Question

Performance evaluation of cold tube heat exchanger for various L/D ratio and mass flow rate.   using Ansys show the temperature distribution.   and make a mathematical model in scilab and perform simulation in fortran 77...

Answer 1

"!This program demonstrates the use of the Integral functions to solve second order equations. "

"Here EES is used to calculate the velocity and position of a freely falling sphere, subject to aerodynamic drag. The unit system is set to English. The graph is set to automatic update - change v_o to -50 to see the impact of an initial upward velocity.

Note how the Integral function displays on the Formatted Equations Window."

D=0.25 [ft]
m=1.0 [lb_m]    "mass of sphere"
v_o=0 [ft/s]    "initial velocity."
z_o=0 [ft]     "initial position"
time=5 [s]   "time period for analysis"
g=32.17 [ft/s^2]    "gravitational acceleration"

F=m*g*Convert(lbm-ft/s^2,lbf)         "Newton's Law"
m*a*Convert(lbm-ft/s^2,lbf)=F-F_d        "force balance"
Area=pi*D^2/4           "frontal area of sphere"
F_d=Area*C_d*(1/2*rho*v^2)*Convert(lbm-ft/s^2,lbf)    "definition of drag coefficient"

"Find Reynolds number"
mu=viscosity(air, T=70)*Convert(1/hr,1/s)
rho=density(Air,T=70,P=14.7)
Re=rho*abs(v)*D/mu

"Find drag coefficient from the Reynolds number. The Lookup table contains ln(Re) and ln(C_d). The max function is used to prevent attempting to find the log of zero (i.e., when the velocity is zero use a small value of Re)"
C_d=exp(interpolate1( 'LnRe', 'LnCd', LnRe=Ln(max(.01, Re))))

"As a test of the need for tthe variable drag coefficient, set C_d to a constant value, say C_d=0.4. Turn off automatic update on the plots (click on the plot window) and overlay the new plots, using the left scale."
{C_d=0.4}

"Use EES integral function to determine velocity and position given the acceleration."
v=v_o+integral(a,t,0,time)   "velocity after 5 seconds"
z=z_o+integral(v,t,0,time)   "vertical position after 5 seconds"

"The following directive instructs EES to store values of v (velocity), z (elevation) and C_d (drag coefficient) as a function of t (time) at increments of 0.2 sec.
"
$integraltable t:0.2, v,z, C_d
$tabstops 1 in

"This equation set uses EES to calculate the heat transfer between air and a flat plate. The heat transfer coefficient is calculated using convection formulae which rely on transport properties. The Prandtl number obtained with a built-in function."

{This problem illustrates

1. Use of EES built-in transport properties.
2. Use of user-written functions.
3. Use of the built-in function, UnitSystem.
4. Formatting options such as greek letters, T_s and T_infinity.

Select Solve from the Calculate menu (or press F2) to obtain the results.}

"!Known conditions"
Fluid$='Air'               {Any EES ideal gas name can be used here}
Q=h*L*(T_infinity-T_s)        "[W/m] heat transfer rate per unit width"
L=0.5 [m]                "Length of plate in flow direction"
T_infinity=300   [°C]             "Air temperature - note Formatted Equation Window"
T_s=27 [°C]                 "Plate surface temperature"
T_film=(T_infinity+T_s)/2       "Film temperature for evaluating properties"
Vel=10 [m/s]                "air velocity"

"!Properties"
rho=1/volume(Fluid$,T=T_film,P=100)    {Air density - could use density function}
k=conductivity(Fluid$,T=T_film)
mu=viscosity(Fluid$,T=T_film)
Pr=Prandtl(Fluid$,T=T_film)  

"!Convection correlation for laminar flow"
Re=(rho*Vel*L)/mu           {Reynold's number}
Nu#=0.664*Re^0.5*Pr^0.333       {The # sign prevents Nu greek.}
Nu#=(h*L)/k

$TabWidth 1 cm