Nonlinear Approximation for Natural Convection Flow Near a Vertical Plate with Thermal Radiation Effect

2021 ◽  
Author(s):  
Basant K. Jha ◽  
Gabriel Samaila
Keyword(s):  
Natural Convection ◽  
Temperature Gradient ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Nonlinear Approximation ◽  
Vertical Wall ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Flow Formation ◽  
Non Linear

Abstract A non-linear approximation for natural convection boundary layer flow near a vertical wall under the influence of thermal radiation is analysed. The governing equation comprises of the set of non-linear partial differential equations is transformed into ordinary differential equations via the similarity transformation. The final dimensionless equations are solved numerically using the Runge Kutta Ferlberg fourth-fifth order (RKF45) method. The effects of the embedded parameters affecting the flow formation, temperature distribution, Nusselt number and the Skin friction are thoroughly examined. It is found that the temperature gradient is proportional to the thermal radiation near the plate whereas inversely proportional to the temperature gradient far away from the plate. The flow formation in the boundary enhanced near the vertical wall with thermal radiation parameter increase but remain constant in the free stream region. The rate of heat transfer enhanced with the thermal radiation whereas decreases with other embedded parameters under consideration.

scholarly journals Mixed convection flow of Jeffrey fluid along an inclined stretching cylinder with double stratification effect

2017 ◽  
Vol 21 (2) ◽  
pp. 849-862 ◽  
Author(s):  
Tasawar Hayat ◽  
Sajid Qayyum ◽  
Muhammad Farooq ◽  
Ahmad Alsaedi ◽  
Muhammad Ayub
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Variable Temperature ◽  
Heat Transfer Analysis ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Convection Boundary Layer ◽  
Stretching Cylinder ◽  
Double Stratification ◽  
Non Linear

This paper addresses double stratified mixed convection boundary layer flow of Jeffrey fluid due to an impermeable inclined stretching cylinder. Heat transfer analysis is carried out with heat generation/absorption. Variable temperature and concentration are assumed at the surface of cylinder and ambient fluid. Non-linear partial differential equations are reduced into the non-linear ordinary differential equations after using the suitable transformations. Convergent series solutions are computed. Effects of various pertinent parameters on the velocity, temperature, and concentration distributions are analyzed graphically. Numerical values of skin friction coefficient, Nusselt, and Sherwood numbers are also computed and discussed.

scholarly journals Effect of Thermal Radiation on Magneto-Convection of a Micropolar Nanoliquid towards a Non-Linear Stretching Surface with Convective Boundary

2018 ◽  
Vol 7 (4.10) ◽  
pp. 417
Author(s):  
K. Jagan ◽  
S. Sivasankaran ◽  
M. Bhuvaneswari ◽  
S. Rajan
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Convective Boundary Condition ◽  
Convection Flow ◽  
Stretching Surface ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Boundary Parameter ◽  
Non Linear

The objective of this paper is to analyze the effect of thermal radiation on MHD mixed convection flow of a micropolar nanoliquid   towards a non-linear stretching surface with convective boundary condition. The governing equations are converted into non-linear    ordinary differential equations by using suitable similarity transformations. The homotopy analysis method is used for solving the non-linear ordinary differential equations. The temperature profiles increase due to increase in thermal radiation parameter. The microrotation   profile increases when boundary parameter is increased. Also, the skin friction coefficient and local Nusselt are plotted for various    parameters.  

scholarly journals Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 393-417 ◽  
Author(s):  
Yahaya Shagaiya Daniel ◽  
Abdul Aziz Zainal ◽  
Zuhaila Ismail ◽  
Faisal Salah
Keyword(s):  
Natural Convection ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Thermal Stratification ◽  
Nonlinear Partial Differential Equations ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Reaction Heat ◽  
Radiation Chemical

In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.

A comparative study of Al2O3 and TiO2 nanofluid flow over a wedge with non-linear thermal radiation

2019 ◽  
Vol 30 (3) ◽  
pp. 1291-1317 ◽  
Author(s):  
Paluru Sreedevi ◽  
P. Sudarsana Reddy ◽  
Mikhail Sheremet
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Field Parameter ◽  
Convection Flow ◽  
Geothermal Systems ◽  
Content Type ◽  
Magnetic Field Parameter ◽  
Non Linear ◽  
The Impact

Purpose The purpose of this study is to analyze the impact of chemical reaction and thermal radiation on mixed convection flow, heat and mass transfer characteristics of nanofluid through a wedge occupied with water–TiO2 and water–Al2O3 made nanofluid by considering velocity, temperature and concentration slip conditions in present investigation. Design/methodology/approach Using acceptable similarity transformations, the prevailing partial differential equations have been altered into non-linear ordinary differential equations and are demonstrated by the diverse thermophysical parameters. The mathematical model is solved numerically by implementing Galarkin finite element method and the outcomes are shown in tables and graphs. Findings The temperature and concentration fields impede as magnetic field parameter improves in both water–Al2O3 and water–TiO2 nanofluid. While there is contradiction in the velocity field as the values of magnetic field parameter rises in both nanofluids. The non-dimensional velocity rate, rate of temperature and rate of concentration rise with improved values of Weissenberg number. Originality/value Nanofluid flows past wedge-shaped geometries have gained much consideration because of their extensive range of applications in engineering and science, such as, magnetohydrodynamics, crude oil extraction, heat exchangers, aerodynamics and geothermal systems. Virtually, these types of nanofluid flows happen in ground water pollution, aerodynamics, retrieval of oil, packed bed reactors and geothermal industries.

scholarly journals Influence of thermal radiation on non-Darcian natural convection in a square cavity filled with fluid saturated porous medium of uniform porosity

2012 ◽  
Vol 17 (2) ◽  
pp. 223-237 ◽  
Author(s):  
Tapas Ray Mahapatra ◽  
Dulal Pal ◽  
Sabyasachi Mondal
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Thermal Radiation ◽  
Horizontal Plane ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Staggered Grid ◽  
Convection Flow ◽  
Physical Parameters ◽  
Square Cavity

Influence of thermal radiation on natural-convection flow in a square cavity filled with a porous medium of uniform porosity having isothermal vertical walls and adiabatic horizontal walls, has been studied numerically by using finite-difference method with staggered grid distribution. The simulation is performed by considering both Darcian and non-Darcian models. Governing momentum and energy equations are solved numerically to obtain velocity and temperature fields for various values of different physical parameters. It is seen that increasing the thermal radiation parameter enhances the local Nusselt number on the left vertical wall whereas the reverse effects are observed due to increase in the heat generating parameter when Ra = 109. The temperature at the mid-horizontal plane decreases with increase in the value of Rayleigh number up to a certain distance from the left vertical wall and beyond that distance the opposite trend is observed. The temperature at the mid-horizontal plane increases with increase in the value of heat generating parameter.

scholarly journals Numerical study of thermal radiation and mass transfer effects on free convection flow over a moving vertical porous plate using cubic B-spline collocation method

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
M. Abu zeid ◽  
Khalid K. Ali ◽  
M. A. Shaalan ◽  
K. R. Raslan
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Thermal Radiation ◽  
Porous Plate ◽  
Convection Flow ◽  
Spline Collocation ◽  
Free Convection Flow ◽  
B Spline ◽  
Vertical Porous Plate

Abstract In this paper, we present a numerical method based on cubic B-spline function for studying the effects of thermal radiation and mass transfer on free convection flow over a moving vertical porous plate. Similarity transformations reduced the governing partial differential equations of the fluid flow to a system of nonlinear ordinary differential equations which are solved numerically using a cubic B-spline collocation method. The effects of various physical parameters on the velocity, temperature, and concentration distributions are shown graphically, and the numerical values of physical quantities like skin friction, Nusselt number, and Sherwood number for various parameters are presented in tabular form and discussed.

Convective transport of thermal and solutal energy in unsteady MHD Oldroyd-B nanofluid flow

2021 ◽  
Author(s):  
Muhammad Yasir ◽  
Masood Khan ◽  
Awais Ahmed ◽  
Malik Zaka Ullah
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Heat Generation ◽  
Axisymmetric Flow ◽  
Convective Transport ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract In this work, an analysis is presented for the unsteady axisymmetric flow of Oldroyd-B nanofluid generated by an impermeable stretching cylinder with heat and mass transport under the influence of heat generation/absorption, thermal radiation and first-order chemical reaction. Additionally, thermal and solutal performances of nanofluid are studied using an interpretation of the well-known Buongiorno's model, which helps us to determine the attractive characteristics of Brownian motion and thermophoretic diffusion. Firstly, the governing unsteady boundary layer equation's (PDEs) are established and then converted into highly non-linear ordinary differential equations (ODEs) by using the suitable similarity transformations. For the governing non-linear ordinary differential equations, numerical integration in domain [0, ∞) is carried out using the BVP Midrich scheme in Maple software. For the velocity, temperature and concentration distributions, reliable results are prepared for different physical flow constraints. According to the results, for increasing values of Deborah numbers, the temperature and concentration distribution are higher in terms of relaxation time while these are decline in terms of retardation time. Moreover, thermal radiation and heat generation/absorption are increased the temperature distribution and corresponding boundary layer thickness. With previously stated numerical values, the acquired solutions have an excellent accuracy.

Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers

2000 ◽  
Vol 123 (1) ◽  
pp. 84-95 ◽  
Author(s):  
C. J. Ho ◽  
F. J. Tu
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Convection Flow ◽  
Oscillatory Convection ◽  
Uniform Temperature ◽  
Density Maximum ◽  
Rectangular Enclosure ◽  
Rayleigh Numbers

An experimental and numerical investigation is presented concerning the natural convection of water near its maximum-density in a differentially heated rectangular enclosure at high Rayleigh numbers, in which an oscillatory convection regime may arise. The water in a tall enclosure of Ay=8 is initially at rest and at a uniform temperature below 4°C and then the temperature of the hot vertical wall is suddenly raised and kept at a uniform temperature above 4°C. The cold vertical wall is maintained at a constant uniform temperature equal to that of the initial temperature of the water. The top and bottom walls are insulated. Using thermally sensitive liquid crystal particles as tracers, flow and temperature fields of a temporally oscillatory convection was documented experimentally for RaW=3.454×105 with the density inversion parameter θm=0.5. The oscillatory convection features a cyclic sequence of onset at the lower quarter-height region, growth, and decay of the upward-drifting secondary vortices within counter-rotating bicellular flows in the enclosure. Two and three-dimensional numerical simulations corresponding to the visualization experiments are undertaken. Comparison of experimental with numerical results reveals that two-dimensional numerical simulation captures the main features of the observed convection flow.

scholarly journals THERMAL RADIATION EFFECT ON MHD NATURAL CONVECTION BOUNDARY LAYER FLOW OVER A PLATE WITH SUCTION (INJECTION) AND VARIABLE VISCOSITY

2017 ◽  
Vol 5 (4RAST) ◽  
pp. 52-58
Author(s):  
Jalaja P ◽  
Venkataramana B.S ◽  
Naveen V ◽  
K.R. Jayakumar
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Natural Convection ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Variable Viscosity ◽  
Convection Boundary Layer ◽  
Implicit Finite Difference Scheme ◽  
Convection Boundary ◽  
Layer Flow

The effect of thermal radiation on steady natural convection boundary layer flow over a plate with variable viscosity and magnetic field has been studied in this paper. The effect of suction and injection is also considered in the investigation. The system of partial differential equations governing the nonsimilar flow has been solved numerically using implicit finite difference scheme along with a quasilinearization technique. The thermal radiation has significant effect on heat transfer coefficient and thermal transport in presence of viscosity variation parameter and magnetic field in case of suction and injection.

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