scholarly journals Effect of Variable Fluid Properties on Natural Convection of Nanofluids in a Cavity with Linearly Varying Wall Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. Bhuvaneswari ◽  
Poo Balan Ganesan ◽  
S. Sivasankaran ◽  
K. K. Viswanathan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Heat Transfer Rate ◽  
Wall Temperature ◽  
Transfer Rate ◽  
Effective Viscosity ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Left Wall

The present study analyzed convective heat transfer and fluid flow characteristics of nanofluid in a two-dimensional square cavity under different combinations of thermophysical models of nanofluids. The right vertical wall temperature is varying linearly with height and the left wall is maintained at low temperature whereas the horizontal walls are adiabatic. Finite volume method is used to solve the governing equations. Two models are considered to calculate the effective thermal conductivity of the nanofluid and four models are considered to calculate the effective viscosity of the nanofluid. Numerical solutions are carried out for different combinations of effective viscosity and effective thermal conductivity models with different volume fractions of nanoparticles and Rayleigh numbers. It is found that the heat transfer rate increases for Models M1 and M3 on increasing the volume fraction of the nanofluid, whereas heat transfer rate decreases for Model M4 on increasing the volume fraction of the nanoparticle. The difference among the effective dynamic viscosity models of nanofluid plays an important role here such that the average Nusselt number demonstrates an increasing or decreasing trend with the concentration of nanoparticle.

Contributions to the theory of heat transfer through a laminar boundary layer

1950 ◽  
Vol 202 (1070) ◽  
pp. 359-377 ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Skin Friction ◽  
Heat Transfer Rate ◽  
Wall Temperature ◽  
Transfer Rate ◽  
Arbitrary Distribution ◽  
Main Stream

An approximation to the heat transfer rate across a laminar incompressible boundary layer, for arbitrary distribution of main stream velocity and of wall temperature, is obtained by using the energy equation in von Mises’s form, and approximating the coefficients in a manner which is most closely correct near the surface. The heat transfer rate to a portion of surface of length l (measured downstream from the start of the boundary layer) and unit breadth is given as -½ k /(⅓)! (3σρ/μ 2 ) ⅓ ∫ l 0 (∫ l x √{ T ( z )} dz ) ⅔ dT 0 ( x ), where k is the thermal conductivity of the fluid, σ its Prandtl number, ρ its density, μ its viscosity, T ( x ) is the skin friction, and T 0 ( x ) the excess of wall temperature over main stream temperature. A critical appraisement of the formula (§3) indicates that it should be very accurate for large σ, but that for σ of order 0.7 (i. e. for most gases) the constant ½3 ⅓ /(⅓) ! = 0.807 should be replaced by 0.73, when the error should not exceed 8 % for the laminar layers that occur in practical aerodynamics. This yields a formula Nu = 0.52σ ⅓ ( R √ C f ) ⅔ for Nusselt number in terms of the Reynolds number R and the mean square root of the skin friction coefficient C f , in the case of uniform wall temperature. However, for the boundary layer with uniform main stream, the original formula is accurate to within 3% even for σ = 0.7. By known transformations an expression is deduced for heat transfer to a surface, with arbitrary temperature distribution along it, and with a uniform stream outside it at arbitrary Mach number (equation (42)). From this, the temperature distribution along such a surface is deduced (§ 4) in the case (of importance at high Mach numbers) when heat transfer to it is balanced entirely by radiation from it. This calculation, which includes the solution of a non-linear integral equation, gives higher temperatures near the nose, and lower ones farther back (figure 2), than are found from a theory which assumes the wall temperature uniform and averages the heat transfer balance. This effect will be considerably mitigated for bodies of high thermal conductivity; the author is not in a position to say whether or not it will be appreciable for metal projectiles. But for stony meteorites at a certain stage of their flight through the atmosphere it indicates that melting at the nose and re-solidification farther back may occur, for which the shape and constitution of a few of them affords evidence. An appendix shows how the method for approximating and solving von Mises’s equation could be used to determine the skin friction as well as heat transfer rate, but this line seems to have no advantage over established approximate methods.

Convective heat transfer in a porous enclosure saturated by nanofluid with different heat sources

2018 ◽  
Vol 7 (1) ◽  
pp. 1-16 ◽  
Author(s):  
M. Muthtamilselvan ◽  
S. Sureshkumar
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
High Heat ◽  
Heated Wall ◽  
Left Wall ◽  
High Heat Transfer

Abstract The present study is proposed to investigate the effects of various lengths and different locations of the heater on the left sidewall in a square lid-driven porous cavity filled with nanofluid. A higher temperature is maintained on the left wall where three different lengths and three different locations of the heat source are considered for the analysis. The right wall is kept at a lower temperature while the top and bottom walls, and the remaining portions of the heated wall are adiabatic. The governing equations are solved by finite volume method. The results show that among the different lengths of the heat source, an enhancement in the heat transfer rate is observed only for the length LH = 1/3 of the heat source. In the case of location of the heat source, the overall heat transfer rate is increased when the heat source is located at the top of the hot wall. For Ri = 1 and 0.01, a better heat transfer rate is obtained when the heat source is placed at the top of the hot wall whereas for Ri = 100, it occurs when the heating portion is at the middle of the hot wall. As the solid volume fraction increases, the viscosity of the fluid is increased, which causes a reduction in the flow intensity. An addition of nanoparticles in the base fluid enhances the overall heat transfer rate significantly for all Da considered. The permeability of the porous medium plays a major role in convection of nanofluid than porosity. A high heat transfer rate (57.26%) is attained for Da = 10−1 and χ = 0.06.

scholarly journals Comparison of mathematical models to estimate the thermal conductivity of titanium oxide-water based nanofluid: A review

2021 ◽  
pp. 224-224
Author(s):  
Bhrant Dandoutiya ◽  
Arvind Kumar
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Mathematical Models ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Maxwell Model ◽  
Working Fluid ◽  
Different Types ◽  
Cell Preservation

Heat transfer is a desirable phenomenon in many industries such as in refrigeration, transportation, power generation, cell preservation, incubator, metallurgy and material processing, health services, etc. Different types of fluids like water, oil, ethylene glycol etc are being used as a heat transfer medium. Water is a commonly used as working fluid for transfer of heat. Nanofluids are developed by adding nano sized particle(s) in existing fluid to improve the heat transfer rate. Thermal conductivity of the nanofluid is an important parameter in estimation of heat transfer rate. Different types of mathematical models were developed by various investigators to predict the thermal conductivity of the nanofluids. In this review paper,the theoretical and mathematical model(s) have been compared to predict the thermal conductivity of nanofluids. The experimental data have been collected from literature and compared with Maxwell model, Hamilton and crosser(H-C) model, Maxwell-Garnetts(MG) model, Pak cho model, Timofeeva et al. model, Li and Peterson model, Bhattacharya et al. model respectively in detail. It has been observed that the prediction wih the help of the mathematical models is good when the value of volume fraction was less than 0.01.

scholarly journals Investigation of the Relationship between Morphology and Thermal Conductivity of Powder Metallurgically Prepared Aluminium Foams

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3623
Author(s):  
Arun Gopinathan ◽  
Jaroslav Jerz ◽  
Jaroslav Kováčik ◽  
Tomáš Dvorák
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flow ◽  
Effective Thermal Conductivity ◽  
Internal Structure ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Thermal Storage ◽  
Aluminium Foam ◽  
Foam Structure

Among different promising solutions, coupling closed-cell aluminium foam composite panels prepared by a powder metallurgical method with pore walls interconnected by microcracks, with low thermal conductivity phase change materials (PCMs), is one of the effective ways of increasing thermal conductivity for better performance of thermal storage systems in buildings. The internal structure of the foam formation, related to the porosity which decides the heat transfer rate, plays a significant role in the thermal energy storage performance. The dependence of the heat transfer characteristics on the internal foam structure is studied numerically in this work. The foamable precursor of 99.7% pure aluminium powder mixed with 0.15 wt.% of foaming agent, TiH2 powder, was prepared by compacting, and extruded to a volume of 20 × 40 × 5 mm. Two aluminium foam samples of 40 × 40 × 5 mm were examined with apparent densities of 0.7415 g/cm3 and 1.62375 g/cm3. The internal porous structure of the aluminium foam samples was modelled using X-ray tomography slices through image processing techniques for finite element analysis. The obtained numerical results for the heat transfer rate and effective thermal conductivity of the developed surrogate models revealed the influence of porosity, struts, and the presence of pore walls in determining the heat flow in the internal structure of the foam. Additionally, it was found that the pore size and its distribution determine the uniform heat flow rate in the entire foamed structure. The numerical data were then validated against the analytical predictions of thermal conductivity based on various correlations. It has been found that the simplified models of Bruggemann and Russell and the parallel–series model can predict the excellent effective thermal conductivity results of the foam throughout the porosity range. The optimal internal foam structure was studied to explore the possibilities of using aluminium foam for PCM-based thermal storage applications.

scholarly journals Control temperature fluctuations in two-phase CuO-water nanofluid by transfiguration of the enclosures

2020 ◽  
pp. 334-334
Author(s):  
Hadi Pourziaei Araban ◽  
Javad Alinejad ◽  
Ganji Domiri
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Wall Temperature ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Temperature Fields ◽  
Two Phase ◽  
Flux Boundary Condition

The innovation of this paper is to simulate two-phase nanofluid natural convection inside the transformable enclosure to control the heat transfer rate under different heat flux. Heat transfer of a two-phase CuO-water nanofluid in an enclosure under different heat flux has many industrial applications including energy storage systems, thermal control of electronic devices and cooling of radioactive waste containers. The Lattice Boltzmann Method based on the D2Q9 method has been utilized for modeling velocity and temperature fields. Streamlines, isotherms and nanoparticle volume fraction, have been investigated for control the heat transfer rate for several cases. The purpose of this feasibility study is to achieve uniform temperature profiles and Tmax < 50?C under different heat flux. Natural convection heat transfer in the rectangular and parallelogram enclosures with positive and negative angular adiabatic walls were simulated. The average wall temperature under heat flux boundary condition has been studied to predict optimal levels of effective factors to control the maximum wall temperature. The results illustrated parallelogram enclosures with positive angle of case 1 and case 3 and 4 with rectangular enclosures were best cases for considering physical conditions. Average of temperature for these cases were 37.9, 29.7 and 38.2, respectively.

Flow and Heat Transfer of Gold-Blood Nanofluid in a Porous Channel with Moving/Stationary Walls

2016 ◽  
Vol 33 (3) ◽  
pp. 395-404 ◽  
Author(s):  
S. Srinivas ◽  
A. Vijayalakshmi ◽  
A. Subramanyam Reddy
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Analytical Solutions ◽  
Transfer Rate ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Porous Channel ◽  
Nanoparticle Volume Fraction ◽  
Similarity Transformations ◽  
Flow And Heat Transfer

AbstractThe present study investigates the flow and heat transfer characteristics of blood carrying gold nanoparticles in a porous channel with moving/stationary walls in the presence of thermal radiation. Blood is considered as Newtonian fluid which is the base fluid and gold (Au) as nanoparticles. The governing equations are transformed into system of ordinary differential equations by using similarity transformations. The analytical solutions are obtained for the flow variables by employing homotopy analysis method (HAM). The analytical solutions are compared with the numerical solutions which are obtained by shooting technique along with Runge-Kutta scheme. It was noticed that there is a good agreement between analytical and numerical results. The influence of various parameters on velocity, temperature and heat transfer rate of gold-blood nanofluid has been discussed in detail. The temperature of the nanofluid increases with increasing the nanoparticle volume fraction. The heat transfer rate at the top wall increases with increasing nanoparticle volume fraction while it decreases for a given increase in radiation parameter.

scholarly journals Significance of Shape Factor in Heat Transfer Performance of Molybdenum-Disulfide Nanofluid in Multiple Flow Situations; A Comparative Fractional Study

Molecules ◽  
2021 ◽  
Vol 26 (12) ◽  
pp. 3711
Author(s):  
Asifa ◽  
Talha Anwar ◽  
Poom Kumam ◽  
Zahir Shah ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Molybdenum Disulfide ◽  
Heat Transfer Rate ◽  
Shape Factor ◽  
Transfer Rate ◽  
Maximum Heat ◽  
Left Wall ◽  
Maximum Heat Transfer ◽  
Mos2 Nanoparticles

In this modern era, nanofluids are considered one of the advanced kinds of heat transferring fluids due to their enhanced thermal features. The present study is conducted to investigate that how the suspension of molybdenum-disulfide (MoS2) nanoparticles boosts the thermal performance of a Casson-type fluid. Sodium alginate (NaAlg) based nanofluid is contained inside a vertical channel of width d and it exhibits a flow due to the movement of the left wall. The walls are nested in a permeable medium, and a uniform magnetic field and radiation flux are also involved in determining flow patterns and thermal behavior of the nanofluid. Depending on velocity boundary conditions, the flow phenomenon is examined for three different situations. To evaluate the influence of shape factor, MoS2 nanoparticles of blade, cylinder, platelet, and brick shapes are considered. The mathematical modeling is performed in the form of non-integer order operators, and a double fractional analysis is carried out by separately solving Caputo-Fabrizio and Atangana-Baleanu operators based fractional models. The system of coupled PDEs is converted to ODEs by operating the Laplace transformation, and Zakian’s algorithm is applied to approximate the Laplace inversion numerically. The solutions of flow and energy equations are presented in terms of graphical illustrations and tables to discuss important physical aspects of the observed problem. Moreover, a detailed inspection on shear stress and Nusselt number is carried out to get a deep insight into skin friction and heat transfer mechanisms. It is analyzed that the suspension of MoS2 nanoparticles leads to ameliorating the heat transfer rate up to 9.5%. To serve the purpose of achieving maximum heat transfer rate and reduced skin friction, the Atangana-Baleanu operator based fractional model is more effective. Furthermore, it is perceived that velocity and energy functions of the nanofluid exhibit significant variations because of the different shapes of nanoparticles.

scholarly journals Heat Transmission Reinforcers Induced by MHD Hybrid Nanoparticles for Water/Water-EG Flowing over a Cylinder

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 623
Author(s):  
Firas A. Alwawi ◽  
Mohammed Z. Swalmeh ◽  
Amjad S. Qazaq ◽  
Ruwaidiah Idris
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Liquid Velocity ◽  
Flow Characteristics ◽  
Hybrid Nanoparticles ◽  
Critical Parameters ◽  
Heat Transmission ◽  
Constant Wall Temperature

The assumptions that form our focus in this study are water or water-ethylene glycol flowing around a horizontal cylinder, containing hybrid nanoparticles, affected by a magnetic force, and under a constant wall temperature, in addition to considering free convection. The Tiwari–Das model is employed to highlight the influence of the nanoparticles volume fraction on the flow characteristics. A numerical approximate technique called the Keller box method is implemented to obtain a solution to the physical model. The effects of some critical parameters related to heat transmission are also graphically examined and analyzed. The increase in the nanoparticle volume fraction increases the heat transfer rate and liquid velocity; the strength of the magnetic field has an adverse effect on liquid velocity, heat transfer, and skin friction. We find that cobalt nanoparticles provide more efficient support for the heat transfer rate of aluminum oxide than aluminum nanoparticles.

scholarly journals Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110240
Author(s):  
Rehan Ali Shah ◽  
Hidayat Ullah ◽  
Muhammad Sohail Khan ◽  
Aamir Khan
Keyword(s):  
Heat Transfer ◽  
Ionic Liquid ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

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