Dynamics and modeling of nonlinear forced convective flow of Carreau-fluid (non-Newtonian fluid) with Marangoni convection

2021 ◽  
pp. 095440622098726
Author(s):  
M Ijaz Khan ◽  
Yu-Ming Chu ◽  
Sumaira Qayyum ◽  
Shahid Farooq ◽  
A Aldabesh
Keyword(s):  
Nusselt Number ◽  
Convective Flow ◽  
Momentum Equation ◽  
Eckert Number ◽  
Bejan Number ◽  
Carreau Fluid ◽  
Thermal Equation ◽  
Fluid Parameter ◽  
Nonlinear Mixed Convection ◽  
Forced Convective Flow

This paper deals with Marangoni convective flow of Carreau fluid. Boundary condition for momentum equation is considered to be Marangoni type. Thermal energy produces when current passes through the electrical conductor and this process is called Joule heating. Viscous dissipation is also applied in thermal equation. Nonlinear mixed convection for temperature is considered. Governing equations of PDE's are converted to ODE's by implementation of transformation. ND-Solve MATHEMATICA method is used to solve the equations. Parameters result against temperature, velocity, entropy rate, Bejan number, Skin friction and Nusselt number is examined via graphs. Due to increase in fluid parameter velocity of the fluid reduces while increasing impact is seen for temperature. Temperature is increasing function of Eckert number. Entropy generation also shows rising impact via fluid parameter while Bejan number decays. Drag force of surface decays via fluid parameter. Nusselt number is in direct relation with Prandtl and Eckert number.

Constructal Design of Rectangular Fin Intruded Into Mixed Convective Lid-Driven Cavity Flows

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
G. Lorenzini ◽  
B. S. Machado ◽  
L. A. Isoldi ◽  
E. D. dos Santos ◽  
L. A. O. Rocha
Keyword(s):  
Nusselt Number ◽  
Aspect Ratio ◽  
Convective Flow ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Lower Surface ◽  
Driven Cavity ◽  
Constructal Design ◽  
Mixed Convective Flow ◽  
Forced Convective Flow

The present work shows a numerical study of laminar, steady, and mixed convective flow inside lid-driven square cavity with intruded rectangular fin in its lower surface. The main purpose here is to maximize the heat transfer between the rectangular fin and the surrounding mixed convective flow inside a lid-driven cavity by means of constructal design. The problem is subject to two constraints, the lid-driven cavity and intruded fin areas. The ratio between the fin and cavity areas is kept fixed (ϕ = 0.05). The investigated geometry has one degree-of-freedom (DOF), the fin aspect ratio (H1/L1), which is varied in the range 0.1 ≤ H1/L1 ≤ 10. The aspect ratio of the cavity is maintained fixed (H/L = 1.0). The effect of the fin geometry over the Nusselt number is investigated for several Rayleigh (RaH = 103, 104, 105 and 106) and Reynolds numbers (ReH = 10, 102, 3.0 × 102, 5.0 × 102, 7.0 × 102 and 103). For all simulations, the Prantdl number is fixed (Pr = 0.71). The conservation equations of mass, momentum, and energy are numerically solved with the finite volume method. Results showed that fin geometry (H1/L1) has strong influence over the Nusselt number in the fin. It was also observed that the effect of H1/L1 over Nusselt number changes considerably for different Rayleigh numbers and for the lowest magnitudes of Reynolds numbers, for example, differences of nearly 770% between RaH = 106 and forced convective flow were observed for the lowest Reynolds number studied (ReH = 10).

On the forced convective flow inside thermal collectors enhanced by porous media: from macro to micro-channels

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Maziar Dehghan ◽  
Zahra Azari Nesaz ◽  
Abolfazl Pourrajabian ◽  
Saman Rashidi
Keyword(s):  
Porous Media ◽  
Velocity Distribution ◽  
General Model ◽  
Convective Flow ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Distribution Profile ◽  
Content Type ◽  
Forced Convective Flow ◽  
Drag Term

Purpose Aiming at finding the velocity distribution profile and other flow characteristic parameters such as the Poiseuille (Po) number, this study aims to focus on the three-dimensional forced convective flow inside rectangular ducts filled with porous media commonly used in air-based solar thermal collectors to enhance the thermal performance. The most general model for the fluid flow (i.e. the non-linear Darcy–Brinkman–Forchheimer partial differential equation subjected to slip and no-slip boundary conditions) is considered. Design/methodology/approach The general governing equations are solved analytically based on the perturbation technique and the results are validated against numerical simulation study based on a finite-difference solution over a non-uniform but structured grid. Findings The analytical velocity distribution profile based on exponential functions for the above-mentioned general case is obtained, and accordingly, expressions for the Po are introduced. It is found that the velocity distribution tends to be uniform by increasing the aspect ratio of the duct. Moreover, a criterion for considering/neglecting the nonlinear drag term in the momentum equation (i.e. the Forchheimer term) is proposed. According to the sensitivity analysis, results show that the nonlinear drag term effects on the Nusselt number are important only in porous media with high Darcy numbers. Originality/value A general analytic solution for three-dimensional forced convection flows through rectangular ducts filled with porous media for the general model of Darcy–Brinkman–Forchheimer and the general boundary condition including both no-slip and slip-flow regimes is obtained. An analytic expression to calculate Po number is obtained which can be practical for engineering estimations and a basis for validation of numerical simulations. A criterion for considering/neglecting the nonlinear drag term in the momentum equation is also introduced.

scholarly journals MHD Free and Forced Convective Flow in a Rotating Channel

2013 ◽  
Vol 74 (18) ◽  
pp. 9-17
Author(s):  
B. C.Sarkar ◽  
S. Das ◽  
R. N. Jana
Keyword(s):  
Convective Flow ◽  
Forced Convective Flow ◽  
Rotating Channel

scholarly journals Ohmic and Viscous Dissipation Effect on Free and Forced Convective Flow of Casson Fluid in a Channel

2021 ◽  
Vol 12 (1) ◽  
pp. 132-148
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Convective Flow ◽  
Casson Fluid ◽  
Pictorial Representation ◽  
Physical Parameters ◽  
Partial Differential ◽  
Buoyancy Parameter ◽  
Forced Convective Flow

Analytical study of the free and forced convective flow of Casson fluid in the existence of viscous dissipation, ohmic effect and uniform magnetic field in a porous channel to the physical model. The nonlinear coupled partial differential equations are converted to linear partial differential equations using similarity transformation and the classical perturbation method. The physical parameters such as Prandtl number (Pr), viscous dissipation (Vi), Schmidt number (Sc), Reynolds number (R), thermal buoyancy parameter (λ), Ohmic number (Oh), Casson fluid parameter (β), Darcy number (Da), Hartmann number (M2), the concentration of buoyancy parameter (N), chemical reaction rate (γ) effect on velocity, temperature and concentration have been studied with pictorial representation. For the particular case, the present paper analysis is compared with the previous work and is found good agreement.

scholarly journals Analysis of MHD Forced Convective Flow of Variable Fluid Properties over a Saturated Porous Medium with Thermal Radiation Effect

2016 ◽  
Vol 9 ◽  
pp. 47-65 ◽  
Author(s):  
Kolawole Sunday Adegbie ◽  
Adeyemi Isaiah Fagbade
Keyword(s):  
Porous Medium ◽  
Heat Loss ◽  
Convective Flow ◽  
Radiative Heat ◽  
Saturated Porous Medium ◽  
Fluid Velocity ◽  
Radiative Heat Loss ◽  
Variable Fluid Properties ◽  
Fluid Properties ◽  
Forced Convective Flow

The present paper addresses the problem of MHD forced convective flow in a fluid saturated porous medium with Brinkman-Forchheimer model, which is an important physical phenomena in engineering applications. The paper extends the previous models to account for effects of variable fluid properties on the forced convective flow through a porous medium in the presence of radiative heat loss using bivariate spectral relaxation method (BSRM). The dynamic viscosity and thermal conductivity of the newtonian fluid are assumed to vary linearly respectively, with temperature whereas the contribution of thermal radiative heat loss is based on Rosseland diffussion approximation. The flow model is described and expressed in form of a highly coupled nonlinear system of partial differential equations. The method of solution BSRM as proposed by Motsa [25] seeks to decouple the original system of PDEs to form a sequence of equations that can be solved in a computationally efficient manner. BSRM is an approach that applies spectral collocation independently in all underlying independent variable is executed to obtain approximate solutions of the problem. The proposed algorithm is supposed to be a very accurate, convergent and very effective in generating numerical results. The results obtained show a significant effects of the flow control parameters on the fluid velocity and temperature respectively. Consequently, the wall shear stress and local heat transfer rate of the present paper are compared with the available results in literatures. Remarkable impacts and a good agreement are found.

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