A Model of Solar Radiation and Joule Heating in Flow of Third Grade Nanofluid

2015 ◽  
Vol 70 (3) ◽  
pp. 177-184 ◽  
Author(s):  
Tariq Hussain ◽  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Ahmed Alsaedi ◽  
Bin Chen

AbstractThe flow problem resulting from the stretching of a surface with convective conditions in a magnetohydrodynamic nanofluid with solar radiation is examined. Both heat and nanoparticle mass transfer convective conditions are employed. An incompressible third grade fluid which exhibits shear thinning and shear thickening characteristics is used as a base fluid. Concept of convective nanoparticle mass condition is introduced. Effects of Brownian motion and thermophoresis on magnetohydrodynamic flow of nanofluid are accounted in the presence of thermal radiation. Energy equation incorporates the features of Joule heating. The impact of physical parameters on the temperature and nanoparticle concentration has been pointed out. Numerical values of skin-friction coefficient are presented and analysed. It is hoped that this present investigation serves as a stimulus for the next generation of solar film collectors, heat exchangers technology, material processing, geothermal energy storage, and all those processes which are highly affected by the heat enhancement concept.

PLoS ONE ◽  
2014 ◽  
Vol 9 (1) ◽  
pp. e83153 ◽  
Author(s):  
Tasawar Hayat ◽  
Anum Shafiq ◽  
Ahmed Alsaedi

2009 ◽  
Vol 64 (9-10) ◽  
pp. 553-558 ◽  
Author(s):  
Sohail Nadeem

The effects of variable viscosity on the flow and heat transfer in a thin film flow for a third grade fluid has been discussed. The thin film is considered on the outer side of an infinitely long vertical cylinder. The governing nonlinear differential equations of momentum and energy are solved analytically by using homotopy analysis method. The expression for the viscous dissipation and entropy generation are also defined. The graphical results are presented for various physical parameters appearing in the problem


2010 ◽  
Vol 88 (12) ◽  
pp. 911-917 ◽  
Author(s):  
T. Hayat ◽  
M. Nawaz ◽  
S. Asghar ◽  
Awatif A. Hendi

This study explores the flow of a second-grade fluid in divergent–convergent channel. The problem formulation is first developed, and then the corresponding nonlinear problem is solved by homotopy analysis method (HAM). The effects of different physical parameters on the velocity profile are shown. The numerical values of the skin friction coefficient for different values of parameters are tabulated.


2017 ◽  
Vol 6 (1) ◽  
Author(s):  
M. M. Bhatti ◽  
M. M. Rashidi ◽  
I. Pop

AbstractIn this article, entropy generation with combined effects of thermal radiation and chemical reaction on MHD boundary layer over a moving surface has been investigated. The governing flow comprises of linear momentum equation, energy, and concentration equations which are modified with the help of similarity variables. The reduced resulting nonlinear coupled ordinary differential equations are solved with the help of Successive linearization method (SLM) and Chebyshev spectral collocation method. The impact of all the physical parameters is demonstrated numerically and graphically. A detailed analysis have been given for all the pertinent parameters such as Hartmann number, porosity parameter, Prandtl number, radiation parameter, suction/injection parameter, moving parameter, Brinkmann number, Reynolds number, chemical reaction parameter and Schmidt number on velocity, temperature, concentration and entropy profile as well as the Skin friction coefficient, Nusselt number and Sherwood number are also conducted. The numerical comparison has also been given to the existing published literature.


2021 ◽  
pp. 159-159
Author(s):  
Sharafat Ali ◽  
Muhammad Raja ◽  
Tahir Cheema ◽  
Iftikhar Ahmad ◽  
Numan Mian ◽  
...  

A novel numerical computing framework through Lobatto IIIA method is presented for the dynamical investigation of nanofluidic problem with Williamson fluid flow on a stretching sheet by considering the thermal slip and velocity. The impact of thermophoresis and brownian motion on phenomena of heat transfer are explored by using Buongiorno model. The governing nonlinear partial differential system representing the mathematical model of the Williamson fluid is transformed in to a system of ODEs by incorporating the competency of non-dimensional similarity variables. The dynamics of the transformed system of ODEs are evaluated through the Lobatto IIIA numerically. Sufficient graphical and numerical illustrations are portrayed in order to investigate and analyze the influence of physical parameters; Williamson parameter, Prandtl number, Lewis number, Schmidt number, ratio of diffusivity parameter and ratio of heat capacitance parameter on velocity, temperature and concentration fields. The numerically computed values of local Nusselt number, local Sherwood number and Skin friction coefficient are also inspected for exhaustive assessment. Moreover, the accuracy, efficiency and stability of the proposed method is analyzed through relative errors.


2014 ◽  
Author(s):  
Νικόλαος Μπενάς

A deterministic spectral shortwave radiative transfer model was used forthe computation of the Earth's atmospheric radiation budget, based on hightemporal and spatial resolution satellite data of aerosols and atmospheric climaticparameters from the Moderate Resolution Imaging Spectroradiometer(MODIS) sensor.The study focused on the evaluation of the aerosol direct radiative effect(DRE) on the radiation budget components. Due to the high spatialand temporal variability of aerosols, the DRE, which constitutes a crucialcomponent of the overall eect of aerosols on climate, is thus also highlyvariable.The aerosol direct eect on the tropospheric ozone photolysis rate, J(O1D),was also examined, being a dominant sink of tropospheric ozone. We notethat tropospheric ozone contributes to the global greenhouse eect. Thus,J(O1D) is an important climatic parameter, which needs to be studied usingmodelling approaches, due to the scarcity of measuring stations, andbecause it takes place primarily below 330 nm, a spectral region where theaerosol eect is a key operating factor.The aerosol direct eect on potential evaporation was also assessed. Potentialevaporation equals actual evaporation in shallow lakes, and constitutesa crucial parameter of the hydrological cycle. The aerosol DRE decreasespotential evaporation by decreasing the solar radiation reaching the Earth'ssurface.The model runs were performed for the period 2000{2010 over severalsites in Greece, which are characterised by high aerosol loads, with uniquecharacteristics in terms of seasonal variation and origin. Two research stationsin Crete (HCMR/AERONET and Finokalia), were selected due to theappropriateness of the island for studying Saharan dust episodes, which arefrequent in the wider Eastern Mediterranean, and the availability of ground{based data for both model supplementary input and validation. The modelwas also run over four lakes in Central Greece, which constitute the mainwater supply reservoirs of the city of Athens, for the evaluation of the aerosol eect on potential evaporation.MODIS Level 2 data of aerosols, clouds and atmospheric parameters wereanalysed and processed, and used as input to the model. These data areavailable since 2000, on a daily basis and at 10km10km and 5km5kmspatial resolution. The model takes into account all physical parameters andprocesses that aect signicantly the solar radiation transfer. The aerosolDRE is determined at the Earth's surface, within the atmosphere and at thetop of the atmosphere.The model output downwelling shortwave radiation was successfully validatedagainst ground{based measurements at the HCMR and Finokalia stationsand at the four lakes in Central Greece. The model output J(O1D) wassuccessfully validated against Finokalia station measurements. The analysisof the aerosol DRE on the model radiation budget, J(O1D) and potentialevaporation was performed on an instantaneous/daily mean, seasonal andinter{annual basis. Dust event eects were also quantied, and trends duringthe period examined were assessed and evaluated in terms of correspondingtrends and eects of operating factors, including aerosols, clouds and totalozone.Results show a decreasing trend in aerosols and the corresponding DREover all sites examined. Changes in the radiation budget components, however,are also controlled by other factors; an increase in cloud fraction overHCMR station counterbalanced the eect that the DRE reduction wouldhave caused. Similarly, although the DRE on J(O1D) has decreased, J(O1D)has not increased as was expected, due to an increase in total atmosphericozone. The presence of aerosols reduces potential evaporation by about 0.5mm on a mean daily basis, reaching up to 2 mm in summer. However, adecreasing trend in the aerosol load and DRE was found over all lakes duringthe period 2001{2010.Depending on the availability of model input data, the methodology developedin this study is applicable to any region of specic interest over theglobe.


2019 ◽  
Vol 24 (1) ◽  
pp. 161-178 ◽  
Author(s):  
N. Vijaya Bhaskar Reddy ◽  
N. Kishan ◽  
C. Srinivas Reddy

Abstract The steady laminar incompressible viscous magneto hydrodynamic boundary layer flow of an Eyring- Powell fluid over a nonlinear stretching flat surface in a nanofluid with slip condition and heat transfer through melting effect has been investigated numerically. The resulting nonlinear governing partial differential equations with associated boundary conditions of the problem have been formulated and transformed into a non-similar form. The resultant equations are then solved numerically using the Runge-Kutta fourth order method along with the shooting technique. The physical significance of different parameters on the velocity, temperature and nanoparticle volume fraction profiles is discussed through graphical illustrations. The impact of physical parameters on the local skin friction coefficient and rate of heat transfer is shown in tabulated form.


Author(s):  
Fazal Subhan ◽  
Suheel Abdullah Malik ◽  
Muhammad Asghar Khan ◽  
Muhammad Adnan Aziz ◽  
M. Irfan Uddin ◽  
...  

This paper presents a stochastic heuristic approach to solve numerically nonlinear differential equation (NLDE) governing the thin film flow of a third-grade fluid (TFF-TGF) on a moving belt. Moreover, the impact on velocity profile due to fluid attribute is also investigated. The estimate solution of the given NLDE is achieved by using the linear combination of Bernstein polynomials with unknown constants. A fitness function is deduced to convert the given NLDE along with its boundary conditions into an optimization problem. Genetic algorithm (GA) is employed to optimize the values of unknown constants. The proposed approach provided results in good agreement with numerical values taken by Runge–Kutta and more accurate than two popular classical methods including Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The error is minimized 10[Formula: see text] times to 10[Formula: see text] times.


2021 ◽  
Vol 409 ◽  
pp. 123-141
Author(s):  
Macha Madhu ◽  
N.S. Shashikumar ◽  
Bijjanal Jayanna Gireesha ◽  
Naikoti Kishan

The impact of space dependent heat source in the transport of micropolar fluid in the existence of magnetic dipole, Joule heating, viscous heating, thermal radiation, hydrodynamic slips and convective condition effects has been numerically investigated. The dimensioned governing equations are non-dimensionlzed by using dimensionless variables then non-dimensional forms of the corresponding equations are than tackled by the versatile Finite Element Method (FEM). The effects of pertinent physical parameters characterize the flow phenomena are presented through graphs and discussed. It is found that, the impact of thermal based heat source advances the heat transfer characteristics significantly than exponential to space dependent. The thermal performance can be improved through the effects of magnetic dipole, viscous heating, Joule heating and convective condition. Further, the present numerical results are compared with previously published results in the literature as a limiting case of the considered problem and found to be in good agreement with the existing results.


Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 297 ◽  
Author(s):  
Ibrahim Alarifi ◽  
Ahmed Abokhalil ◽  
M. Osman ◽  
Liaquat Lund ◽  
Mossaad Ayed ◽  
...  

A steady laminar flow over a vertical stretching sheet with the existence of viscous dissipation, heat source/sink, and magnetic fields has been numerically inspected through a shooting scheme based Runge—Kutta–Fehlberg-integration algorithm. The governing equation and boundary layer balance are expressed and then converted into a nonlinear normal system of differential equations using suitable transformations. The impact of the physical parameters on the dimensionless velocity, temperature, the local Nusselt, and skin friction coefficient are described. Results show good agreement with recent researches. Findings reveal that the Nusselt number at the sheet surface augments, since the Hartmann number, stretching velocity ratio A, and Hartmann number Ha increase. Nevertheless, it reduces with respect to the heat generation/absorption coefficient δ.


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