A new approximate analytical technique for dual solutions of nonlinear differential equations arising in mixed convection heat transfer in a porous medium

2017 ◽  
Vol 27 (2) ◽  
pp. 486-503 ◽  
Author(s):  
S. Abbasbandy ◽  
Elyas Shivanian ◽  
K. Vajravelu ◽  
Sunil Kumar
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Nonlinear Differential Equations ◽  
Convection Heat Transfer ◽  
Dual Solutions ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Infinite Domain ◽  
Content Type ◽  
Mixed Convection Heat Transfer

Purpose The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Padé-approximation and homotopy–Padé technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering. Design/methodology/approach Homotopy–Padé method. Findings The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium. Research limitations/implications The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity. Social implications Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. Originality/value In this study, the authors are using two modified methods.

Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

2021 ◽  
Vol 8 (4) ◽  
pp. 807-820
Author(s):  
M. Zaydan ◽  
◽  
A. Wakif ◽  
E. Essaghir ◽  
R. Sehaqui ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Nonlinear Differential Equations ◽  
Convection Heat Transfer ◽  
Local Heat Transfer ◽  
Physical Parameters ◽  
Convection Heat ◽  
Linear Temperature ◽  
Mixed Convection Heat Transfer

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity. By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature. Note here that the density quantity in the buoyancy body force is a linear temperature-dependent function. The characteristic quantities are computed realistically via the commonly used phenomenological laws and the more accurate experimental correlations. A feasible non-dimensionalization procedure has been employed to derive the dimensionless conservation equations. The resulting nonlinear differential equations are solved numerically for realistic boundary conditions by employing the fourth-order compact finite-difference method (FOCFDM). After performing extensive validations with the previously published findings, the dynamical and thermal features of the studied convective nanofluid flow are revealed to be in good agreement for sundry values of the involved physical parameters. Besides, the present numerical outcomes are discussed graphically and tabularly with the help of streamlines, isotherms, velocity fields, temperature distributions, and local heat transfer rate profiles.

Unsteady mixed convection flow at a three-dimensional stagnation point

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Amin Noor ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Unsteady Mixed Convection

Purpose This paper aims to probe the problem of an unsteady mixed convection stagnation point flow and heat transfer past a stationary surface in an incompressible viscous fluid numerically. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically by a Runge – Kutta – Fehlberg method with shooting technique and a collocation method, namely, the bvp4c function. Findings The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value The case of suction on unsteady mixed convection flow at a three-dimensional stagnation point has not been studied before; hence, all generated numerical results are claimed to be novel.

Analysis of unsteady mixed convection triple diffusive transport phenomena

2019 ◽  
Vol 29 (2) ◽  
pp. 773-789 ◽  
Author(s):  
Prabhugouda Mallanagouda Patil ◽  
Shashikant A. ◽  
P.S. Hiremath
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mixed Convection ◽  
Aqueous Solutions ◽  
Mass Transfer Rate ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Partial Differential ◽  
Content Type

Purpose The purpose of this study is to analyze the impacts of aqueous solutions such as NaCl-water and Sucrose-water on unsteady triple diffusive mixed convection flow along an exponentially decreasing external flow velocity in presence of suction/injection. Design/methodology/approach The proposed problem is modelled into dimensional partial differential equations which are nonlinear and coupled in nature. Non-similar transformations are used to transform these equations into non-dimensional form. To linearize the equations, quasilinearization technique has been used and then implicit finite difference scheme is used to discretise the linear partial differential equations. Findings The variations of various dimensionless parameters have been depicted on velocity, temperature and species concentration profiles for NaCl and Sucrose aqueous solutions through graphical representations. In addition, several results have been expressed through graphs pertaining to skin-friction coefficient, heat and mass transfer rates. The results indicate that the increase in Schmidt number raises the mass transfer rate for the case of NaCl-water and Sucrose-water solutions. Originality/value As per the authors’ best of knowledge, no investigations have been carried out in the literature on unsteady triple diffusive mixed convection flow along an exponentially decreasing mainstream velocity.

Dual Solutions in Magnetohydrodynamic Mixed Convection Flow Near a Stagnation-Point on a Vertical Surface

2007 ◽  
Vol 129 (9) ◽  
pp. 1212-1216 ◽  
Author(s):  
A. Ishak ◽  
R. Nazar ◽  
N. M. Arifin ◽  
I. Pop
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Heated Surface ◽  
Vertical Surface ◽  
Dual Solutions ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Heat Transfer Characteristics ◽  
Flow And Heat Transfer

The steady magnetohydrodynamic (MHD) mixed convection stagnation-point flow toward a vertical heated surface is investigated in this study. The external velocity impinges normal to the vertical surface and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions also exist for the assisting flow, besides that usually reported in the literature for the opposing flow.

Mixed convection flow of a hybrid nanofluid past a vertical wedge with thermal radiation effect

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Natalia C. Roșca ◽  
Alin V. Roșca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Radiation Effect ◽  
Convection Flow ◽  
Hybrid Nanofluid ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Thermal Radiation Effect ◽  
Vertical Wedge

Purpose The purpose of this paper is to numerically study the problem of mixed convection flow of a hybrid nanofluid past a vertical wedge with thermal radiation effect. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically through the function bvp4c from MATLAB for different values of the governing parameters. The solutions contain a mixed convection parameter λ that has a considerable impact on the flow fields. Findings It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the mixed convection and several other parameters. To establish which of these solutions are stable and which are not, a stability analysis has been performed. The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions. Practical implications This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans. Originality/value The case of mixed convection flow of a hybrid nanofluid past a vertical wedge with thermal radiation effects has not been studied before, and hence all generated numerical results are claimed to be original and novel.

Three-dimensional mixed convection flow of viscoelastic nanofluid over an exponentially stretching surface

2015 ◽  
Vol 25 (2) ◽  
pp. 333-357 ◽  
Author(s):  
Tasawar Hayat ◽  
Bilal Ashraf ◽  
Sabir Ali Shehzad ◽  
A. Alsaedi ◽  
N. Bayomi
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Three Dimensional ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Content Type ◽  
Viscoelastic Nanofluid ◽  
Exponentially Stretching Surface ◽  
Exponentially Stretching

Purpose – The purpose of this paper is to investigate the three-dimensional mixed convection flow of viscoelastic nanofluid induced by an exponentially stretching surface. Design/methodology/approach – Similarity transformations are utilized to reduce the partial differential equations into the ordinary differential equations. The corresponding non-linear problems are solved by homotopy analysis method. Findings – The authors found that an increase in thermophoresis and Brownian motion parameter enhance the temperature. Here thermal conductivity of fluid is enhanced due to which higher temperature and thicker thermal boundary layer thickness is obtained. Practical implications – Heat and mass transfer effects in mixed convection flow over a stretching surface have numerous applications in the polymer technology and metallurgy. Such flows are encountered in metallurgical processes which involve the cooling of continuous strips or filaments by drawing them through a quiescent fluid and that in the process of drawing, these strips are sometimes stretched. Originality/value – Three-dimensional flows over an exponentially stretching surface are very rare in the literature. Three-dimensional flow of viscoelastic nanofluid due to an exponentially stretching surface is first time investigated.

scholarly journals Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere

Molecules ◽  
2020 ◽  
Vol 25 (11) ◽  
pp. 2694
Author(s):  
Amir Abbas ◽  
Muhammad Ashraf ◽  
Yu-Ming Chu ◽  
Saqib Zia ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mixed Convection ◽  
Computational Study ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Partial Differential ◽  
Primitive Form ◽  
The Mathematical Model

The main goal of the current work was to study the coupled mechanism of thermophoretic transportation and mixed convection flow around the surface of the sphere. To analyze the characteristics of heat and fluid flow in the presence of thermophoretic transportation, a mathematical model in terms of non-linear coupled partial differential equations obeying the laws of conservation was formulated. Moreover, the mathematical model of the proposed phenomena was approximated by implementing the finite difference scheme and boundary value problem of fourth order code BVP4C built-in scheme. The novelty point of this paper is that the primitive variable formulation is introduced to transform the system of partial differential equations into a primitive form to make the line of the algorithm smooth. Secondly, the term thermophoretic transportation in the mass equation is introduced in the mass equation and thus the effect of thermophoretic transportation can be calculated at different positions of the sphere. Basically, in this study, some favorite positions around the sphere were located, where the velocity field, temperature distribution, mass concentration, skin friction, and rate of heat transfer can be calculated simultaneously without any separation in flow around the surface of the sphere.

Non-uniform mass transfer in MHD mixed convection flow of water over a sphere with variable viscosity and Prandtl number

2016 ◽  
Vol 26 (7) ◽  
pp. 2235-2251 ◽  
Author(s):  
J. Rajakumar ◽  
P. Saikrishnan ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mixed Convection ◽  
Skin Friction ◽  
Variable Viscosity ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Content Type ◽  
Slot Suction

Purpose The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field. Design/methodology/approach The non-similar solutions have been obtained from the origin of the streamwise co-ordinate to the point of zero skin friction using quasilinearization technique with an implicit finite-difference scheme. Findings The effect of M is not notable on the temperature and heat transfer coefficient when λ is large. The skin friction coefficient and velocity profile are enhance with the increase of MHD parameter M when λ is small. Viscous dissipation has no significant on the skin friction coefficient under MHD effect. For M=1, the movement of the slot or slot suction or slot injection do not cause any effect on flow separation. The slot suction and the movement of the slot in downstream direction delay the point of zero skin friction for M=0. Originality/value The present results are original and new for water boundary-layer flow over sphere in mixed convection flow with MHD effect and non-uniform mass transfer. So this study would be useful in analysing the skin friction and heat transfer coefficient on sphere of mixed convection flow of water boundary layer with MHD effect.

scholarly journals Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation

2013 ◽  
Vol 18 (4) ◽  
pp. 1151-1164 ◽  
Author(s):  
G.V.R. Reddy ◽  
B.A. Reddy ◽  
N.B. Reddy
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Convection Flow ◽  
Physical Parameters ◽  
Mixed Convection Flow ◽  
Stretching Surface ◽  
Porous Stretching Surface

Abstract The effects of thermal radiation and mass transfer on an unsteady hydromagnetic boundary layer mixed convection flow along a vertical porous stretching surface with heat generation are studied. The fluid is assumed to be viscous and incompressible. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables. Numerical solutions of these equations are obtained by using the Runge-Kutta fourth order method along with the shooting technique. Velocity, temperature, concentration, the skin-friction coefficient, Nusselt number and Sherwood number for variations in the governing thermo physical parameters are computed, analyzed and discussed.

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