Electro-osmotic flow of fractional second-grade fluid with fractional Cattaneo heat flux through a vertical microchannel

This study investigates the unsteady electro-osmotic flow (EOF) of a fractional second-grade fluid through a vertical microchannel with convection heat transfer. The fractional Cattaneo heat flux model will be used to modify the heat equation. The solutions for the velocity and the temperature have been derived by employing the Laplace and finite Fourier sine transforms and their numerical inverses. The results show that at the beginning of the time period, the fractional parameter postpones the movement of the fluid. Furthermore, the results show that at the high values of retardation time (non-Newtonian case), the required time for the velocity and the flow rate to reach the steady state increases. Moreover, the heat relaxation time reduces the heat transfer until a critical time, and then the effect reverses.     

Magnetized mixed convection second‐grade fluid flow adjacent to a lubricated vertical surface

The aspects of magnetized mixed convection in second‐grade fluid flow near stagnant point induced by vertical wall are reported. The fluid is impinging orthogonally on the power law lubricant surface. The convective surface temperature and concentration distribution have been assumed. Both the lubricant and the base fluid are governed by the partial differential mathematical expressions. The velocity of the second‐grade fluid and the lubricant are supposed to be continuous at interface. To get the solution of defined nonlinear problem, an implicit numerical technique namely Keller‐Box scheme is applied. The influential constraints are visualized by plotting graphs on velocity, concentration, and thermal profiles. The results of skin‐friction factors, and mass and heat transport rates for both opposing and assisting flows are tabulated and evaluated. The obtained results are validated through available data for limiting conditions.     

Fractional heat conduction in a space with a source varying harmonically in time and associated thermal stresses

Time-nonlocal generalization of the classical Fourier law with the “long-tail” power kernel can be interpreted in terms of fractional calculus (theory of integrals and derivatives of noninteger order) and leads to the time-fractional heat conduction equation with the Caputo derivative. Fractional heat conduction equation with the harmonic source term under zero initial conditions is studied. Different formulations of the problem for the standard parabolic heat conduction equation and for the hyperbolic wave equation appearing in thermoelasticity without energy dissipation are discussed. The integral transform technique is used. The corresponding thermal stresses are found using the displacement potential.     

An exact analysis of radiative heat transfer and unsteady MHD convective flow of a second‐grade fluid with ramped wall motion and temperature

The influence of simultaneously applied ramped boundary conditions on unsteady magnetohydrodynamic natural convective motion of a second‐grade fluid is investigated and analyzed in this study. The motion of the fluid is considered near an infinite upright plate that is nested in a porous medium subject to nonlinear thermal radiation effects. The Laplace transformation technique is utilized to acquire the exact solutions of momentum and energy equations. To effectively examine the rate of heat transfer and shear stress, the Nusselt number and skin friction coefficient are also established. The outcomes of mathematical computations are elucidated through tables and figures to highlight some physical aspects of the problem. Some limiting models of the present problem are also deduced and presented. On comparison, it is observed that the fluid exhibits lower temperature and velocity profiles under ramped boundary conditions. It is also found that wall shear stress can be controlled by choosing large values of the magnetic parameter (M) and Prandtl number (Pr). In addition, the heat transfer rate specifies inverse trends for growing values of radiation parameter (Nr) and Prandtl number (Pr), while it increases rapidly under a ramped surface condition and decreases slowly under a constant surface condition.     

Fundamental solution for a line source of heat in the fractional order theory of thermoelasticity using the new Caputo definition

Abstract

The new Caputo Fabrizio fractional differential operator is used to investigate a problem in the fractional order theory of thermoelasticity. The problem concerns an infinite elastic space under the effect of a continuous line source of heat. The problem is solved using asymptotic expansions valid for short times. Laplace and Hankel transforms are used to solve the problem. A brief study to the nature of propagation of waves is introduced. Graphical results are presented and discussed.     

Numerical modelling of second‐grade fluid flow past a stretching sheet

The present numerical study reports the chemically reacting boundary layer flow of a magnetohydrodynamic second‐grade fluid past a stretching sheet under the influence of internal heat generation or absorption with work done due to deformation in the presence of a porous medium. To distinguish the non‐Newtonian behaviour of the second‐grade fluid with those of Newtonian fluids, a very popularly known second‐grade fluid flow model is used. The fourth order momentum equation with four appropriate boundary conditions along with temperature and concentration equations governing the second‐grade fluid flow are coupled and highly nonlinear in nature. Well‐established similarity transformations are efficiently used to reduce the dimensional flow equations into a set of nondimensional ordinary differential equations with the necessary conditions. The standard bvp4c MATLAB solver is effectively used to solve the fluid flow equations to get the numerical solutions in terms of velocity, temperature, and concentration fields. Numerical results are obtained for a different set of physical parameters and their behaviour is described through graphs and tables. The viscoelastic parameter enhances the velocity field whereas the magnetic and porous parameters suppress the velocity field in the flow region. The temperature field is magnified for increasing values of the heat source/sink parameter. However, from the present numerical study, it is noticed that the flow of heat occurs from sheet to the surrounding ambient fluid. Before concluding the considered problem, our results are validated with previous results and are found to be in good agreement.     

Cattaneo–Christov heat flux model for heat transfer of Marangoni boundary layer flow in a copper–water nanofluid

The Cattaneo–Christov heat flux is first utilized to explore the heat transfer characteristics of Marangoni boundary layer flow in a copper–water nanofluid. The Marangoni boundary layer flow is driven by exponential temperature. Five different types of nanoparticle shapes including sphere, hexahedron, tetrahedron, column and lamina are considered for the copper–water nanofluid. The nonlinear system of partial differential equations is reduced by similarity transformations and then solved numerically by the shooting method. It is found that sphere nanoparticle has better heat transfer enhancement than other nanoparticle shapes and both the temperature and the thickness of the thermal boundary layer are lower for the Cattaneo–Christov heat flux model than the classical Fourier's law of heat conduction.     

Investigating heat conduction in a sphere with heat absorption using generalized Caputo fractional derivative

In this paper, we study the ρ-Laplace transform and the finite sin-Fourier transform as powerful tools in solving fractional differential equations with generalized Caputo derivative. We use these transforms to solve the time-fractional heat equation with a generalized Caputo fractional derivative associated with heat absorption in spherical coordinates. We obtain the solutions in two cases of Dirichlet boundary conditions. The effect of the parameter $\rho$, which characterizes the generalized Caputo derivative is illustrated through some numerical examples.     

Double‐diffusive natural convection in a partially heated enclosure using a nanofluid

This paper analyzes numerically the effect of double‐diffusive natural convection of a water–Al₂O₃ nanofluid in a partially heated enclosure with Soret and Dufour coefficients. The top horizontal wall has constant temperature T_c, while the bottom wall is partially heated T_h, with T_h > T_c . The concentration in the top wall is maintained higher than the bottom wall C_c < C_h. The remaining bottom wall and the two vertical walls are considered adiabatic. Water is considered as the base fluid. The governing equations are solved by the Penalty Finite Element Method using Galerkin's weighted residual scheme. The effect of the parameters, namely, Rayleigh number and solid volume fraction of the nanoparticles on the flow pattern and heat and mass transfer has been depicted. Comprehensive average Nusselt and Sherwood numbers, average temperature and concentration, and mid‐height horizontal and vertical velocities at the middle of the cavity are presented as functions of the governing parameters mentioned above. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21010     

Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

Analysis of a combined power and cooling cycle for low‐grade heat sources

This paper presents a parametric analysis of a combined power/cooling cycle, which combines the Rankine and absorption refrigeration cycles, uses ammonia–water mixture as the working fluid and produces power and refrigeration, while power is the primary goal. This cycle, also known as the Goswami Cycle, can be used as a bottoming cycle using waste heat from a conventional power cycle or as an independent cycle using low‐temperature sources such as geothermal and solar energy. Optimum operating conditions were found for a range of ammonia concentration in the basic solution, isentropic turbine efficiency and boiler pressure. It is shown that the cycle can be optimized for net work, cooling output, effective first law and exergy efficiencies. The effect of rectification cooling source (external and internal) on the cycle output was investigated, and it was found that an internal rectification cooling source always produces higher efficiencies. When ammonia vapor is superheated after the rectification process, cycle efficiencies increase but cooling output decreases. Copyright © 2010 John Wiley & Sons, Ltd.     

Influence of wall properties on peristaltic transport of second grade fluid with heat and mass transfer

This paper discusses the effects of heat and mass transfer on the magnetohydrodynamic (MHD) peristaltic flow of second grade fluid in a channel with flexible walls. Expressions of stream function, temperature, concentration field, and heat transfer coefficient have been computed. The effects of sundry parameters are sketched and examined. The known results of viscous fluid are obtained as the limiting cases of the present expressions. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20361     

Natural convection in a parabolic enclosure with an internal vertical heat source filled with Cu–water nanofluid

The numerical investigation of the natural convection in concave and convex parabolic enclosures with a nanofluid consisting of water and copper nanoparticles is carried out by using the finite volume method. The upper and lower walls of the enclosures are adiabatic while the sidewalls are isothermal at a cold temperature. An internal heat source of constant length (ε = 0.2) and negligible thickness is placed at various vertical positions along the center of the enclosure. It was found that the increase in the location of the heat source leads to a drop in the water and nanofluid flow circulation in both types of enclosures. For both considered Cases I and II, the average Nusselt number increases when the Rayleigh number and solid volume fraction increase. Moreover, it was concluded that Case I with δ = 0.8 is the optimum case for heat transfer enhancement for Ra = 10³ and Ra = 10⁴. Case II with δ = 0.5 is optimum for Ra = 10⁵. Both cases are satisfied when the nanofluid is used with ? = 0.2.     

Oil fouling in double‐pipe heat exchanger under liquid‐liquid dispersion and the influence of copper oxide nanofluid

Dispersions of oil in water are encountered in a variety of industrial processes leading to a reduction in the performance of the heat exchangers when thermally treating such two phase fluids. This reduction is mainly due to changes in the thermal and hydrodynamical behavior of the two phase fluid. In the present work, an experimental investigation was performed to study the effects of light oil fouling on the heat transfer coefficient in a double‐pipe heat exchanger under turbulent flow conditions. The effects of different operating conditions on the fouling rate were investigated including: hot fluid Reynolds number (the dispersion), cold fluid Reynolds number, and time. The oil fouling rate was analyzed by determining the growth of fouling resistance with time and through pressure drop measurements. The influence of copper oxide (CuO) nanofluid on the fouling rate in the dispersion was also determined. It was found that the presence of dispersed oil causes a reduction in heat transfer coefficient by percentages depending on the Reynolds number of both cold and hot fluids and the concentration of oil. In addition, the time history of fouling resistance exhibited different trends with the flow rates of both fluids and its trend was influenced appreciably by the presence of CuO nanofluid.     

Numerical study of radiation‐convection heat transfer

In this study, the authors attempted to introduce a simulation technique for radiation‐convection heat transfer in the high‐temperature fields of industrial furnaces, boilers, and gas turbine combustors. The convection effect was analyzed by a differential equation, but the radiation effect was analyzed by an integral equation. Thus, it was not easy to arrange both effects using the same type of equations. Then, the authors introduced the zone method and Monte Carlo method for the integral equation of the radiation effect and the finite difference method for the differential equation of the convection effect. A three‐dimensional analysis of the high‐temperature furnace was performed by this simulation technique to obtain its temperature distribution. Furthermore, another radiation‐convection heat transfer analysis in the low‐temperature living room was performed by the same technique. Finally, the authors tried to develop a computer software for radiation‐convection heat transfer and described their idea of software construction for the above. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(5): 391–407, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10042     

Experimental investigation of Al2O3–MgO hot hybrid nanofluid in a plate heat exchanger

Exergy–energy analysis of the plate heat exchanger is experimentally performed with different Al₂O₃–MgO hybrid nanofluid (HyNf) as a hot fluid. There were six combinations of fluids, namely, deionized (DI) water, ethylene glycol–DI water brine (1:9 volume ratio), propylene glycol–DI water brine (1:9 volume ratio), base fluids and their respective Al₂O₃–MgO (4:1 particle volume ratio) HyNfs of 0.1% total volume concentration. The effects of different flow rates and hot inlet temperatures on the heat transfer rate, heat transfer coefficient, pump work, irreversibility, and performance index (PI) are investigated. It is witnessed that the heat transfer rate, heat transfer coefficient, pump work, and irreversibility enhances with the flow rate and nanoparticle suspension. While the PI declines with a rise in the flow rate, the heat transfer rate, heat transfer coefficient, PI, and irreversibility rise up maximum for MgO–alumina (1:4) DI water HyNf upto 11.8%, 31.7%, 11.1%, and 4.05%, respectively. The pump work enhances upto 1.6% for MgO–alumina (1:4)/EG–DI water (1:9) HyNf.     

Zero‐mass flux and Cattaneo–Christov heat flux through a Prandtl non‐Newtonian nanofluid in Darcy–Forchheimer porous space

The Darcy–Forchheimer Prandtl fluid flow due to moving sheet is described here. The familiar energy transfer model, namely, the Cattaneo–Christov model of heat transportation, is adopted under thermal radiation phenomenon. The Prandtl non‐Newtonian nanofluid is accounted as a functioning fluid. The functioning fluid flows in Darcy–Forchheimer porosity space. The boundary‐layer and similarity variables are executed to reframe the mathematical expressions into simplified and single independent variable. Numerical solutions of nonlinear dimensionless expressions are calculated. The variations of distinct constraints on important quantities are demonstrated through tabular and pictorial forms. It is visualized that the velocity of non‐Newtonian nanofluid is enhanced significantly by incrementing the elastic parameter. Improving the thermophoretic and Brownian movement parametric values leads to higher profile of Prandtl nanofluid temperature.     

Effects of double stratification on MHD chemically reacting second‐grade fluid through porous medium between two parallel plates

The present study focuses on the study of heat transfer in a magnetohydrodynamic double stratification fluid flow through porous channel. In getting the solution of Navier‐Stokes equations, we have adapted the similarity transformation technique to convert the partial differential equations into a coupled system of nonlinear ordinary differential equations. We further applied the fourth‐order Runge‐Kutta method with shooting technique to solve the problem numerically. The results are exhibited via graphs, and the analysis has been addressed for various flow characteristics with respect to the parameters concerned. It is found that thermal stratification enhances both temperature and heat transfer rates, and solutal stratification enhances concentration and mass transfer rates. Concentration decreases with increasing chemical reaction and it increases with stratification. A significant variation is observed between concentration profiles in the presence of stratification.     

Radiative nanofluid flow and heat transfer between parallel disks with penetrable and stretchable walls considering Cattaneo–Christov heat flux model

In this work, we explore the unsteady squeezing flow and heat transfer of nanofluid between two parallel disks in which one of the disks is penetrable and the other is stretchable/shrinkable, in the presence of thermal radiation and heat source impacts, and considering the Cattaneo–Christov heat flux model instead of the more conventional Fourier's law of heat conduction. A similarity transformation is utilized to transmute the governing momentum and energy equations into nonlinear ordinary differential equations with the proper boundary conditions. The achieved nonlinear ordinary differential equations are solved by the Duan–Rach Approach (DRA). This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of diverse active parameters, such as the suction/injection parameter, the solid volume fraction, the heat source parameter, the thermal relaxation parameter, and the radiation parameter on flow and heat transfer traits are examined. In addition, the value of the Nusselt number is calculated and portrayed through figures.