Abstract: In this paper we consider heat transfer in a hot body with different geometries. Here, the thermal conductivity and internal heat generation are both temperature-dependent. This assumption rendered the model considered to be nonlinear. We assume that thermal conductivity is given by a power law function. We employ the preliminary group classification to determine the cases of internal heat generation for which the principal Lie algebra extends by one. Exact solutions are constructed for the case when thermal conductivity is a differential consequence of internal heat generation term. We derive the approximate numerical solutions for the cases where exact solutions are difficult to construct or are nonexistent. The effects of parameters appearing in the model on temperature profile are studied.
Abstract: This paper examines the problem of nonlinear heat transfer in a cylindrical solid of combustible materials with two-step exothermic kinetics and radiative heat loss to the ambient surrounding. The reactant diffusion and temperature dependent pre-exponential factors with respect to sensitized, Arrhenius, and bimolecular kinetics are taken into account in the model energy balanced equation. Both regular perturbation method and numerical shooting technique coupled with Runge-Kutta-Fehlberg iteration scheme are employed to tackle the nonlinear model problem. The effects of various thermophysical parameters on the reactive cylindrical solid temperature, Nusselt number and thermal stability are discussed quantitatively with the help of computational illustrations. It is found that radiative heat loss enhances thermal stability of the material while the two-step exothermic kinetics promotes the onset of thermal instability.
Abstract: This article explores the problem of Blasius flow of water based hybrid nanofluid containing Al2O3 and Cu as nanoparticles over a convectively heated surface. Five different geometries of nanoparticles shape viz spherical, bricks, cylindrical, platelets and blades are considered in our analysis. The nonlinear model equations are obtained and tackled numerically using shooting method coupled with Runge-Kutta Fehlberg numerical scheme. The effects of nanoparticle shapes and other relevant thermophysical parameters on fluid velocity, temperature, skin friction and Nusselt number are discussed with the help of computational illustrations. The result for skin friction coefficient is compared with already existing results in the literature and excellent agreement was obtained. It is found that the heat transfer rate of hybrid nanofluid (Cu-Al2O3/Water) is higher than that of nanofluid (Al2O3/Water) and the Nusselt number increment for blade shaped nanoparticles is the highest as compared to that of platelet, cylindrical, brick and spherical shaped nanoparticles.
Abstract: In this investigation, a magnetohydrodynamic (MHD) flow of AlO /water nanofluid and Cu-AlO /water hybrid nanofluid through a porous channel is analyzed in the presence of a transverse magnetic field. An exact solution of the governing equations has been obtained in closed form. The entropy generation number and the Bejan number are also obtained. The influences of each of the governing parameters on velocity, temperature, entropy generation and Bejan number are displayed graphically and the physical aspects are discussed. In addition, a comparison of the heat transfer enhancement level due to the suspension of AlO and Cu nanoparticles in water as regular nanofluids and as hybrid Cu-AlO /water nanofluid is reported.
Abstract: The hydromagnetic peristaltic motion of Carreau and Casson nanofluids flow in an irregular channel in the presence of diffusion thermo (Soret) and thermo diffusion (Dufour) impacts has been examined. The effect of thermal radiation is incorporated in the energy equation and velocity slip included in the boundary conditions. The dimensionless governing equations for the flow, fluid temperature and nanoparticle concentration are acquired for the suppositions of low Reynolds number and large wavelength. Resulting flow problem has been solved numerically. Outcome of emerging sundry variables on these three flow profiles are graphically analyzed. Axial velocity enhances near the walls of the irregular channel to the mounting values of Hartmann number where as the velocity declines in the central part of the irregular channel. Temperature magnifies considerably with the boosting values of Dufour number. Impact of Soret number decays concentration. Also, a comparative study is made for the numerical results of axial velocity with the existing reports. In addition the numerical results of the friction factor, energy and mass transfer rates for both Carreau and Casson nanofluids are analyzed through the tables.
Abstract: Mathematical modeling to study the effect of nonlinear thermal radiation on Casson nanofluid flow between parallel plates is established. Second order velocity slip condition is implemented at the boundary of the lower plate. An appropriate transformation is applied to alter the PDEs into ODEs and then tackled numerically by employing RKF-45. The consequence of several prevailed parameters on the Casson nanoliquid velocity components, temperature and concentration fields are portrayed graphically and deliberated in detail. Velocity component decreases near the region of lower plate while it increases along the upper plate region for magnetic and slip parameter whereas opposite behavior is obtained for the Casson parameter for the same component.
Abstract: The effects of Cu-nanoparticles on the entropy generation of steady magnetohydrodynamic incompressible flow with viscous dissipation and Joule heating through convergent-divergent channel are analysed in this paper. The basic nonlinear partial differential equations are transformed into a system of coupled ordinary differential equations using suitable transformations which are then solved using power series with Hermite- Padé approximation technique. The velocity profiles, temperature distributions, entropy generation rates, Bejan number as well as the rate of heat transfer at the wall are presented in convergent-divergent channels for various values of nanoparticles solid volume fraction, Eckert number, Reynolds number and channel angle. A stability analysis has been performed for the shear stress which signifies that the lower solution branch is stable and physically realizable, whereas the upper solution branch is unstable. It is interesting to remark that the entropy generation of the system increases at the two walls as well as the heat transfer irreversibility is dominant there whereas the fluid friction irreversibility is dominant along the centreline of the channel.
Abstract: In this study, we investigated the 2D MHD flow of a dissipative Maxwell nanofluid past an elongated sheet with uneven heat source/sink, Brownian moment and thermophoresis effects. The flow governing PDEs are transmuted into nonlinear ODEs adopting the suitable similarity transmissions. Further, the RK-4 technique is employed to acquire the numerical solutions. The impact of pertinent parameters such as thermal radiation, frictional heating, irregular heat source/sink, biot number, Brownian moment and thermophoresis on the flow quantities such as velocity, thermal and concentration fields likewise friction factor, heat and mass transfer rates are bestowed with the succour of graphs and tables. Dual nature is witnessed for Newtonian and non-Newtonian fluid cases. It is noticed that the heat and mass transfer rate in Newtonian fluid larger as compared with non-Newtonian fluid.
Abstract: This study covers a numerical investigation of gyrotactic microorganisms contained MHD flow over a vertical plate bearing thermal radiation, thermophoresis, Brownian motion, chemical reaction and inclined magnetic field effects. With the assistance of similarity transforms, the derived governed equations are transformed as set of ODEs and solved numerically by R-K and Newton’s methods. Graphs are exhibited and explained for various parameters of interest. For engineering interest, we mainly talked about the Skin friction coefficient, reduced Sherwood, Nusselt numbers and density of motile microorganisms. We noticed a rise in the heat transfer rate of motile microorganisms for rising values of the thermophoresis and Brownian motion parameters. Increasing values of the aligned angle hikes the drag force.