Momentum and heat transfer of a special case of the unsteady stagnation-point flow

This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer,which is also an exact solution to the unsteady Navier-Stokes(NS)equations.The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions.The wall temperature and heat flux have power dependence on both time and spatial distance.The solution domain,the velocity distribution,the flow field,and the temperature distribution in the fluids are studied for different controlling parameters.These parameters include the Prandtl number,the mass transfer parameter at the wall,the wall moving parameter,the time power index,and the spatial power index.It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems.The heat transfer solutions are given by the confluent hypergeometric function of the first kind,which can be simplified into the incomplete gamma functions for special conditions.The wall heat flux and temperature profiles show very complicated variation behaviors.The wall heat flux can have multiple poles under certain given controlling parameters,and the temperature can have significant oscillations with overshoot and negative values in the boundary layers.The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified.The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed.Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations,which can be used as a benchmark problem for numerical code validation.

Progress on Heat Transfer in Fractures of Hot Dry Rock Enhanced Geothermal System

Hot Dry Rock(HDR)is the most potential renewable geothermal energy in the future.Enhanced Geothermal System(EGS)is the most effective method for the development and utilization of HDR resources,and fractures are the main flow channels and one of the most important conditions for studying heat transfer process of EGS.Therefore,the heat transfer process and the heat transfer mechanism in fractures of EGS have been the hot spots of research.Due to the particularity of the mathematical models of heat transfer,research in this field has been at an exploratory stage,and its methods are mainly experimental tests and numerical simulations.This paper introduces the progress on heat transfer in fractures of Hot Dry Rock EGS in detail,provides a comparative analysis of the research results and prospects for future research directions:It is suggested that relevant scholars should further study the mathematical equations which are applicable to engineering construction of seepage heat transfer in irregular fractures of the rock mass,the unsteady heat transfer process between multiple fractures of the rock mass and the heat transfer mechanism of the complex three-dimensional models of EGS.

Nanofluids Transport Model Based on Fokker-Planck Equation and the Convection Heat Transfer Calculation

In current research about nanofluid convection heat transfer, random motion of nanoparticles in the liquid distribution problem mostly was not considered. In order to study on the distribution of nanoparticles in liquid, nanofluid transport model in pipe is established by using the continuity equation, momentum equation and Fokker-Planck equation. The velocity distribution and the nanoparticles distribution in liquid are obtained by numerical calculation, and the effect of particle size and particle volume fraction on convection heat transfer coefficient of nanofluids is analyzed. The result shows that in high volume fraction （ 0 _-- 0.8% ）, the velocity distribution of nanofluids characterizes as a ＂cork-shaped＂ structure, which is significantly different from viscous fluid with a parabolic distribution. The convection heat transfer coefficient increases while the particle size of nanoparticle in nanofluids decreases. And the convection heat transfer coefficient of nanofluids is in good agreement with the experimental result both in low （0 ~〈 0.1% ） and high （ q = 0.6% ） volume fractions. In presented model, Brown motion, the effect of interactions between nanoparticles and fluid coupling, is also considered, but any phenomenological parameter is not introduced. Nanoparticles in liquid transport distribution can be quantitatively calculated by this model.

Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient

The effect of internal heating source on the film momentum and thermal transport characteristic of thin finite power-law liquids over an accelerating unsteady horizontal stretched interface is studied. Unlike most classical works in this field, a general surface temperature distribution of the liquid film and the generalized Fourier＇s law for varying thermal conductivity are taken into consideration. Appropriate similarity transformations are used to convert the strongly nonlinear governing partial differential equations （PDEs） into a boundary value problem with a group of two-point ordinary differential equations （ODEs）. The correspondence between the liquid film thickness and the unsteadiness parameter is derived with the BVP4C program in MATLAB. Numerical solutions to the self-similarity ODEs are obtained using the shooting technique combined with a Runge-Kutta iteration program and Newton＇s scheme. The effects of the involved physical parameters on the fluid＇s horizontal velocity and temperature distribution are presented and discussed.

Extended Generalized Riccati Equation Mapping for Thermal Traveling-Wave Distribution in Biological Tissues through a Bio-Heat Transfer Model with Linear/Quadratic Temperature-Dependent Blood Perfusion

Analytical thermal traveling-wave distribution in biological tissues through a bio-heat transfer (BHT) model with linear/quadratic temperature-dependent blood perfusion is discussed in this paper. Using the extended generalized Riccati equation mapping method, we find analytical traveling wave solutions of the considered BHT equation. All the travelling wave solutions obtained have been used to explicitly investigate the effect of linear and quadratic coefficients of temperature dependence on temperature distribution in tissues. We found that the parameter of the nonlinear superposition formula for Riccati can be used to control the temperature of living tissues. Our results prove that the extended generalized Riccati equation mapping method is a powerful tool for investigating thermal traveling-wave distribution in biological tissues.

A Numerical Method for Shape Optimal Design in the Oseen Flow with Heat Transfer

This paper is concerned with the optimal design of an obstacle located in the viscous and incompressible fluid which is driven by the steady-state Oseen equations with thermal effects. The structure of shape gradient of the cost functional is derived by applying the differentiability of a minimax formulation involving a Lagrange functional with a space parametrization technique. A gradient type algorithm is employed to the shape optimization problem. Numerical examples indicate that our theory is useful for practical purpose and the proposed algorithm is feasible.

Mathematical Modeling of Heat Flux Distribution in Raw Cotton Stored in Bunt

The scientific article examines the physical and mechanical properties of raw cotton stored in buntings in cotton palaces. Because during the storage of raw cotton in bunts, some of its properties deteriorate, some improvements. Therefore, the mathematical modeling of storage conditions of raw cotton in bunts and the physical and mechanical conditions that occur in it is of great importance. In the developed mathematical model, the main factor influencing the physical and mechanical properties of raw cotton is the change in temperature. Due to the temperature, kinetic and biological processes accumulated in the raw cotton in Bunt, it can spread over a large surface, first in a small-local state, over time with a nonlinear law. As a result, small changes in temperature lead to a qualitative change in physical properties. In determining the law of temperature distribution in the raw cotton in Bunt, Laplace’s differential equation of heat transfer was used. The differential equation of heat transfer in Laplace’s law was replaced by a system of ordinary differential equations by approximation. Conditions are solved in MAPLE-17 program by numerical method. As a result, graphs of temperature changes over time in raw cotton were obtained. In addition, the table shows the changes in density, pressure and mass of cotton, the height of the bun. As the density of the cotton raw material increases from the top layer of the bunt to the bottom layer, an increase in the temperature in it has been observed. This leads to overheating of the bottom layer of cotton and is the main reason for the deterioration of the quality of raw materials.

Heat transfer performance for DCLL blanket with no-wetting insulator walls

Magnetohydrodynamic (MHD) effect and heat transfer are two key issues for design of dual coolant lead lithium (DCLL) blanket. Flow channel insert (FCI) has been applied to decouple the liquid metal from the walls to efficiently decline MHD pressure drops and reduce heat losses from the liquid metal for increasing bulk exit temperatures of the blanket. However, there are still big pressure drops and a higher velocity jet located at the gap flow. Moreover, the FCI made from silicon carbide (SiC) constitutes a complex blanket structures which potentially causes special flow phenomena. In the present work, the characteristics of fluid flow and heat transfer in the DCLL blanket channel are investigated for the first wall (FW) sprayed a layer of no-wetting nano coating (NWNC) on its inner surface. The results show that the pressure drop with NWNC wall is oneorder magnitude lower than that with FCI in the general DCLL blanket. The Nusselt number on the NWNC wall is about half of that on the general wall. On this basis, a heat transfer criterion equation of DCLL channel is achieved for the NWNC wall without FCI. The results are compared with that criterion equation of general wall conditions, which indicates the criterion equation can well predict the convection heat transfer of DCLL channel.

A numerical analysis to the non-linear fin problem

In this paper a numerical analysis is carried out to obtain the temperature distribution within a single fin. It is assumed that the heat transfer coefficient depends on the temperature. The complete highly non-linear problem is solved numerically and the variations of both, dimensionless surface temperature and dimensionless surface temperature gradient as well as heat transfer characteristics with the governing non-dimensional parameters of the problem are graphed and tabulated.

New Immersed Boundary Method on the Adaptive Cartesian Grid Applied to the Local Discontinuous Galerkin Method

Currently, many studies on the local discontinuous Galerkin method focus on the Cartesian grid with low computational e ciency and poor adaptability to complex shapes. A new immersed boundary method is presented, and this method employs the adaptive Cartesian grid to improve the adaptability to complex shapes and the immersed boundary to increase computational e ciency. The new immersed boundary method employs different boundary cells(the physical cell and ghost cell) to impose the boundary condition and the reconstruction algorithm of the ghost cell is the key for this method. The classical model elliptic equation is used to test the method. This method is tested and analyzed from the viewpoints of boundary cell type, error distribution and accuracy. The numerical result shows that the presented method has low error and a good rate of the convergence and works well in complex geometries. The method has good prospect for practical application research of the numerical calculation research.

Finite Element Simulation of an Unimolecular Thermal Decomposition inside a Reactor

This numerical study investigates the steady state unimolecular thermal decomposition of a chemical dissolved in water inside a parallel-plate reactor containing four heated circular rods using a penalty Galerkin finite element approach. The reactant fluid enters from the left inlet and exits from the right outlet of the reactor. All solid walls of the reactor are assumed to be thermodynamically isolated. The aim of the investigation is to illustrate the effects of the energy expelled during the reaction, temperature of the heated rods and fluid inlet velocity on the thermal field and concentration of the heat sensitive chemical. The simulation is conducted for different values of inlet velocity and rods temperature taking into consideration and neglecting the reaction energy. From the results, it is concluded that the thermal field and decomposition process of the chemical are significantly influenced by fluid velocity, rods temperature and the reaction type.

Transient Heat Transfer Study of Direct Contact Condensation of Steam in Spray Cooling Water

We conducted a transient experimental investigation of steam–water direct contact condensation in the absence of noncondensible gas in a laboratory-scale column with the inner diameter of 325 mm and the height of 1045 mm. We applied a new analysis method for the steam state equation to analyze the molar quantity change in steam over the course of the experiment and determined the transient steam variation. We also investigated the influence of flow rates and temperatures ofcooling water on the efficiency ofsteam condensation. Our experimental results show that appropriate increasing of the cooling water flow rate can significantly accelerate the steam condensation. We achieved a rapid increase in the total volumetric heat transfer coefficient by increasing the flow rate of cooling water, which indicated a higher thermal convection between the steam and the cooling water with higher flow rates. We found that the temperature ofcooling water did not play an important role on steam condensation. This method was confirmed to be effective for rapid recovering ofsteam.

A Numerical Tackling on Sakiadis Flow with Thermal Radiation

Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.

Modifed pennes' equation modelling bio-heat transfer in living tissues: analytical and numerical analysis

Based on modified version of the Pennes' bio-heat transfer equation, a simplified one- dimensional bio-heat transfer model of the living tissues in the steady state has been applied on whole body heat transfer studies, and by using the Weierstrass' elliptic function, its corresponding analytic periodic and non-periodic solutions have been derived in this paper. Using the obtained analytic solutions, the effects of the thermal diffusivity, the temperature-inde- pendent perfusion component, and the temperature-dependent perfusion component in living tissues are analyzed numerically. The results show that the derived analytic solution is useful to easily and accurately study the thermal behavior of the biological system, and can be extended to applications such as parameter measurement, temperature field reconstruction and clinical treatment.

SINGULAR INTEGRAL EQUATIONS AND BOUNDARY ELEMENT METHOD OF CRACKS IN THERMALLY STRESSED PLANAR SOLIDS

Using the method of the boundary integral equation, a set of singular integral equations of the hear transfer problems and the thermo-elastic problems of a crack embedded in a two-dimensional finite body is derived, and then,its numerical method is proposed by the numerical method of the singular integral equations combined with boundary element method. Moreover, the singular nature of temperature gradient field near the crack front is proved by the main-part analysis method of the singular integral equation, and the singular temperature gradients are exactly obtained. Finally, several typical examples calculated.

Similarity solution to a heat equation with convection in an infinite medium

A second order heat equation with convection in an infinite medium isstudied. Suitable similarity transformations are used to reduce the parabolic heat equation to aClass of singular nonlinear boundary value problems. Numerical solutions are presented for differentrepresehtations of heat conduction, heat convection, heat flux, and power law parameters byutilizing the shooting technique. The results reveal the heat transfer characteristic and the effectof parameters on the solutions.

Study on the Irreversible Thermodynamics of a Marine Engine Exhaust-powered Adsorption Refrigerating System

This study investigates the heat and mass transfer mechanism of a marine engifie exhaust-powered adsorption refrigerating system by using irreversible thermodynamics. The equations of entropy-production rate and the linear phenomenological equations of thermodynamic flux and force are established. The conventional experimental facilities of unit tube are developed and the phenomenological coefficients are obtained by fitting the experimental data. It is concluded that the thermodynamic process in the adsorbent bed is determined by the coupling effect of the heat and mass transfer; furthermore, the mass transfer is determined by the heat transfer. Taking some measures to increase heat transfer can improve the performance of the adsorption refrigerating system. The conclusions presented in this paper may be of value to the engineering applications of the system.

Simulation of Non-Isothermal Turbulent Flows Through Circular Rings of Steel

This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries.Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation.Because of little maintenance,the heat exchanger of such type is extensively used.Here,we generate simulation of flow and heat transfer using nonisothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation(RANS)model of the turbulent flow together with heat equation.Simulation is tested with Prandtl number(Pr=0.7)with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2×10^(5) to 4.4×10^(5) with turbulence kinetic energy and the dissipation rate in ranges(3.75×10^(−3) to 1.5×10^(−2))and(3.73×10^(−3)−3×10^(−2))respectively.Two correlations available in the literature are used in order to check validity.The results are displayed through streamlines,surface plots,contour plots,isothermal lines,and graphs.It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15%to a maximum of 514%.The temperature at the middle shows the consistency in value but declines immediately at the end.This process becomes faster with the decrease in inlet velocity magnitude.

Qualitative Properties and Numerical Solution of the Kolmogorov-Fisher Type Biological Population Task with Double Nonlinear Diffusion

In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.

Application of First-Order Differential Equation to Heat Convection in Fluid

Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.