Trabalho de Historia
Gois no Perodo Monrquico
CEPP
Alunos:
Luclia Oliveira Muniz
Victor Pereira Araujo
Werik Borges Teixeira
Introduo
A histria de Gois se inicia no fim do sculo XVI, quando as exploraes portuguesas
no limitaram-se apenas regio do litoral.
Trabalho de Filosofia
Kant
CEPP
Alunos:
Luclia Oliveira Muniz
Victor Pereira Araujo
Werik Borges Teixeira
Raisleny Alves da Silva
Introduo
Immanuel Kant (Knigsberg, 22 de abril de 1724 Knigsberg, 12 de fevereiro de
1804) foi um filsofo prussiano. Amplamen
Examples of Kinematic Computations in MATLAB
This short tutorial, given in terms of a series of examples, is intended to get you a quick
start on using MALTAB to perform kinematic computations and plotting in MATLAB.
Helpful tips:
You can always type hel
PROBLEM 7.2
KNOWN: Temperature and velocity of engine oil. Temperature and length of flat plate.
FIND: (a) Velocity and thermal boundary layer thickness at trailing edge, (b) Heat flux and surface shear
stress at trailing edge, (c) Total drag force and he
PROBLEM 7.9
KNOWN: Dimensions and surface temperature of electrically heated strips. Temperature and velocity
of air in parallel flow.
FIND: (a) Rate of convection heat transfer from first, fifth and tenth strips as well as from all the strips,
(b) For ai
PROBLEM 7.1
KNOWN: Temperature and velocity of fluids in parallel flow over a flat plate.
FIND: (a) Velocity and thermal boundary layer thicknesses at a prescribed distance from the leading
edge, and (b) For each fluid plot the boundary layer thicknesses
PROBLEM 7.3
KNOWN: Velocity and temperature of air in parallel flow over a flat plate.
FIND: (a) Velocity boundary layer thickness at selected stations. Distance at which boundary layers
merge for plates separated by H = 3 mm. (b) Surface shear stress and
PROBLEM 7.4
KNOWN: Liquid metal in parallel flow over a flat plate.
FIND: An expression for the local Nusselt number.
SCHEMATIC:
ASSUMPTIONS: (1) Steady, incompressible flow, (2) < t, hence u(y) u, (3) Boundary layer
approximations are valid, (4) Constant
PROBLEM 7.6
KNOWN: Velocity and temperature profiles and shear stress-boundary layer thickness
relation for turbulent flow over a flat plate.
FIND: (a) Expressions for hydrodynamic boundary layer thickness and average friction
coefficient, (b) Expressions
PROBLEM 7.5
KNOWN: Form of velocity profile for flow over a flat plate.
FIND: (a) Expression for profile in terms of u and , (b) Expression for (x), (c) Expression for
Cf,x.
SCHEMATIC:
ASSUMPTIONS: (1) Steady state conditions, (2) Constant properties, (3)
PROBLEM 7.7
KNOWN: Parallel flow over a flat plate and two locations representing a short span x1 to x2
where (x2 - x1) < L.
FIND: Three different expressions for the average heat transfer coefficient over the short
span x1 to x2, h1 2 .
SCHEMATIC:
ASSUMP
PROBLEM 7.8
KNOWN: Flat plate comprised of rectangular modules of surface temperature Ts, thickness a and
length b cooled by air at 25C and a velocity of 30 m/s. Prescribed thermophysical properties of the
module material.
FIND: (a) Required power generat
PROBLEM 7.10
KNOWN: Speed and temperature of atmospheric air flowing over a flat plate of prescribed
length and temperature.
5
5
6
FIND: Rate of heat transfer corresponding to Rex,c = 10 , 5 10 and 10 .
SCHEMATIC:
ASSUMPTIONS: (1) Flow over top and bottom
PROBLEM 8.10
KNOWN: Thermal energy equation describing laminar, fully developed flow in a circular pipe with
viscous dissipation.
FIND: (a) Left hand side of equation integrated over the pipe volume, (b) viscous dissipation term
integrated over the same v
PROBLEM 8.9
KNOWN: Flow rate and properties of oil flowing in pipe. Dimensions of pipe.
FIND: Pressure drop, flow work, temperature rise caused by flow work.
SCHEMATIC:
L = 100 km
Oil
.
m = 500 kg/s
= 900 kg/m3
cp = 2000 J/kgK
= 0.765
D = 1.2 m
Ns/m2
AS
PROBLEM 8.8
KNOWN: Velocity and temperature profiles for laminar flow in a parallel plate channel.
FIND: Mean velocity, um, and mean (or bulk) temperature, Tm, at this axial position. Plot the velocity
and temperature distributions. Comment on whether val
PROBLEM 8.6
KNOWN: Water, engine oil and NaK flowing in a 20 mm diameter tube, temperature of the
fluids.
FIND: (a) The mean velocity as well as hydrodynamic and thermal entrance lengths, for a flow
rate of 0.01 kg/s and mean temperature of 366 K, (b) The
PROBLEM 8.7
KNOWN: Velocity and temperature profiles for laminar flow in a tube of radius ro = 10 mm.
FIND: Mean (or bulk) temperature, Tm, at this axial position.
SCHEMATIC:
ASSUMPTIONS: (1) Laminar incompressible flow, (2) Constant properties.
ANALYSIS:
PROBLEM 8.5
KNOWN: The x-momentum equation for fully developed laminar flow in a parallel-plate channel
dp
d 2u
= constant = 2
dx
dy
FIND: Following the same approach as for the circular tube in Section 8.1: (a) Show that the velocity
profile, u(y), is pa
PROBLEM 8.4
KNOWN: Number, diameter and length of tubes and flow rate for an engine oil cooler.
FIND: Pressure drop and pump power (a) for flow rate of 24 kg/s and (b) as a function of flow rate for
&
the range 10 m 30 kg/s.
SCHEMATIC:
ASSUMPTIONS: (1) Fu
PROBLEM 8.3
KNOWN: Temperature and velocity of water flow in a pipe of prescribed dimensions.
FIND: Pressure drop and pump power requirement for (a) a smooth pipe, (b) a cast iron pipe with a clean
surface, and (c) smooth pipe for a range of mean velociti
PROBLEM 8.2
KNOWN: Temperature and mean velocity of water flow through a cast iron pipe of
prescribed length and diameter.
FIND: Pressure drop.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Fully developed flow, (3) Constant
properties.
3
-6
2
PROBLEM 8.1
KNOWN: Flowrate and temperature of water in fully developed flow through a tube of
prescribed diameter.
FIND: Maximum velocity and pressure gradient.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Isothermal flow, (3) Horizontal tube
PROBLEM 5.1
KNOWN: Electrical heater attached to backside of plate while front surface is exposed to
convection process (T,h); initially plate is at a uniform temperature of the ambient air and
suddenly heater power is switched on providing a constant q .
PROBLEM 5.4
KNOWN: Plate initially at a uniform temperature Ti is suddenly subjected to convection
process (T,h) on both surfaces. After elapsed time to, plate is insulated on both surfaces.
FIND: (a) Assuming Bi > 1, sketch on T - x coordinates: initial
PROBLEM 5.3
KNOWN: Microwave and radiant heating conditions for a slab of beef.
FIND: Sketch temperature distributions at specific times during heating and cooling.
SCHEMATIC:
ASSUMPTIONS: (1) One-dimensional conduction in x, (2) Uniform internal heat
gen
PROBLEM 5.2
KNOWN: Plane wall whose inner surface is insulated and outer surface is exposed to an
airstream at T. Initially, the wall is at a uniform temperature equal to that of the airstream.
Suddenly, a radiant source is switched on applying a uniform
PROBLEM 5.5
KNOWN: Geometries of various objects. Material and/or properties. Cases (a) through (d):
Convection heat transfer coefficient between object and surrounding fluid. Case (e): Emissivity of
sphere, initial temperature, and temperature of surroun
PROBLEM 5.7
KNOWN: Diameter and initial temperature of steel balls in air. Expression for the air
temperature versus time.
FIND: (a) Expression for the sphere temperature, T(t), (b) Graph of T(t) and explanation of
special features.
SCHEMATIC:
D = 0.012 m
PROBLEM 5.6
KNOWN: Diameter and initial temperature of steel balls cooling in air.
FIND: Time required to cool to a prescribed temperature.
SCHEMATIC:
ASSUMPTIONS: (1) Negligible radiation effects, (2) Constant properties.
ANALYSIS: Applying Eq. 5.10 to a