Boundary layers are thin regions next to the wall in the flow where viscous forces are important and affect the engineering process of producing materials. For example viscous forces play essential rules in glass fiber drawing, crystal growing, plastic extrusion, etc.[1] The final product quality depends on the rate of cooling in the process so the thickness of the thermal boundary layer have to be estimated. Blasius [2] studied the simplest boundary layer over a flat plate. He employed a similarity transformation that reduces the partial differential boundary layer equations to a nonlinear third-order ordinary differential equation before solving it analytically. The dynamics of the boundary layer flow over a stretching surface originated from the pioneering work of Crane [3]. Later on, various aspects of the problem have been investigated by Dutta et al. [4], Chen and Char [5], etc. Vajravelu [6] studied flow and heat transfer in a viscous fluid over a nonlinear stretching sheet with neglecting the viscous dissipation, then Cortell [7] presented his study about the flow and heat transfer on a nonlinear stretching sheet for two different types of thermal boundary conditions on the sheet, constant surface temperature and prescribed surface temperature. Nadeem et al. [8] studied the effects of heat transfer on the stagnation flow of a third-order fluid over a shrinking sheet. Recently, Prasad et al. [9] studied the mixed convection heat transfer over a non-linear stretching surface with variable fluid properties.
Due to recent studies, scientists realized that devices have to be cooled in a more effective way and the conventional fluids such as water are not appropriate anymore, so the idea of adding nanometer-sized particles to a...
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...low are studied as well.
Nu= (xq_w)/(K(T_w-T_∞)) ,Sh= (xq_m)/(D_B (C_w-C_∞)),C_f=τ_w/(ρ〖〖 u〗_∞〗^2 ) (13)
Here τ_w is the surface shear stress and q_w, q_m are heat and mass flux at the surface respectively and are defined as follows:
τ_w=├ μ(∂u/∂y) ┤| y=0 (14)
q_w=-K(T_w-T_∞ ) x^((n-1)/2) √(2&(n+1)a/2ν)θ^' (0) (15)
q_m=-D_B (C_w-C_∞ ) x^((n-1)/2) √(2&(n+1)a/2ν)ϕ^' (0) (16)
It is worh mentionig that using dimanssionless variables Eq.7, we can obtaine the rate of heat and mass transfer and skin friction coeficient as follows:
Nu/√(2&〖Re〗_x )=-θ^' (0) (17)
Sh/√(2&〖Re〗_x )=-ϕ^' (0)
√(2&2〖Re〗_x )C_f=f^'' (0)
As mentioned before there is no exact solution for the case n≠1 so we have solved the highly nonlinear Eqs.(8) to (10) with Homotopy Analysis Method [HAM] as a semi-analytical technique which will disscus in the next section of this paper.
Baseball is Michael’s only way to a better future. Michael, the main character in the book “Heat” by Mike Lupica, is a 12 year old boy who moved to New York from Cuba. Michael is gifted. He has an arm that throws baseballs super fast. But with his dad gone Michael can’t prove his age to the baseball team and the team needs his pitching skills. In the book Heat the symbol is Yankee Stadium. This symbol represents the main characters future. But the theme of the book is “family can come from the most unexpected places.”
“Mr. Hunter, Raucsh said in a ringing voice,”you are under arrest put your hands on the top of your head”. This quote was said by Mr. Rausch the Police officer in the novel High Heat to Mr. Hunter to arrest him at his sons baseball game. He was arresting Mr. Hunter because he sold drug dealers a car which a false check. The Puritans would support the novel High Heat due to hardworking, respected authority, and strong family values.
In classical fluid dynamics, the Navier-Stokes equations for incompressible viscous fluids and its special (limiting) case the Euler equations for inviscid fluids are sets of non-linear partial differential equations that describes the spatiotemporal evolution of a fluid (gas). Both equations are derived from conservative principles and they model the behavior of some macroscopic variables namely: mass density, velocity and temperature.
The frictional effects due to viscosity were taken into account by the term , where is the effective viscosity of the fluid that flowing through the porous medium and is the porosity of the medium.
Can be calculated dynamic viscosity ƞ from the kinematic viscosity μ and the density ρ according to equation (2.1.2).
example and the results of the analyses are presented. We close with concluding remarks in Section 5.
When a viscous fluid flows along a fixed impermeable wall, or past the rigid surface of an immersed body, an essential condition is that a velocity at any point on the wall or other fixed surface is zero. To the extent to which the condition modifies the general character of the flow is dependent on the viscosity of the fluid. If a body has a streamlined shape and the fluid flowing over the body has a small viscosity that is not negligible, the modifying effect appears to be confined to the narrowest regions adjacent to the solid surfaces; these are called boundary layers. Within these layers, there is a rapid change in velocity which gives rise to a large velocity gradient normal to the boundary which produces a shear stress [1]. At the boundary layer where the flow of fluid at the surface of the body is where the shearing stress is not zero. However, outside the boundary layer there are negligible stresses therefore the fluid velocity increases further away for the wall or boundary [2].
Zigrang, D. J. and Sylvester, N. D., “Explicit approximations to the Colebrook’s friction factor”, AICHE Journal 28, 3, 514, 1982
Heat transfer from high temperature heated surfaces finds considerable application in engineering. Because of its large number of applications in industries, considerable efforts have been made by researchers to investigate various aspects of the heat transfer and its fundamental principles involved. Fluid flow problems involving heat transfer viz. in presence of convention and radiation represents an idealization of many meaningful problems in engineering practice. Due to the presence of higher level of temperature required in many system like boiler, nuclear reactor; the effect of radiation heat transfer increases. So, there becomes a need of including radiative effect of the participating medium and also their boundary conditions. Keeping this in mind, an attempt was made to investigate the heat transfer in the Indian Pressurized Heavy Water Reactor (IPHWR) during Loss of Coolant Accident (LOCA) with low steam flow. This study will help in estimating the safe working limits for the heat dissipation in the reactor.
where J is the moment of inertia of the armature–flapper assembly, Br is the damping coefficient for rotation of the armature–flapper assembly, Tnozzle is the torque produced by the net flow force, m is the mass of the armature–flapper assembly, and Bt is the damping coefficient for translation of the armature–flapper assembly.
cooling the extruded product is held under water, completely immersion as it is cooled by
Nodal methods were first introduced and developed to solve neutron diffusion equations in 1970’s [2]. The success of Nodal methods in the field of neutronics was stimulated into the heat flow and fluid flow problems in 1980 [3]. The Nodal Integral Method scheme is developed by approximately satisfying the governing differential equations on finite size brick-like elements. These differential equations are obtained by discretizing the space of independent variables [4]. In the early development of nodal schemes these brick-like elements were referred to as nodes and hence the scheme was called nodal. Nodes in Nodal Integral Method is however similar to the elements of the finite element approach, but the nodes have finite volumes and not only the points in the space of independent variables [5]. An error analysis on NIM methodology is performed to establish the convergence of the solution of two-dimensional heat diffusion equation to the exact solution [1].
Ideally, in the absence of fluid friction, the flow of incompressible fluids can be described by Bernoulli’s Equation:
Heat transfer is by virtue thermal energy stored in temperature-dependent motion of particles. The exchange of kinetic energy of particles occurs through the boundary between two systems which are at different temperatures from each other or from their surroundings. Heat transfer constantly occurs from a region of high temperature to the region of lower temperature. Heat transfer changes the internal energy of both systems according to the Thermodynamics. The Second Law of Thermodynamics defines the concept of thermodynamic entropy. Heat transfer is the study of thermal energy transport within a medium or among neighboring media by molecular interaction, fluid motion, and electro-magnetic waves, resulting from a spatial
This is the transport of heat in a fluid by the motion of the fluid