scholarly journals Unsteady Convective MHD Flow and Heat Transfer of a Viscous Nanofluid across a Porous Stretching/Shrinking Surface: Existence of Multiple Solutions

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1359
Author(s):  
Nawal A. Alshehri ◽  
Awatef Abidi ◽  
Muhammad Riaz Khan ◽  
Yanala Dharmendar Reddy ◽  
Saim Rasheed ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Solid Particles ◽  
Friction Drag ◽  
Shrinking Surface

The suspension of tiny solid particles inside the energy transport liquids could enhance their thermal conductivity as well as provide an efficient and inventive approach to significantly improve their properties of heat transport. Therefore, our aim is to explore the radiative two-dimensional unsteady flow of a viscous nanofluid about an aligned magnetic field that includes the joint effect of suction, velocity slip, and heat source across a porous convective stretching/shrinking surface. Initially, using non-dimensional variables, the nonlinear governing partial differential equations (PDEs) were transformed into ordinary differential equations (ODEs) which were subsequently solved with the help of bvp4c built-in package in MATLAB. The results declare that escalating the values of the unsteadiness parameter escalates the friction drag whereas it reduces with the escalation of the slip parameter. Furthermore, the heat transfer rate escalates with the escalation of radiation and concentration parameter, and the escalation of the heat source parameter causes to reduce the heat transfer rate. Finally, it is found that the rate of heat transfer and friction drag continuously improve and decline against the rising rates of stretching, respectively.

scholarly journals MHD Flow and Heat Transfer of Hybrid Nanofluid over an Exponentially Shrinking Surface with Heat Source/Sink

2021 ◽  
Vol 11 (17) ◽  
pp. 8199
Author(s):  
Mohamad Nizam Othman ◽  
Alias Jedi ◽  
Nor Ashikin Abu Bakar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Mhd Flow ◽  
Hybrid Nanofluid ◽  
Flow And Heat Transfer ◽  
Source Sink ◽  
Shrinking Surface

In nanotechnology research, nanofluid technology contributes many applications to engineering applications and industry, such as power generation, solar collection, heat exchangers for cooling, and many more. However, there are still a few constraints in terms of heat transfer enhancement, although nanofluid properties show the best heat transfer rate compared with conventional fluids. Thus, this study was conducted for the purpose of investigating the behaviors of flow and heat transfer of hybrid nanofluid with carbon nanotubes (CNTs) on a permeable exponentially shrinking surface, as well as investigating the effects of a magnetic field and heat source/sink. This study was conducted by developing a mathematical model, which was the Tiwari–Das model for momentum and energy equations, and then transforming the model’s partial differential equations (PDEs) to ordinary differential equations (ODEs) using a similarity solution. Next, these equations were solved numerically using the MATLAB bvp4c boundary value problem solver. The authors particularly explored these behaviors with a few variations. Based on the results obtained, it was found that dual solutions exist in a specific range of the shrinking case, and that the critical point also exists in a range of −1.5 < < −1 with different parameters. For the heat source/sink effect, the Nusselt number was higher when heat sink case ε < 0, whereas it decreased when the heat source case ε > 0. Therefore, this study deduced that the heat transfer rate of hybrid nanofluid (CNTs/Cu–water) is better than regular nanofluid (CNT–water) and conventional fluid (water). The present study took into consideration the problem of MHD flow and heat transfer analysis of a hybrid nanofluid towards an exponentially shrinking surface with the presence of heat source/sink and thermal radiation effects. The authors show that dual solutions exist within a specific range of values due to the shrinking case. The current work is predicted to have numerous benefits in equivalent real-world systems.

scholarly journals Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110240
Author(s):  
Rehan Ali Shah ◽  
Hidayat Ullah ◽  
Muhammad Sohail Khan ◽  
Aamir Khan
Keyword(s):  
Heat Transfer ◽  
Ionic Liquid ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

A Numerical Study of Impulsively Started External Convection at Microscale

2014 ◽  
Vol 31 (1) ◽  
pp. 79-90
Author(s):  
K. Ramadan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Thermal Boundary Layer ◽  
Numerical Study ◽  
Velocity Slip ◽  
Transition Time ◽  
Surface Cooling ◽  
Linear Ordinary Differential Equations

ABSTRACTImpulsively started external convection at microscale level is studied numerically in both planar and axisymmetric geometries. Using similarity transformation, the resulting coupled partial and non-linear ordinary differential equations are simultaneously solved by finite differences together with a well established ordinary differential equation solver, over a range of problem parameters. Rarefaction effects within the slip flow regime on the thermal boundary layer response, heat transfer rate and transition time when system experiences sudden changes in surface temperature are analyzed, and a comparison between sudden surface cooling and heating is presented. The results show that the thermal boundary layer thickness, heat transfer rate and the transition time is considerably influenced by the degree of rarefaction. The transition time tends to be less sensitive with increasing rarefaction. The velocity slip and temperature jump factors are found to have opposite effects on the transition time and the heat transfer rate, with the velocity slip factor having the most profound influence on these parameters.

scholarly journals Non-linear radiation influence on oblique stagnation point flow of Maxwell fluid

2018 ◽  
Vol 64 (4) ◽  
pp. 420 ◽  
Author(s):  
Abuzar Ghaffari ◽  
T. Javed ◽  
I. Mustafa
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Maxwell Fluid ◽  
Stagnation Point Flow ◽  
Non Linear ◽  
Linear Radiation

Non-linear thermal radiation effects on non-aligned stagnation point flow of Maxwell fluid have been carried out in the present investigation. It is observed that the non-linear radiation augments the temperature and heat transfer rate. This physical phenomenon is translated into a system of partial differential equations (PDEs). After useful transformation, these non-linear constitutive equations are transformed into a system of ordinary differential equations (ODEs) and interpreted numerically by means of parallel shooting technique. Effects of pertinent parameters on flow and heat transfer are elaborated through tables and graphs. It is observed that radiation and surface heating enhance the rate of heat transfer, however Prandtl number has inverse relation with thermal boundary layer thickness. It has been observed that for increasing Prandtl number, heat transfer rate enhances. The detailed discussion of heat transfer rate is also presented in this study. Flow pattern is judged through streamlines graphs. It is also observed that oblique stagnation point flow behaves like orthogonal stagnation point flow, when free stream velocity is very large as compared to stretching velocity.

HEAT GENERATION AND ABSORPTION IN MHD FLOW OF CASSON FLUID PAST A STRETCHING WEDGE WITH VISCOUS DISSIPATION AND NEWTONIAN HEATING

2018 ◽  
Vol 80 (3) ◽  
Author(s):  
Imran Ullah ◽  
Sharidan Shafie ◽  
Ilyas Khan
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Heat Transfer Rate ◽  
Heat Generation ◽  
Transfer Rate ◽  
Fluid Velocity ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Fluid Temperature

The dissipative flow of Casson fluid in the presence of heat generation and absorption is investigated. The flow is induced due to stretching wedge. The similarity transformations were used to to transformed the governing equations into ordinary differential equations. The transformed equations are solved numerically via Keller-box method. Numerical results for skin friction coefficient are compared and found in excellent agreement with published results. The effects of pertinent parameters on velocity and temperature profiles as well as skin friction and heat transfer rate are graphically displayed and analyzed. It is noticed that fluid velocity drops with the increase of Casson fluid and magnetic parameters when the wedge is stretching faster than free stream. It is also noted that the heat transfer rate at wedge surface reduces with the increase of Eckert number, whereas the reverse trend is noted in the case of Casson and radiation parameters. Moreover, with increasing of heat generation or absorption parameter the fluid temperature rises.

Hall effect on MHD flow and heat transfer of nanofluids over a stretching wedge in the presence of velocity slip and Joule heating

Open Physics ◽  
2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Xiaohong Su ◽  
Liancun Zheng
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Hall Effect ◽  
Joule Heating ◽  
Volume Fraction ◽  
Wedge Angle ◽  
Mhd Flow ◽  
Velocity Slip ◽  
Temperature Fields ◽  
Flow And Heat Transfer

AbstractThis paper deals with the boundary layer flow and heat transfer of nanofluids over a stretching wedge with velocity-slip boundary conditions. In this analysis, Hall effect and Joule heating are taken into consideration. Four different types of water-base nanofluids containing copper (Cu), silver (Ag), alumina (Al2O3), and titania (TiO2) nanoparticles are analyzed. The partial differential equations governing the flow and temperature fields are converted into a system of nonlinear ordinary differential equations using a similarity transformation. The resulting similarity equations are then solved by using the shooting technique along with the fourth order Runge-Kutta method. The effects of types of nanoparticles, the volume fraction of nanoparticles, the magnetic parameter, the Hall parameter, the wedge angle parameter, and the velocityslip parameter on the velocity and temperature fields are discussed and presented graphically, respectively.

Convective heat transfer in a porous enclosure saturated by nanofluid with different heat sources

2018 ◽  
Vol 7 (1) ◽  
pp. 1-16 ◽  
Author(s):  
M. Muthtamilselvan ◽  
S. Sureshkumar
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
High Heat ◽  
Heated Wall ◽  
Left Wall ◽  
High Heat Transfer

Abstract The present study is proposed to investigate the effects of various lengths and different locations of the heater on the left sidewall in a square lid-driven porous cavity filled with nanofluid. A higher temperature is maintained on the left wall where three different lengths and three different locations of the heat source are considered for the analysis. The right wall is kept at a lower temperature while the top and bottom walls, and the remaining portions of the heated wall are adiabatic. The governing equations are solved by finite volume method. The results show that among the different lengths of the heat source, an enhancement in the heat transfer rate is observed only for the length LH = 1/3 of the heat source. In the case of location of the heat source, the overall heat transfer rate is increased when the heat source is located at the top of the hot wall. For Ri = 1 and 0.01, a better heat transfer rate is obtained when the heat source is placed at the top of the hot wall whereas for Ri = 100, it occurs when the heating portion is at the middle of the hot wall. As the solid volume fraction increases, the viscosity of the fluid is increased, which causes a reduction in the flow intensity. An addition of nanoparticles in the base fluid enhances the overall heat transfer rate significantly for all Da considered. The permeability of the porous medium plays a major role in convection of nanofluid than porosity. A high heat transfer rate (57.26%) is attained for Da = 10−1 and χ = 0.06.

scholarly journals Numerical simulation for bioconvectional flow of burger nanofluid with effects of activation energy and exponential heat source/sink over an inclined wall under the swimming microorganisms

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hassan Waqas ◽  
Umar Farooq ◽  
Aqsa Ibrahim ◽  
M. Kamran Alam ◽  
Zahir Shah ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Activation Energy ◽  
Differential Equations ◽  
Heat Source ◽  
Lewis Number ◽  
Numerical Results ◽  
Solid Particles ◽  
Liquid Component ◽  
Pharmaceutical Industries ◽  
The Impact

AbstractNanofluids has broad applications such as emulsions, nuclear fuel slurries, molten plastics, extrusion of polymeric fluids, food stuffs, personal care products, shampoos, pharmaceutical industries, soaps, condensed milk, molten plastics. A nanofluid is a combination of a normal liquid component and tiny-solid particles, in which the nanomaterials are immersed in the liquid. The dispersion of solid particles into yet another host fluid will extremely increase the heat capacity of the nanoliquid, and an increase of heat efficiency can play a significant role in boosting the rate of heat transfer of the host liquid. The current article discloses the impact of Arrhenius activation energy in the bioconvective flow of Burger nanofluid by an inclined wall. The heat transfer mechanism of Burger nanofluid is analyzed through the nonlinear thermal radiation effect. The Brownian dispersion and thermophoresis diffusions effects are also scrutinized. A system of partial differential equations are converted into ordinary differential equation ODEs by using similarity transformation. The multi order ordinary differential equations are reduced to first order differential equations by applying well known shooting algorithm then numerical results of ordinary equations are computed with the help of bvp4c built-in function Matlab. Trends with significant parameters via the flow of fluid, thermal, and solutal fields of species and the area of microorganisms are controlled. The numerical results for the current analysis are seen in the tables. The temperature distribution increases by rising the temperature ratio parameter while diminishes for a higher magnitude of Prandtl number. Furthermore temperature-dependent heat source parameter increases the temperature of fluid. Concentration of nanoparticles is an decreasing function of Lewis number. The microorganisms profile decay by an augmentation in the approximation of both parameter Peclet number and bioconvection Lewis number.

scholarly journals Free and Forced Convective Heat Transfer through a Nanofluid with Two Dimensions past Stretching Vertical Plate

2020 ◽  
Vol 7 (3) ◽  
Author(s):  
B. Sailaja ◽  
G. Srinivas ◽  
B.S. Babu
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Convective Heat Transfer ◽  
Forced Convection ◽  
Heat Transfer Rate ◽  
Convective Heat ◽  
Transfer Rate ◽  
Vertical Plate ◽  
Two Dimensions ◽  
Forced Convective Heat Transfer

The present study focus on both free and forced convective heat transfer through a nanofluid in two dimensions past stretching vertical plate. This free and forced convective heat transfer in Cu–water Nanofluid past permeable flat vertical semi-infinite plate was due to high conductivity and its occurrence. In this paper magnetic field and also heat source were considered. In graphs the effect on various parameters such as Reynolds number (Re) , solid volume fraction (φ), magnetic field parameter (M), inclination angle of the plate (γ ), heat source parameter (Qh), on linear velocity (U), vertical velocity (V) and temperature (θ) were exhibited. The profile of every governing parameter is displayed for natural as well as forced convection by considering the Ar >> 1 and Ar << 1 respectively. This rate of heat transfer in forced convection is more than equivalent in free convection. So these problems have several applications in engineering and petroleum industries such as electroplating, chemical processing of heavy metals and solar water heaters. Inertial force reducing the heat transfer rate in natural convection but the enhancement of Nu observed in forced convection. The composition of metal particles enhances the heat transfer rate in both convections, which emphasizes the nanofluid significance. Lorentz force is enhancing the heat transfer rate slightly. Heat source obviously increase the rate of heat transfer in both convections. The present paper aims to study the convective high temperature transfer of nanofluids into which viscosity proposed by Einstein and thermal conductivity proposed by Corcione were used.

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