Critical points arising in transonic flow profiles of the steady compressible Euler equations with heat conduction are investigated. Two examples of transonic flow profiles are studied, namely, radial outflow in a gravitational field, and flow in a quasi-one-dimensional nozzle. The stationary flow equations are reformulated in terms of a dynamical system that parametrizes the flow profiles. Add...

In the present era, fractional calculus plays an important role in various fields. Fractional Calculus is a field of mathematic study that grows out of the traditional definitions of the calculus integral and derivative operators in much the same way fractional exponents is an outgrowth of exponents with integer value. Based on the wide applications in engineering and sciences such as physics, ...

the falling and settling of solid particles in gases and liquids is a natural phenomenon happens in many industrial processes. this phenomenon has altered pure forced convection to a combination of heat conduction and heat convection in a flow over a plate. in this paper, the coupling of conduction (inside the plate) and forced convection of a non-homogeneous nanofluid flow (over a flat plate) ...

Heat conduction by phonons is a ubiquitous process that incorporates a wide range of physics and plays an essential role in applications ranging from space power generation to LED lighting. Heat conduction has been studied for over two hundred years, yet many microscopic aspects of heat conduction have remained unclear in most crystalline solids, including which phonons carry heat and how natur...

The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a ...

The present article mainly focuses on the transient thermal dispersal within a moving plate using non-Fourier heat flux model. Furthermore, innovative, sophisticated artificial neural network strategy with Levenberg-Marquardt backpropagated scheme (ANNS-LMBS) is proposed for determining temperature in convective-radiative plate. Using dimensionless terms, energy model exchange simplified into n...

This article deals with the determination of temperature distribution, displacement and thermal stresses of a rectangular plate having nonhomogeneous material properties with internal heat generation. The plate is subjected to sectional heating. All the material properties except Poisson’s ratio and density are assumed to be given by a simple power law along x direction. Solution of the two-dim...

Experiments were conducted to investigate local heat transfer coefficients and flow characteristics of air flow in a 962 lm inner diameter stainless steel microtube (minichannel). The effects of heat loss, axial heat conduction and viscous heating were systematically analyzed. Heat losses during the experiments with gas flow in small diameter tubes vary considerably along the flow length, causi...

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat flu...