try to change the pictures and add more

pictures about Electric water heater. Also, paraphrase and rewrite the file and

make it good. if you can change the design of the equation change it please ,

but do not change the same equation. Also , organize the report if you finish and make it good for the final project. in general do not change the meaning. important

things:####do

not change the equations , graphs, tables, appendix, and any thing relate to

the solution of software ###Purpose:

The purpose of this project is choosing an item that is familiar to you and which interacts with its

environment via heat transfer. The temperature of the item should very significantly with time, in

space, or both. Perform a heat transfer analysis of this item to model its temperature change with

time and/or variation in space.

Objectives:

I selected Hot Water Heater for the design. The design include the important calculations used in

the analysis, including assumptions, governing equations, and boundary conditions. The main

purposes for our design see the relationship between the temperature and time.

The part of Work:

•

Introduction:

The hot water heater is a device to change the temperature from lower to higher .this process

called thermodynamic process by using a heating source. The water entered from outside by

initial temperature, the heater change the temperature until which we need to using. The figure

below showing the process more clearly.

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The analysis in general:

The first step I did the One-Dimensional Steady-State for our design to get the thermal

resistances of represented the design. The shape for the design like a cylinder.

I used at the first the governing equations:

0

0

̇ + ̇ = ̇ + ̇

̇ = ̇ +

̇

0

2 ̇ 2

̇ = ̇ + + 2

2!

0=

[−

]

0=

[− (2 )

]

0=

[

]

+⋯

Integrating the differential equation:

= 1

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Dividing both sides of the equation above by D:

1

=

Integrating the differential equation again to get 2 :

( ) = 1 ln + 2 …..(1)

Applying the boundary conditions:

Where

( ) =

( ) =

= 1 ln + 2

…..(2)

= 1 ln + 2

……(3)

By subtracts between eq (2) and (3):

− = 1 ln − 1 ln + 2 − 2

( − ) = 1 ln

1 =

( − )

ln

Put the value of 1 in eq (3) to get the 2 :

=

( − )

ln + 2

ln

2 = −

( − )

ln

ln

Substituting the value of 1 and 2 in equation (1):

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( ) =

( − )

( − )

ln + −

ln

ln

ln

By arrangement the equation we will get:

( ) = + ( − )

ln

ln

After that we can get the value of ̇ :

̇ = − (2 )

So,

1

=

( − ) 1

=

∗

ln

̇ = − (2 )

̇ =

( − )

ln

1

∗

2

( − )

ln

Now we can get the thermal resistances:

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̇ =

∆

From the last steps to get the thermal resistances, we can get thermal resistance for many cases:

,

ln

=

2

ln

, =

+ 2 ℎ

2

, =

1

ℎ̅

, =

1

ℎ̅ ( + 2 ℎ )

= ( 2 + 2 )(

∞

1

+ ∞ )( +2 ℎ )

where, ℎ̅ = ( 2 + ∞2 )( + ∞ )

The analysis for the assumption design:

I got from the website the assumption hot water heater which I will do the analysis for it.the hot

water heater which I choice is Whirlpool. It has 50 (gallons) capacity of tank and 4500W of

Wattage (the reference below showing all the specifications of hot water heater which I choice.

However, I will calculate the heat loss from the hot water heater.

NOW,

Analysis the assumption design:

Applying the boundary conditions and the governing equations for the assumption design:

The energy balance:

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̇ + ̇ = ̇ + ̇

̇ + ̇ = ̇ + ̇ +

Which;

̇ = ℎ̅ ( − ∞ )

=

That leads:

̇ + ̇ = ̇ + ℎ̅ ( − ∞ ) +

=

̇

( − ) +

̇

−

̅

ℎ

( − ∞ ) ….(4)

The heat transient in our design:

In our case of transieat ( non-steady) model.The temperatur varies with time.So,we will see that

in our assumption design. I will apply the equation (4) in EES with the specifications for the hot

water heater. For our design I used Heun’s Method. So, the relationship between Euler’s Method

and Heun’s Method, the Euler’s Method is the simplest example of a numerical integration

technique; it is a first order explicit technique. The Heun’s Method is a second order explicit

technique (but with the same stability characteristics as Euler’s method).

EES programmed:

“Inputs”

D=0.6096[m]

“The diameter of the hot water heater”

H=1.27[m]

“The height of the hot water heater”

r=D/2

“The radius of the hot water heater”

L_ins=0.0762[m]

“The thickness of insulation”

q_dot_coil=4500[w]

“The Wattage of the coil”

M_total=50*convert(gal,m^3)*rho “The Tank Capacity ”

A_s=pi*(D^2/4)*rho

“The Area”

m_dot=5*convert(L/min,m^3/s)

“guess mass flow rate”

T_s=converttemp(C,K,30)

“guess surface temperature”

T_inf=converttemp(C,K,25)

“guess ambient air temperature”

T_ini=converttemp(C,K,10)

“guess initial temperature”

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T_out=converttemp(C,K,47)

T_film=(T_s+T_inf)/2

“guess the out temperature from the hot water heater”

“film temperature”

The properties of air (ρ, k, μ, cp and β) are obtained using EES:

“Water properties”

P=1*convert(atm,kpa)

rho=Density(Water,T=T_film,P=P)

k=Conductivity(Water,T=T_film,P=P)

mu=Viscosity(Water,T=T_film,P=P)

cp=SpecHeat(Water,T=T_film,P=P)

beta=VolExpCoef(Water,T=T_film,P=P)

“guess pressure”

“density”

“conductivity of material”

“viscosity”

“specific heat capacity”

“volumetric thermal expansion coefficient”

The thermal diffusivity, kinematic viscosity and Prandtl number are computed:

=

=

=

nu=mu/rho

alpha=k/(rho*cp)

Pr=nu/alpha

“kinematic viscosity”

“thermal diffusivity”

“Prandtl number”

The Reynolds number and Nusselt number are computed:

3 ( − ∞ )

=

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̅̅̅̅

=

ℎ̅

Ra=g#*L_ins^3*beta*(T_s-T_inf)/(nu*alpha) “Reynolds number”

h_eff=3.259 [W/m^2-k]

“heat transfer coefficient”

Nusselt=h_eff*H/k

“Nusselt number”

“Heun’s Method”

T[1]=T_out

DELTAt=1

“number of time steps”

duplicatej=1,360

“The time step duration (it considered the time which we used the water for shower

about (6 min)”

time[j]=j-1

dTdt[j]=((m_dot/M_total)*(T_ini-T[j]))+(q_dot_coil/(M_total*cp))-(((h_eff*A_s)/(M_total*cp))*(T[j]-T_inf))

T_hat[j]=T[j]+dTdt[j]*DELTAt;

dTdt_hat[j]=((m_dot/M_total)*(T_ini-T_hat[j]))+(q_dot_coil/(M_total*cp))-(((h_eff*A_s)/(M_total*cp))*(T_hat[j]-T_inf))

T[j+1]=T[j]+(dTdt[j]+dTdt_hat[j])*DELTAt/2;

end

And clicks solve at the top;

Table below will show the relationship between the temperature and time in our design:

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Plot the graph that showing the relationship between the temperature and time in our design:

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It can be clearly seen that from previously table and graph. The temperature which is started

from 47℃ (320.2 K) decreased slowly by the time about 6 minutes (around shower time) until

reached around 40.95℃ (314.1 K) with mass flow rate around 5 L/min in our design.

The second step:

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We will consider the mass flow rate which we used for previously step equal zero in the principle

equation and see what will happened for the temperature with time in this case. We will use EES

for analysis the design.

0

=

̇

( − ) +

̇

−

̅

ℎ

( − ∞ ) ….(4)

EES programmed:

“Inputs”

D=0.6096[m]

“The diameter of the hot water heater”

H=1.27[m]

“The height of the hot water heater”

r=D/2

“The radius of the hot water heater”

L_ins=0.0762[m]

“The thickness of insulation”

q_dot_coil=4500[w]

“The Wattage of the coil”

M_total=50*convert(gal,m^3)*rho ” The Tank Capacity ”

A_s=pi*(D^2/4)*rho

“The Area”

m_dot=5*convert(L/min,m^3/s)

“guess mass flow rate”

T_s=converttemp(C,K,30)

“guess surface temperature”

T_inf=converttemp(C,K,25)

“guess ambient air temperature”

T_ini=converttemp(C,K,10)

“guess initial temperature”

T_out=converttemp(C,K,47)

“guess the out temperature from the hot water heater”

T_film=(T_s+T_inf)/2

“film temperature”

P=1*convert(atm,kpa)

rho=Density(Water,T=T_film,P=P)

“density”

k=Conductivity(Water,T=T_film,P=P)

“conductivity of material”

mu=Viscosity(Water,T=T_film,P=P)

“viscosity”

cp=SpecHeat(Water,T=T_film,P=P)

“specific heat capacity”

beta=VolExpCoef(Water,T=T_film,P=P)

“volumetric thermal expansion coefficient”

nu=mu/rho

“kinematic viscosity”

alpha=k/(rho*cp)

“thermal diffusivity”

Pr=nu/alpha

“Prandtl number”

Ra=g#*L_ins^3*beta*(T_s-T_inf)/(nu*alpha) “Reynolds number”

h_eff=3.259 [W/m^2-k]

“heat transfer coefficient”

Nusselt=h_eff*H/k

“Nusselt number”

T[1]=T_out

DELTAt=1

“Heun’s Method”

duplicate j=1,360

time[j]=j-1

dTdt[j]=((0)*(T_ini-T[j]))+(q_dot_coil/(M_total*cp))-(((h_eff*A_s)/(M_total*cp))*(T[j]-T_inf))

T_hat[j]=T[j]+dTdt[j]*DELTAt;

dTdt_hat[j]=((0)*(T_ini-T_hat[j]))+(q_dot_coil/(M_total*cp))-(((h_eff*A_s)/(M_total*cp))*(T_hat[j]-T_inf))

T[j+1]=T[j]+(dTdt[j]+dTdt_hat[j])*DELTAt/2;

end

And clicks solve at the top;

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Table below will show the relationship between the temperature and time in our design:

Plot the graph that showing the relationship between the temperature and time in this case:

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It can be clearly seen that from previously table and graph. The temperature which is started

from 47℃ (320.2 K) increased very fast by the time about 6 minutes until reached around (6474

K) without mass flow rate in the equation that means there is an imbalance in the equation in this

case.

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Conclusion:

In this project, I choice the hot water heater as a design for the project. The hot water as the

cylinder in the shape so, I used the general equations for the cylinder to get the boundary condition

by using the governing equations. I chose randomly for the hot water heater from the website to

more realistic in our results (see appendix below for the specifications for hot water heater). The

main ideas for our design see the relationship between the temperature and time what will happen

for them. We selected time for using the hot water heater such as the take shower. As normal for

the person to take shower, the person need for 6 minutes. We see after applied the test for the

design the temperature decreased very slowly by the time which is the temperature loss ( 1 K )

after 5 sec with considering we used 5 L/min .Finally, in the second previously step, we get the

impossible results because the temperatures go very fast increased and we get a high temperature.

Appendix:

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Purchase answer to see full

attachment