Abstract: This paper examines the heat transfer in living skin tissue that is subjected to a convective heating. The tissue temperature evolution over time is classically described by the one-dimensional Pennes' bioheat transfer equation which is solved by applying Laplace transform method. The heat transfer analysis on skin tissue (dermis and epidermis) has only been studied defining the Biot number. The result shows that the temperature in skin tissue is less subject to the convected heating skin compared to constant skin temperature. The study also shows that the Biot number has a significant impact on the temperature distribution in the layer of living tissues. This study finds its application in thermal treatment.
Abstract: In this paper we analyse the heat transfer in a cylindrical spine fin. Here, both the heat transfer coefficient and thermal conductivity are temperature dependent. The resulting 2+1 dimension partial differential equation (PDE) is rendered nonlinear and difficult to solve exactly, particularly with prescribed initial and boundary conditions. We employ the three dimensional differential transform methods (3D DTM) to contract the approximate analytical solutions. Furthermore we utilize numerical techniques to determine approximate numerical solutions. The effects of parameters, appearing in the boundary value problem (BVP), on temperature profile of the fin are studied.
Abstract: In this paper we consider heat transfer in a wall with temperature dependent heat conductivity and internal heat generation. It turns out the model considered is non-linear. We employ the classical Lie point symmetry analysis to determine the exact solutions. A number of cases for thermal conductivity and internal heat generation are considered. In some cases the exact solutions are not possible to construct. However, we first use the obtained exact solution as a bench mark for the quasilinear method. Since confidence is established, we then use the quasilinear method to solve some other applicable problem.
Abstract: Nanofluid flow and heat transfer in a rotating system between two parallel plates in the presence of thermal radiation and heat source impacts are examined. One of the plates of the considered system is penetrable and the other one is stretchable or shrinkable. A similarity transformation is used to convert the governing momentum and energy equations into non-linear ordinary differential equations with the relevant boundary conditions. The achieved non-linear ordinary differential equations are solved by Duan-Rach Approach (DRA). This method allows us to realize a solution without applying numerical methods to evaluate the unspecified coefficients. The impacts of diverse active parameters such as the stretching/shrinking parameter, the radiation parameter, the heat source parameter, the suction/blowing parameter, the Reynolds number and the volume fraction of nanofluid on the velocity and temperature profiles are explored. Also, the correlation for the Nusselt number has been developed in terms of active parameters of the present study. The outcomes indicate that the Nusselt number is a raising function of the injection parameter, nanofluid volume fraction and the radiation parameter, while it is a decreasing function of the suction and heat source parameters. Furthermore, for injection case by soaring the shrinking parameter, the probability of occurrence of the backflow phenomenon soars.
Abstract: In this paper, rheology of laminar incompressible Copper-Kerosene nanofluid in a channel with stretching walls under the influence of transverse magnetic field is investigated. The main structure of the partial differential equations was taken from the law of conservation of mass, momentum and energy equations. Governing boundary layer equations are transformed into nonlinear ordinary differential equations by using similarity variables and then solved with 3-stage Lobatto IIIA formula. Numerical results were compared with another numerical method (Runge-Kutta-Fehlberg) and found excellent agreement. The influence of physical parameters Reynolds number, magnetic number, solid volume fraction, momentum and thermal slip parameters on velocity and temperature profile considered. Numerical results revealed that solid volume fraction decreases the velocity of nanofluid particles near the lower wall of the channel and increase the thermal boundary layer thickness in the channel.
Abstract: This article aims to present the non-similar solution of MHD mixed convection flow using the Sparrow-Quack-Boerner local non-similarity method. Entropy analysis is also performed in the presence of energy dissipation and Joule heating. The buoyancy parameter is chosen as the non-similarity variable and the equations are derived up to the second level of truncation. The dependency of dimensionless velocity profile, temperature distribution, Bejan and entropy generation number on physical parameters has been discussed. As far as the knowledge of the authors is concerned, no attempt has been made on the entropy analysis of MHD mixed convection flow by the local non-similarity method.
Abstract: The objective of investigation is to study the hydro-magnetic boundary layer micropolar nanofluid steady flow past a stretching sheet with a non-uniform heat suction/sink by taking into account of nanofluids containing Cu– water, TiO2–water, Al2O3–water, and Ag–water. As per the geometry of the flow configuration the conservation laws are transformed into a non-linear model. Using the appropriate analoguestransformations, the resultant equations are employing order approach along with shooting technique to derive closed form solutions for momentum, angular velocity, and temperature fields as well as couple stress, skin friction, local Nusselt number, and then to analyse and physical insight of various flow parameters on these fields. Also the numerical computations are performed and plotted through graphs and tables. It is found that the effect of volume fraction of nanoparticles on the fluid velocity, it decreases due to the absence of surface tension forces and hence, the momentum boundary layer thickness reduced. Furthermore, comparisons with published results are in very good agreement. Nomenclature
Abstract: A theoretical investigation of a hydromagnetic boundary layer flow of Carreau fluid over a stretching cylinder with surface slippage and temperature jump is presented in this paper. It is assumed that heat transfer characteristics of the flow follows Cattaneo-Christov heat flux model base on conventional Fourier’s law with thermal relaxation time. The spectral relaxation method (SRM) is being utilized to provide the solution of highly nonlinear system of coupled partial differential equations converted into dimensionless governing equations. The behaviour of flow parameters on velocity, temperature distributions are sketched as well as analyzed physically. The result indicates that the temperature distribution decay for higher temperature jump and thermal relaxation parameters respectively.
Abstract: A mathematical model is established to examine the influence of viscous dissipation and joule heating on magnetohydrodynamic (MHD) flow of an incompressible viscoelastic nanofluid over a convectively heated stretching sheet. Brownian motion and thermophoresis effects have been introduced in this nanofluid model. The governing equations are transformed into ODE’s by using suitable similarity conversions and are then solved numerically by the most robust shooting technique. The significance of numerous physical flow constraints is performed for, and distributions through graphs. It is noticed that, the increases for higher values of and reduces for rising values of heat source and Biot numbers. An outstanding contract was found between our numerical results and previously publicised results.