scholarly journals Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
O. D. Makinde ◽  
S. Khamis ◽  
M. S. Tshehla ◽  
O. Franks
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Perturbation Methods ◽  
Regular Perturbation ◽  
Convective Cooling ◽  
Navier Slip ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Friction Pressure Drop

Heat transfer characteristics of a Berman flow of water based nanofluids containing copper (Cu) and alumina (Al2O3) as nanoparticles in a porous channel with Navier slip, viscous dissipation, and convective cooling are investigated. It is assumed that the exchange of heat with the ambient surrounding takes place at the channel walls following Newton’s law of cooling. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. These equations are solved analytically by regular perturbation methods with series improvement technique and numerically using an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop, and Nusselt numbers are presented graphically and discussed quantitatively.

Influence of Lorentz force, Cattaneo-Christov heat flux and viscous dissipation on the flow of micropolar fluid past a nonlinear convective stretching vertical surface

2017 ◽  
Vol 6 (4) ◽  
Author(s):  
Machireddy Gnaneswara Reddy
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Lorentz Force ◽  
Micropolar Fluid ◽  
Vertical Surface ◽  
Skin Friction Coefficient ◽  
Similarity Transformations ◽  
Flow Parameters

AbstractThe problem of micropolar fluid flow over a nonlinear stretching convective vertical surface in the presence of Lorentz force and viscous dissipation is investigated. Due to the nature of heat transfer in the flow past vertical surface, Cattaneo-Christov heat flux model effect is properly accommodated in the energy equation. The governing partial differential equations for the flow and heat transfer are converted into a set of ordinary differential equations by employing the acceptable similarity transformations. Runge-Kutta and Newton’s methods are utilized to resolve the altered governing nonlinear equations. Obtained numerical results are compared with the available literature and found to be an excellent agreement. The impacts of dimensionless governing flow pertinent parameters on velocity, micropolar velocity and temperature profiles are presented graphically for two cases (linear and nonlinear) and analyzed in detail. Further, the variations of skin friction coefficient and local Nusselt number are reported with the aid of plots for the sundry flow parameters. The temperature and the related boundary enhances enhances with the boosting values of

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

Slip flow over a non-Newtonian fluid through a Darcy–Forchheimer medium: Numerical approach

2019 ◽  
Vol 33 (35) ◽  
pp. 1950448
Author(s):  
K. Ganesh Kumar ◽  
M. N. Khan ◽  
M. Osman ◽  
Abdulaziz R. Alharbi ◽  
Mohammad Rahimi-Gorji ◽  
...  
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Convective Boundary Condition ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Liquid Suspension

This work focused on slip flow over a non-Newtonian nanofluid fluid flow past a stretching sheet with particles–liquid suspension. The convective boundary condition is taken into account. Similarity transformations are utilized to reduce the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Runge–Kutta–Fehlberg scheme is used to get the numerical solution. Important parameters are analyzed through graphs and skin friction coefficient. Nusselt numbers are presented in tables. Investigation reveals that slip parameter decreases the velocity field and Biot number increases the temperature field.

scholarly journals Insights into the Stability of Mixed Convective Darcy–Forchheimer Flows of Cross Liquids from a Vertical Plate with Consideration of the Significant Impact of Velocity and Thermal Slip Conditions

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 31 ◽  
Author(s):  
Umair Khan ◽  
Aurang Zaib ◽  
Ilyas Khan ◽  
Kottakkaran Sooppy Nisar ◽  
Dumitru Baleanu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Vertical Plate ◽  
Thermal Slip ◽  
Slip Conditions ◽  
Drag Forces ◽  
Similarity Transformations ◽  
Mixed Convective Flow ◽  
The Stability ◽  
The Impact

This paper reflects the effects of velocity and thermal slip conditions on the stagnation-point mixed convective flow of Cross liquid moving over a vertical plate entrenched in a Darcy–Forchheimer porous medium. A Cross liquid is a type of non-Newtonian liquid whose viscosity depends on the shear rate. The leading partial differential equations (PDEs) are altered to nonlinear ordinary differential equations (ODEs) via feasible similarity transformations. These transmuted equations are computed numerically through the bvp4c solver. The authority of sundry parameters on the temperature and velocity distributions is examined graphically. In addition, the characteristics of heat transfer are analyzed in the presence of the impact of drag forces. The outcomes reveal that the permeability parameter decelerates the drag forces and declines the rate of heat transfer in both forms of solutions. Moreover, it is found that the drag forces decline with the growing value of the Weissenberg parameter in the upper branch solutions, while a reverse trend is revealed in the lower branch solutions. However, the rate of heat transfer shows a diminishing behavior with an increasing value of the Weissenberg parameter.

Effects of Creep Flow and Viscous Dissipation in the Slip Regime for Isoflux Rectangular Microchannels

2007 ◽  
Author(s):  
Jennifer van Rij ◽  
Tim Ameel ◽  
Todd Harman
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Pressure Drop ◽  
Convective Heat Transfer ◽  
Viscous Dissipation ◽  
Convective Heat ◽  
Numerical Algorithm ◽  
Slip Flow ◽  
Creep Flow ◽  
Nusselt Numbers

The effects of rarefaction on convective heat transfer and pressure drop characteristics are numerically evaluated for uniform wall heat flux rectangular microchannels. Results are obtained by numerically solving the momentum and energy equations with both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature fields are then evaluated to obtain the microchannel Poiseuille and Nusselt numbers. In addition to the effects of rarefaction, the effects of aspect ratio, thermal creep flow, and viscous dissipation are investigated for locally fully developed Poiseuille and Nusselt numbers. The constant wall heat flux results obtained in this study are compared to constant wall temperature results obtained previously, using the same numerical algorithm, at various aspect ratios including the limiting case of parallel plate microchannels. In addition to supplying previously unreported data on slip flow convective heat transfer and pressure drop characteristics, these results verify the numerical algorithm for more complex future slip flow analyses.

scholarly journals Numerical Study of Lorentz Force Interaction with Micro Structure in Channel Flow

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4286
Author(s):  
Shabbir Ahmad ◽  
Kashif Ali ◽  
Sohail Ahmad ◽  
Jianchao Cai
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Numerical Study ◽  
Nonlinear Differential Equations ◽  
Thermal Control ◽  
Shear Stresses ◽  
Fluid Temperature ◽  
X Rays ◽  
Micro Particles

The heat transfer Magnetohydrodynamics flows have been potentially used to enhance the thermal characteristics of several systems such as heat exchangers, electromagnetic casting, adjusting blood flow, X-rays, magnetic drug treatment, cooling of nuclear reactors, and magnetic devices for cell separation. Our concern in this article is to numerically investigate the flow of an incompressible Magnetohydrodynamics micropolar fluid with heat transportation through a channel having porous walls. By employing the suitable dimensionless coordinates, the flow model equations are converted into a nonlinear system of dimensionless ordinary differential equations, which are then numerically treated for different preeminent parameters with the help of quasi-linearization. The system of complex nonlinear differential equations can efficiently be solved using this technique. Impact of the problem parameters for microrotation, temperature, and velocity are interpreted and discussed through tables and graphs. The present numerical results are compared with those presented in previous literature and examined to be in good contact with them. It has been noted that the imposed magnetic field acts as a frictional force which not only increases the shear stresses and heat transfer rates at the channel walls, but also tends to rotate the micro particles in the fluid more rapidly. Furthermore, viscous dissipation may raise fluid temperature to such a level that the possibility of thermal reversal exists, at the geometric boundaries of the domain. It is therefore recommended that external magnetic fields and viscous dissipation effects may be considered with caution in applications where thermal control is required.

scholarly journals Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

2021 ◽  
Vol 50 (12) ◽  
pp. 3753-3764
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Theoretical Investigations ◽  
Suitable Form ◽  
Layer Flow

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

scholarly journals Magnetohydrodynamic Flow Past a Nonlinear Stretching or Shrinking Cylinder in Nanofluid with Viscous Dissipation and Heat Generation Effect

2021 ◽  
Vol 90 (1) ◽  
pp. 102-114
Author(s):  
Mahani Ahmad Kardri ◽  
Norfifah Bachok ◽  
Norihan Md. Arifin ◽  
Fadzilah Md. Ali ◽  
Yong Faezah Rahim
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Flow And Heat Transfer ◽  
Controlling Parameter ◽  
Numerical Computing ◽  
Nonlinear Stretching

The Tiwari-Das model is used to investigate magnetohydrodynamic stagnation point flow and heat transfer past a nonlinear stretching or shrinking cylinder in nanofluid with viscous dissipation and heat generation using. The partial differential equations, also known as governing equations, were reduced to nonlinear ordinary differential equations using similarity transformation. MATLAB with the bvp4c solver is used for numerical computing. The controlling parameter, such as nanoparticle volume fraction, magnetic, curvature, nonlinear, radiation, and heat generation parameters, as well as Eckert and Grashof numbers, influence the skin friction coefficient, heat transfer rate, velocity, and temperature profiles. The results are presented as graphs to show the influence of the variables studied. In some circumstances of stretching and shrinking cases, dual solutions can be obtained.

scholarly journals Magnetohydrodynamic stagnation point on a Casson nanofluid flow over a radially stretching sheet

2020 ◽  
Vol 11 ◽  
pp. 1303-1315
Author(s):  
Ganji Narender ◽  
Kamatam Govardhan ◽  
Gobburu Sreedhar Sarma
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Casson Nanofluid ◽  
Similarity Transformations ◽  
Program Language ◽  
The Impact

This article proposes a numerical model to investigate the impact of the radiation effects in the presence of heat generation/absorption and magnetic field on the magnetohydrodynamics (MHD) stagnation point flow over a radially stretching sheet using a Casson nanofluid. The nonlinear partial differential equations (PDEs) describing the proposed flow problem are reduced to a set of ordinary differential equations (ODEs) via suitable similarity transformations. The shooting technique and the Adams–Moulton method of fourth order are used to obtain the numerical results via the computational program language FORTRAN. Nanoparticles have unique thermal and electrical properties which can improve heat transfer in nanofluids. The effects of pertinent flow parameters on the nondimensional velocity, temperature and concentration profiles are presented. Overall, the results show that the heat transfer rate increases for higher values of the radiation parameter in a Casson nanofluid.

Viscous Dissipation Effect on Heat Transfer Through Nano Fluid in a Vertical Wavy Channel with Travelling Thermal Wave

2020 ◽  
Vol 28 ◽  
pp. 17-31
Author(s):  
Paladugu Venkata Ramana ◽  
Gosukonda Srinivas ◽  
G.V.P.N Srikanth
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Fluid Flow ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Thermal Wave ◽  
Transfer Rate ◽  
Wavy Channel ◽  
Nano Fluid ◽  
Flow And Heat Transfer

The effect of viscous dissipation on heat transfer through nano-fluid in a vertical wavy channel filled with porous media has been studied. The consequential differential equations are simplified by the R-K method of 6th order. The numerical obtained results are shown in the graphs. The significant results of fluid flow and heat transfer rate and its properties are shown graphically. Nusslet values are calculated a for varying the governing parameters φ Da, Gr, ε, Ec and the remaining parameters are to be constants.

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