), length, thickness and position of baffle, conductivity ratio and volume fraction of the nanoparticle (0<<0.2) on heat transfer. The thermal conductivity ratio of the baffle plays a major role on the conjugate heat transfer inside the enclosure. Higher the baffle length better is the effectiveness of the baffle. The average Nusselt number is found to be an increasing function of both thermal conductivity ratio and volume fraction of the nanofluid. The minimum enhancement of conjugate heat transfer is 30% when Al2O3/water nanofluid of 0.1 volume fraction is used for the entire range of Rayleigh number considered.

scholarly journals Numerical Simulation of Entropy Generation of Conjugate Heat Transfer in A Porous Cavity with Finite Walls and Localized Heat Source

2021 ◽  
Vol 84 (2) ◽  
pp. 116-151
Author(s):  
Ahmed Kadhim Hussein ◽  
Muhaiman Alawi Mahdi ◽  
Obai Younis
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat Source ◽  
Entropy Production ◽  
Conjugate Heat Transfer ◽  
Thermal Conductivity Ratio ◽  
Conductivity Ratio ◽  
Porous Cavity

In this research, the entropy production of the conjugate heat transfer in a tilted porous cavity in respect to heat source and solid walls locations has been studied numerically. Three different cases of the cavity with finite walls thickness and heat source locations are considered in the present study. For both cases one and two, the cavity considered has a vertical finite walls thickness, while the cavity with the horizontal finite walls thickness is considered for case three. For cases one and two, the left sidewall of the cavity is exposed to heat source, whereas the rest of this wall as well as the right sidewall are adiabatic. The upper and lower cavity walls are adiabatic. For case three, the lower wall is exposed to a localized heat source, while the rest of it is assumed adiabatic. The upper wall is cold, whereas the left and right sidewalls are adiabatic. The flow and thermal fields properties along with the entropy production are computed for the modified Rayleigh number (150 ? Ram ? 1000), thermal conductivity ratio (1 ? Kr ? 10), heat source length (0.2 ? B ? 0.6), aspect ratio (0.5 ? AR ? 2) and walls thickness (0.1 ? D1 ? 0.2 and 0.1 ? D2 ? 0.2) respectively. The results show that, the maximum values of the entropy generated from fluid friction develop close to the cavity wall-fluid interfacial, while the maximum values of the entropy generated from heat transfer develop nearby the heat source region. The average Bejan number (Beav) is higher than (0.5) for cases one and two. While for case three, it was found to be less than (0.5). Also, the results show that as the modified Rayleigh number, thermal conductivity ratio, heat source length and aspect ratio increased, the fluid flow intensity in the cavity increased. While, it decreased when the walls thickness increased. From the results, it is concluded that case three gives a higher heat transfer enhancement. The obtained results are compared against another published results and a good agreement is found between them.

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