Analysis of thermally stratified radiative flow of Sutterby fluid with mixed convection

2021 ◽  
pp. 095440622110078
Author(s):  
Saif-ur- Rehman ◽  
Nazir Ahmad Mir ◽  
Muhammad Farooq ◽  
Naila Rafiq ◽  
Shakeel Ahmad
Keyword(s):  
Mixed Convection ◽  
Convergent Series ◽  
Radiation Parameter ◽  
Boundary Layer Approximation ◽  
Similar Relation ◽  
Opposite Behavior ◽  
Velocity Increments ◽  
Transport Analysis ◽  
Convection Parameter ◽  
Linear Pdes

In this attempt, we investigate the mixed convection in Sutterby fluid flow based on boundary layer approximation. Heat transport analysis is composed of stratification and thermal radiative phenomena. The system of non-linear PDEs is transformed into coupled ODEs. Convergent series approximations are evaluated via homotopic technique. Influence of various pertinent parameters is sketched and graphically analyzed. It is found that horizontal velocity increments for higher mixed convection parameter. The radiation parameter has a similar relation with temperature whereas the stratification parameter shows opposite behavior for temperature field.

scholarly journals Darcy-Forchheimer flow with nonlinear mixed convection

2020 ◽  
Vol 41 (11) ◽  
pp. 1685-1696
Author(s):  
T. Hayat ◽  
F. Haider ◽  
A. Alsaedi
Keyword(s):  
Mixed Convection ◽  
Reaction Rate ◽  
Concentration Field ◽  
Convergent Series ◽  
Analysis Method ◽  
Stretching Surface ◽  
Nonlinear Mixed Convection ◽  
Mixed Convective Flow ◽  
Physical Quantities ◽  
Convection Parameter

Abstract An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed. Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy, respectively. The nonlinear Darcy-Forchheimer relation is deliberated. The dimensionless problem is obtained through appropriate transformations. Convergent series solutions are obtained by utilizing an optimal homotopic analysis method (OHAM). Graphs depicting the consequence of influential variables on physical quantities are presented. Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.

On bio-convection thermal radiation in Darcy – Forchheimer flow of nanofluid with gyrotactic motile microorganism under Wu’s slip over stretching cylinder/plate

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
H. Waqas ◽  
M. Imran ◽  
Taseer Muhammad ◽  
Sadiq M. Sait ◽  
R. Ellahi
Keyword(s):  
Mixed Convection ◽  
Volume Fraction ◽  
Research Work ◽  
Concentration Field ◽  
Second Order ◽  
Original Research ◽  
Stretching Cylinder ◽  
Content Type ◽  
Mixed Convection Parameter ◽  
Convection Parameter

Purpose The purpose of this study is to discuss the Darcy–Forchheimer nanoliquid bio-convection flow by stretching cylinder/plate with modified heat and mass fluxes, activation energy and gyrotactic motile microorganism features. Design/methodology/approach The proposed flow model is based on flow rate, temperature of nanomaterials, volume fraction of nanoparticles and gyrotactic motile microorganisms. Heat and mass transport of nanoliquid is captured by the usage of popular Buongiorno relation, which allows us to evaluate novel characteristics of thermophoresis diffusion and Brownian movement. Additionally, Wu’s slip (second-order slip) mechanisms with double stratification are incorporated. For numerical and graphical results, the built-in bvp4c technique in computational software MATLAB along with shooting technique is used. Findings The influence of key elements is illustrated pictorially. Velocity decays for higher magnitude of first- and second-order velocity slips and bioconvection Rayleigh number. The velocity of fluid has an inverse relation with mixed convection parameter and local inertia coefficient. Temperature field enhances with the increase in estimation of thermal stratification Biot number and radiation parameter. A similar situation for concentration field is observed for mixed convection parameter and concentration relaxation parameter. Microorganism concentration profile decreases for higher values of bioconvection Lewis number and Peclet number. A detail discussion is given to see how the graphical aspects justify the physical ones. Originality/value To the best of the authors’ knowledge, original research work is not yet available in existing literature.

Mixed Convection in a Vertical Parallel Plate Microchannel With Asymmetric Wall Heat Fluxes

2006 ◽  
Vol 129 (8) ◽  
pp. 1091-1095 ◽  
Author(s):  
Mete Avcı ◽  
Orhan Aydın
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Mixed Convection ◽  
Convective Heat Transfer ◽  
Parallel Plate ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Heat Fluxes ◽  
Limiting Case ◽  
Convection Parameter

In this study, exact analytical results are presented for fully developed mixed convective heat transfer of a Newtonian fluid in an open-ended vertical parallel plate microchannel with asymmetric wall heating at uniform heat fluxes. The velocity slip and the temperature jump at the wall are included in the formulation. The effects of the modified mixed convection parameter, Grq∕Re, the Knudsen number, Kn, and the ratio of wall heat flux, rq=q1∕q2, on the microchannel hydrodynamic and thermal behaviors are determined. Finally, a Nu=f(Grq∕Re,Kn,rq) expression is developed. For, the limiting case of Kn=0, the results are found to be in an excellent agreement with those in the existing literature.

Mixed convection boundary layer flow from a vertical truncated cone in a nanofluid

2014 ◽  
Vol 24 (5) ◽  
pp. 1175-1190 ◽  
Author(s):  
F.O. Pătrulescu ◽  
T. Groşan ◽  
I. Pop
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Convection Boundary Layer ◽  
Particle Volume ◽  
Content Type ◽  
Mixed Convection Parameter ◽  
Layer Flow ◽  
Convection Parameter

Purpose – The purpose of this paper is to investigate the steady mixed convection boundary layer flow from a vertical frustum of a cone in water-based nanofluids. The problem is formulated to incorporate three kinds of nanoparticles: copper, alumina and titanium oxide. The working fluid is chosen as water with the Prandtl number of 6.2. The mathematical model used for the nanofluid incorporates the particle volume fraction parameter, the effective viscosity and the effective thermal diffusivity. The entire regime of the mixed convection includes the mixed convection parameter, which is positive for the assisting flow (heated surface of the frustum cone) and negative for the opposing flow (cooled surface of the frustum cone), respectively. Design/methodology/approach – The transformed non-linear partial differential equations are solved numerically for some values of the governing parameters. The derivatives with respect to? were discretized using the first order upwind finite differences and the resulting ordinary differential equations with respect to? were solved using bvp4c routine from Matlab. The absolute error tolerance in bvp4c was 1e-9. Findings – The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. The effects of the particle volume fraction parameter \phi, the mixed convection parameter \lambda and the dimensionless coordinate? on the flow and heat transfer characteristics are determined only for the Cu nanoparticles. It is found that dual solutions exist for the case of opposing flows. The range of the mixed convection parameter for which the solution exists increases in the presence of the nanofluids. Originality/value – The paper models the mixed convection from a vertical truncated cone using the boundary layer approximation. Multiple (dual) solutions for the flow reversals are obtained and the range of existence of the solutions was found. Particular cases for ?=0 (full cone), ? >>1 and (free convection limit) \lambda>>1were studied. To the authors best knowledge this problem has not been studied before and the results are new and original.

Viscous Dissipation Effect on a Steady Generalised Couette Flow of Heat-Generating/Absorbing Fluid in a Vertical Channel

2019 ◽  
Vol 74 (7) ◽  
pp. 605-616
Author(s):  
Abiodun O. Ajibade ◽  
Tafida M. Kabir
Keyword(s):  
Mixed Convection ◽  
Couette Flow ◽  
Viscous Dissipation ◽  
Reverse Flow ◽  
Vertical Channel ◽  
Heated Wall ◽  
Fluid Temperature ◽  
Dissipation Effect ◽  
Mixed Convection Parameter ◽  
Convection Parameter

AbstractThis article investigates the viscous dissipation effect on steady generalised Couette flow of heat-generating/absorbing fluid in a vertical channel. Equations of energy and momentum are obtained and solved using the homotopy perturbation method. The influences of the dimensionless flow parameter have been plotted graphically and discussed for varying values of the controlling parameters. During the course of computation, it is found that fluid temperature and velocity increase with an increase in viscous dissipation and also seen that growing mixed convection parameter Gre leads to a corresponding rise in temperature and velocity. It is further discovered that heat absorption leads to increase in the heat transfer on the heated wall. Finally, it is concluded that heat generation contributes to increase the mixed convection, hence, it requires decrease in mixed convection parameter to bring about a reverse flow near the stationary plate.

Mixed convection flow due to a moving vertical plate parallel to free stream under the influence of Newtonian heating and thermal radiation

2014 ◽  
Vol 5 (3) ◽  
pp. 859-870
Author(s):  
Prabhugouda Patil ◽  
S. Roy
Keyword(s):  
Prandtl Number ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Vertical Plate ◽  
Free Stream ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Newtonian Heating ◽  
Mixed Convection Parameter ◽  
Convection Parameter

The steady mixed convection flow from a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of thermal radiation as well as Newtonian heating effects. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in conjunction with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter ( ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity ( ) and the radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skinfriction coefficient ( ) and surface temperature ( ) are also presented. The results show that the streamwise co-ordinate  significantly influences the flow and thermal fields which indicate the importance of non-similar solutions. Also, it is observed that the increase of mixed convection parameter causes the increase in the magnitude of velocity profile about 65% for lower Prandtl number fluids (Pr=0.7), while it decreases in the temperature profile about 30%. Present results are compared with previously published work and are found to be in excellent agreement.

Periodic momentum and thermal boundary layer mixed convection flow around the surface of a sphere in the presence of viscous dissipation

2017 ◽  
Vol 95 (10) ◽  
pp. 976-986 ◽  
Author(s):  
Muhammad Ashraf ◽  
Almas Fatima ◽  
R.S.R. Gorla
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Viscous Dissipation ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Implicit Finite Difference ◽  
Convection Parameter

Numerical solutions for the periodic laminar boundary layer mixed convection flow around the surface of a heated sphere in the presence of viscous dissipation have been obtained by solving the governing equations using an implicit finite difference numerical technique. The fluid under consideration is assumed to be viscous and incompressible. Periodic momentum and thermal boundary layer profiles for different positions of x around the surface of the sphere are evaluated. The features of the obtained results for different values of mixed convection parameter λ, Prandtl number Pr, viscous dissipation parameter N, and frequency parameter ω are shown graphically. The obtained results confirm significant effect of all these mentioned parameters on periodic momentum and thermal boundary layer mixed convection flow around different positions of the sphere.

scholarly journals MHD mixed convection of hybrid nanofluid in a wavy porous cavity employing local thermal non-equilibrium condition

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zehba Raizah ◽  
Abdelraheem M. Aly ◽  
Noura Alsedais ◽  
Mohamed Ahmed Mansour
Keyword(s):  
Heat Transfer ◽  
Absorption Coefficient ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Equilibrium Condition ◽  
Volume Fraction ◽  
Hybrid Nanofluid ◽  
Radiation Parameter ◽  
Non Equilibrium

AbstractThe current study treats the magnetic field impacts on the mixed convection flow within an undulating cavity filled by hybrid nanofluids and porous media. The local thermal non-equilibrium condition below the implications of heat generation and thermal radiation is conducted. The corrugated vertical walls of an involved cavity have $${T}_{c}$$ T c and the plane walls are adiabatic. The heated part is put in the bottom wall and the left-top walls have lid velocities. The controlling dimensionless equations are numerically solved by the finite volume method through the SIMPLE technique. The varied parameters are scaled as a partial heat length (B: 0.2 to 0.8), heat generation/absorption coefficient (Q: − 2 to 2), thermal radiation parameter (Rd: 0–5), Hartmann number (Ha: 0–50), the porosity parameter (ε: 0.4–0.9), inter-phase heat transfer coefficient (H*: 0–5000), the volume fraction of a hybrid nanofluid (ϕ: 0–0.1), modified conductivity ratio (kr: 0.01–100), Darcy parameter $$\left(Da: 1{0}^{-1}\,\mathrm{ to }\,1{0}^{-5}\right)$$ D a : 1 0 - 1 to 1 0 - 5 , and the position of a heat source (D: 0.3–0.7). The major findings reveal that the length and position of the heater are effective in improving the nanofluid movements and heat transfer within a wavy cavity. The isotherms of a solid part are significantly altered by the variations on $$Q$$ Q , $${R}_{d}$$ R d , $${H}^{*}$$ H ∗ and $${k}_{r}$$ k r . Increasing the heat generation/absorption coefficient and thermal radiation parameter is improving the isotherms of a solid phase. Expanding in the porous parameter $$\varepsilon$$ ε enhances the heat transfer of the fluid/solid phases.

scholarly journals Mixed convection boundary-layer flow of a viscoelastic fluid due to horizontal elliptic cylinder with constant heat flux

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 519-531 ◽  
Author(s):  
Tariq Javed ◽  
Hussain Ahmad ◽  
Abuzar Ghaffari
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Skin Friction ◽  
Viscoelastic Fluid ◽  
Major Axis ◽  
Convection Boundary Layer ◽  
Viscoelastic Parameter ◽  
Mixed Convection Parameter ◽  
Convection Parameter

This article presents numerical analysis of mixed convection laminar flow of a second grade viscoelastic fluid due to cylinder of elliptic cross-section with prescribed surface heat flux. Dimensionless non-linear analysis is computed employing Keller-box method. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed graphically to examine their behavior along the surface of cylinder. The flow and heat transfer rates are carefully judged while varying the important resulting parameters (mixed convection parameter, viscoelastic parameter aspect ratio, etc.) through sketched graphs keeping major axis of ellipse along and perpendicular to the horizontal. These two positions of major axis are termed as blunt and slender orientations, respectively. The values of skin friction and Nusselt number increase with rise in mixed convection parameter. On the other hand, these quantities lessen by increasing the value of viscoelastic parameter.

General Analysis of Steady Laminar Mixed Convection Heat Transfer on Vertical Slender Cylinders

1989 ◽  
Vol 111 (2) ◽  
pp. 393-398 ◽  
Author(s):  
T.-Y. Wang ◽  
C. Kleinstreuer
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Skin Friction ◽  
Cooling Mode ◽  
Local Skin ◽  
Friction Parameter ◽  
Laminar Mixed Convection ◽  
Local Skin Friction ◽  
Convection Parameter ◽  
Heat Transfer Parameter

A general analysis has been developed to study fluid flow and heat transfer characteristics for steady laminar mixed convection on vertical slender cylinders covering the entire range from pure forced to pure natural convection. Two uniquely transformed sets of axisymmetric boundary-layer equations for the constant wall heat flux case and the isothermal surface case are solved using a two-point finite difference method with Newton linearization. Of interest are the effects of the new mixed convection parameter, the cylinder heating/cooling mode, the transverse curvature parameter, and the Prandtl number on the velocity/temperature profiles and on the local skin friction parameter and the heat transfer parameter. The results of the validated computer simulation model are as follows. Depending upon the magnitude and direction of the buoyancy force, i.e., the value of the mixed convection parameter and the heating or cooling mode applied, natural convection can have a significant effect on the thermal flow field around vertical cylinders. Specifically, strong variations of the local skin friction parameter and reversing trends in the heat transfer parameter are produced as the buoyancy force becomes stronger in aiding flow. The skin friction parameter increases with higher curvature parameters and Prandtl numbers. Similarly, the modified Nusselt number is larger for higher transverse curvature parameters; however, this parameter may reverse the impact of the Prandtl number on the Nusselt number for predominantly forced convection.

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