scholarly journals Hydromagnetic Flow Over a Heated Stretching Surface

2021 ◽  
pp. 332-338
Author(s):  
Kotagiri Srihari
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Viscous Incompressible Fluid ◽  
Temperature Fields ◽  
Hydromagnetic Flow ◽  
Stretching Surface ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Velocity And Temperature Fields ◽  
Energy Equations

In the present paper on steady flow of a viscous incompressible fluid past a heated stretching sheet with thermal radiation is studied. Magnetic field is applied normal to the flow. With suitable similarity transformations, the momentum and energy equations are reduced to ordinary differential equations. The governing differential equations with corresponding boundary conditions are solved numerically using MATLAB inbuilt solver bvp4c,. Graphical results for velocity and temperature fields, tabular values of Skin-friction and Nusselt numbers are presented and discussed. It is found the temperature of the fluid increases for the increasing values of radiation parameter.

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.

scholarly journals Calculation of evaporation length of a liquid bridge flowing between inclined hot tubes

2021 ◽  
Vol 2119 (1) ◽  
pp. 012056
Author(s):  
P I Geshev
Keyword(s):  
Nonlinear Integral Equation ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Method Of Boundary Elements ◽  
Hydrostatic Equation ◽  
Velocity And Temperature Fields ◽  
Energy Equations ◽  
Surface Tension Forces

Abstract The bridge consists of liquid held by surface tension forces between two inclined tubes in an LNG heat exchanger. The shape of the bridge is calculated by the hydrostatic equation, which is reduced to a nonlinear integral equation and resolved by the Newton method. The velocity and temperature fields in the bridge are described by the Navier-Stokes and energy equations, respectively. They are reduced to the boundary integral equations and calculated by the method of boundary elements. Heat transfer coefficient is calculated for evaporating bridge and the length of total bridge evaporation is estimated.

Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

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.

Radiation and Partial Slip Effects on Magnetohydrodynamic Jeffrey Nanofluid Containing Gyrotactic Microorganisms Over a Stretching Surface

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
K. Kumaraswamy Naidu ◽  
D. Harish Babu ◽  
S. Harinath Reddy ◽  
P. V. Satya Narayana
Keyword(s):  
Nusselt Number ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Coupled System ◽  
Partial Slip ◽  
Stretching Surface ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Jeffrey Nanofluid ◽  
The Impact

Abstract In this study, the impact of thermal radiation and partial slip on magnetohydrodynamic flow of the Jeffrey nanofluid comprising motile gyrotactic microorganisms via vertical stretching surface is analyzed. The governing partial differential equations are reformed to a system of coupled ordinary differential equations by utilizing the similarity transformations. The transformed equations are of order four, which are complex to solve analytically and hence, the coupled system is solved computationally by using the shooting technique along the Runge–Kutta integrated scheme. The ramifications of different thermophysical parameters on the density of gyrotactic microorganisms, Jeffrey nanofluid velocity, nanoparticles concentration, temperature, Sherwood number, and Nusselt number are illustrated graphically. Comparing this study with the results already published favors the validity of this study. It is established that the Nusselt number is boosted on enhancing the thermal radiation parameter, and the reverse trend has been observed on increasing the Richardson number, whereas the gyrotactic microorganisms density is more in case of viscous nanofluid compared to the Jeffrey nanofluid.

Heat transfer over an unsteady stretching surface with prescribed heat flux

2008 ◽  
Vol 86 (6) ◽  
pp. 853-855 ◽  
Author(s):  
A Ishak ◽  
R Nazar ◽  
I Pop
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Method Comparison ◽  
Temperature Fields ◽  
Stretching Surface ◽  
Keller Box Method ◽  
Unsteady Stretching Surface ◽  
Layer Flow

The unsteady laminar boundary-layer flow over a continuously stretching surface in a viscous and incompressible quiescent fluid is studied. The unsteadiness in the flow and temperature fields is caused by the time dependence of the stretching velocity and the surface heat flux. The nonlinear partial differential equations of continuity, momentum, and energy, with three independent variables, are reduced to nonlinear ordinary differential equations, before they are solved numerically by the Keller-box method. Comparison with available data from the open literature as well as the exact solution for the steady-state case of the present problem is made, and found to be in good agreement. Effects of the unsteadiness parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined.PACS No.: 47.15.Cb

Stagnation Point Flow through a Porous Medium towards a Radially Stretching Sheet in the Presence of Uniform Suction or Injection and Heat Generation

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Hazem Ali Attia ◽  
Karem Mahmoud Ewis ◽  
Mostafa A. M. Abdeen
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Stagnation Point Flow ◽  
Uniform Suction ◽  
Flow Through ◽  
Energy Equations

An analysis is made of the steady laminar axisymmetric stagnation point flow of an incompressible viscous fluid in a porous medium impinging on a permeable radially stretching sheet with heat generation or absorption. A uniform suction or blowing is applied normal to the plate which is maintained at a constant temperature. Similarity transformation is used to transform the governing partial differential equations to ordinary differential equations. The finite difference method and generalized Thomas algorithm are used to solve the governing nonlinear momentum and energy equations. The effects of the uniform suction/blowing velocity, the stretching parameter and the heat generation/absorption coefficient on both the flow field and heat transfer are presented and discussed. The results indicate that increasing the stretching parameter or the suction/blowing velocity decreases both the velocity and thermal boundary layer thicknesses. The effect of the stretching parameter on the velocity components is more apparent for suction than blowing while its effect on the temperature and rate of heat transfer at the wall is clearer in the case of blowing than suction.

An Analytical Study of Natural Convective Heat Transfer within a Trapezoidal Enclosure

1980 ◽  
Vol 102 (4) ◽  
pp. 640-647 ◽  
Author(s):  
L. Iyican ◽  
Y. Bayazitogˇlu ◽  
L. C. Witte
Keyword(s):  
Heat Transfer ◽  
Analytical Study ◽  
Temperature Fields ◽  
Nusselt Numbers ◽  
Method Of Solution ◽  
Different Temperatures ◽  
Nonlinear Form ◽  
Trapezoidal Enclosure ◽  
Energy Equations ◽  
Rayleigh Numbers

The natural convection motion and the heat transfer within a trapezoidal enclosure with parallel cylindrical top and bottom walls at different temperatures and plane adiabatic sidewalls are studied. Two-dimensional natural convective fields for a range of Rayleigh numbers, up to 2.7 × 106, and enclosure tilt angles, 0 to 180 deg measured from vertical, are investigated. The Galerkin’s method of solution is applied to nonlinear form of the momentum and energy equations to determine the velocity and temperature fields. The average and local Nusselt numbers are also presented.

scholarly journals Flow and Heat Transfer in a Liquid Film over a Permeable Stretching Sheet

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
R. C. Aziz ◽  
I. Hashim ◽  
A. K. Alomari
Keyword(s):  
Heat Transfer ◽  
Liquid Film ◽  
Stretching Sheet ◽  
Temperature Fields ◽  
Temperature Profiles ◽  
Suction Parameter ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis

An analysis has been carried out to study the flow and heat transfer in a liquid film over a permeable stretching sheet. Using similarity transformations, the time-dependent boundary layer equations are reduced to a set of nonlinear ordinary differential equations. The resulting parameter problem and velocity as well as temperature fields are solved using the homotopy analysis method (HAM). Analytic series solutions are given, and numerical results for velocity and the temperature profiles are presented through graphs of different values for pertinent parameter. The effects of unsteadiness parameter and permeability parameter on the velocity and temperature profiles are explored for different values of blowing or suction parameter.

scholarly journals Role of Brownian Motion and Thermophoresis Effects on Hydromagnetic Flow of Nanofluid Over a Nonlinearly Stretching Sheet with Slip Effects and Solar Radiation

2019 ◽  
Vol 24 (3) ◽  
pp. 489-508
Author(s):  
S.P. Anjali Devi ◽  
S. Mekala
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Hydromagnetic Flow ◽  
Nonlinearly Stretching Sheet

Abstract Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

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