Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles

Thermal conduction which happens in all phases(liquid,solid,and gas)is the transportation of internal energy through minuscule collisions of particles and movement of electrons within a working body.The colliding particles comprise electrons,molecules,and atoms,and transfer disorganized microscopic potential and kinetic energy,mutually known as the internal energy.In engineering sciences,heat transfer comprises the processes of convection,thermal radiation,and sometimes mass transportation.Typically,more than one of these procedures may happen in a given circumstance.We use the Cattaneo-Christov(CC)heat flux model instead of the Fourier law of heat conduction to discuss the behavior of heat transportation.A mathematical model is presented for the Cattaneo-Christov double diffusion(CCDD)in the flow of a non-Newtonian nanofluid(the Jeffrey fluid)towards a stretched surface.The magnetohydrodynamic(MHD)fluid is considered.The behaviors of heat and mass transportation rates are discussed with the CCDD.These models are based on Fourier’s and Fick’s laws.The convective transportation in nanofluids is discussed,subject to thermophoresis and Brownian diffusions.The nonlinear governing flow expression is first altered into ordinary differential equations via appropriate transformations,and then numerical solutions are obtained through the built-in-shooting method.The impact of sundry flow parameters is discussed on the velocity,the skin friction coefficient,the temperature,and the concentration graphically.It is reported that the velocity of material particles decreases with higher values of the Deborah number and the ratio of the relaxation to retardation time parameter.The temperature distribution enhances when the Brownian motion and thermophoresis parameters increase.The concentration shows contrasting impact versus the Lewis number and the Brownian motion parameter.It is also noticed that the skin friction coefficient decreases when the ratio of the relaxation to retardation time parameter increases.

Absorption Rate into a Small Sphere for a Diffusing Particle Confined in a Large Sphere

We study the problem of a diffusing particle confined in a large sphere in the n-dimensional space being absorbed into a small sphere at the center. We first non-dimensionalize the problem using the radius of large confining sphere as the spatial scale and the square of the spatial scale divided by the diffusion coefficient as the time scale. The non-dimensional normalized absorption rate is the product of the physical absorption rate and the time scale. We derive asymptotic expansions for the normalized absorption rate using the inverse iteration method. The small parameter in the asymptotic expansions is the ratio of the small sphere radius to the large sphere radius. In particular, we observe that, to the leading order, the normalized absorption rate is proportional to the (n - 2)-th power of the small parameter for .

Theoretical Approach to Concentration Distribution and Adhesion Efficiency of Fine Particles Around a Rising Bubble in Slurry Systems

Quantitative prediction of distribution function and adhesionefficiency of particles around a rising bubble in slurry systems ispresented in this work. By solving the convection-diffusion equation(Fokker-Planck equation), the influence of Brownian diffusivity offine particles on concentration distribution and adhesion efficiencyis demonstrated with the hydrodynamic force and van der Waalsattractive potential between particles and bubble considered. It isfound that two kinds of mechanism dominate the adhesion process ofparticles on bubble according to different Peclet number or size ofparticles and bubble, as well as other properties of the slurrysystems. In addition, the viscosity ratio of bubble to the suspendingfluid was found to have obvious influence on particle adhesion.

DIFFUSION PROCESSES ON COMPLETE RIEMANNIAN MANIFOLDS

In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.

Significance of Stefan blowing effect on flow and heat transfer of Casson nanofluid over a moving thin needle

The current mathematical model explains the influence of non-linear thermal radiation on the Casson liquid flow over a moving thin needle by considering Buongiorno’s nanofluid model.The influences of Stefan blowing,Dufour and Soret effects are also considered in the model.The equations which represent the described flow pattern are reduced to ordinary differential equations(ODEs)by using apt similarity transformations and then they are numerically solved with Runge–Kutta-Fehlberg’s fourth fifth-order method(RKF-45)with shooting process.The impacts of pertinent parameters on thermal,mass and velocity curves are deliberated graphically.Skin friction,rate of heat and mass transfer are also discussed graphically.Results reveal that,the increase in values of Brownian motion,thermophoresis,Dufour number,heating and radiative parameters improves the heat transfer.The increasing values of the Schmidt number deteriorates the mass transfer but a converse trend is seen for increasing values of the Soret number.Finally,the escalating values of the radiative parameter decays the rate of heat transfer.