Universidad Nacional Autónoma de México
Dirección General de Cómputo y de Tecnologías de Información y Comunicación
Trabajo realizado con el apoyo del Programa UNAM-DGAPA-PAPIME PE110517

Asignatura de Transporte de Energía
Paredes compuestas: Rectangulares y Cilíndricas

txt1="Problema";
txt2="Se desea estudiar la transferencia de calor a través de una sucesión de capas de diferentes materiales, cuyas fronteras están en contacto con un fluido.

 Se quiere hacerlo en dos geometrías:

a) Cartesiana (paredes rectangulares)

b) Cilíndrica";
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,FrameMargins->Large,Background->RGBColor["#1c3d6d"]]

txt3="
* Objetivos

* PAREDES COMPUESTAS RECTANGULARES

* PAREDES COMPUESTAS CILÍNDRICAS

* DIFERENCIAS Y SEMEJANZAS ENTRE EL 
  CASO DE GEOMETRÍA CARTESIANA Y EL DE GEOMETRÍA CILÍNDRICA.

* RESISTENCIA DE CONTACTO

* EJEMPLOS

";

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]}],RoundingRadius->5,FrameMargins->Large]

txt4="
* Conocer las ecuaciones para el cálculo de transferencia de calor a 
  través de paredes compuestas en coordenadas rectangulares y 
  cilíndricas

* Utilizar dichas ecuaciones para resolver problemas  en coordenadas 
  rectangulares y cilíndricas.

* Comprender el efecto de la geometría en el proceso de conducción del 
  calor en paredes paralelas.

* Poder sugerir mecanismos de ahorro de energía con base en cálculos 
  de transferencia de energía a través de paredes compuestas.



";




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img1=;
txt29=Style["Paredes compuestas rectangulares",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt5=Style["
Conducción de calor a través de 
una pared compuesta situada entre 
dos corrientes de fluido a temperaturas 
Ta y Tb",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt6=Style["Pasos para conocer el perfil de temperatura y el flujo de calor",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt7=Style["
*Balance
*Ecuacion Diferencial para q y condiciones a la frontera
*Integracion para q
*Ecuacion de Fourier
*Integracion para T
*Perfil de Temperaturas 
*Calculo de flujo de calor en la superficie",FontColor->RGBColor["#1C3D6C"],FontFamily->"Times New Roman",16];

txt8=Style["Balance de energia",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt9=Style["Aplicado un balance a la lámina de volumen WHdx, se obtiene, para la conducción del calor en la primera región: 
 
(Subscript[q, x01])(Subscript[|, x])WH - (Subscript[q, x01])(Subscript[|, x + ΔX])WH=0
 
Que lleva a:
\!\(\*FractionBox[\(\(\\n\)\*SubscriptBox[\(dqx\), \(01\)]\), \(dx\)]\)=0

Integrando

(Subscript[q, 01])=(Subscript[q, 0])

abemos tambien que

(Subscript[q, x01])=-(Subscript[k, 01])((Subscript[dT, 01])/dx)=(Subscript[q, 0]) ",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]
];
txt10=Style["Analogamente",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt11=Style["
(Subscript[k, 01])((Subscript[dT, 01])/dx)=(Subscript[q, 0])
(Subscript[k, 12])((Subscript[dT, 12])/dx)=(Subscript[q, 0])
(Subscript[k, 23])((Subscript[dT, 23])/dx)=(Subscript[q, 0])
Siendo
(Subscript[k, 01]), -(Subscript[k, 12]) y -(Subscript[k, 23])  constantes",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];

txt12=Style["Integrando",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]] ;
txt13=Style["
(Subscript[T, 0])-(Subscript[T, 1])=-(Subscript[q, 0])((((Subscript[x, 0]) - (Subscript[x, 1]))/(Subscript[k, 01])))

(Subscript[T, 1])-(Subscript[T, 2])=-(Subscript[q, 0])((((Subscript[x, 1]) - (Subscript[x, 2]))/(Subscript[k, 12])))

(Subscript[T, 2])-(Subscript[T, 3])=-(Subscript[q, 0])((((Subscript[x, 2]) - (Subscript[x, 3]))/(Subscript[k, 23])))

En las fronteras

(Subscript[T, a])-(Subscript[T, 0])=(((Subscript[q, 0])/(Subscript[h, 0])))

(Subscript[T, 3])-(Subscript[T, b])=(((Subscript[q, 0])/(Subscript[h, 3])))",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt14=Style["Sumando las ecuaciones",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt15=Style["

(Subscript[T, a])-(Subscript[T, b])=-(Subscript[q, 0])((1/(Subscript[h, 0]))+(((Subscript[x, 1]) - (Subscript[x, 0]))/(Subscript[k, 01]))+(((Subscript[x, 2]) - (Subscript[x, 1]))/(Subscript[k, 12]))+(((Subscript[x, 3]) - (Subscript[x, 2]))/(Subscript[k, 23]))+(1/(Subscript[h, 3])))


(Subscript[q, 0])=(((Subscript[T, a]) - (Subscript[T, b]))/((1/(Subscript[h, 0])) + (∑_(i = 1)^3)(((Subscript[x, i]) - (Subscript[x, i - 1]))/(Subscript[k, i - 1, i])) + (1/h3)))

",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt16=Style["Que puede escribirse",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt17=Style["
(Subscript[q, 0])=U((Subscript[T, a])-(Subscript[T, b]))

(Subscript[Q, 0])=U(WH)((Subscript[T, a])-(Subscript[T, b]))

En las fronteras

U=((1/(Subscript[h, 0]))+(∑_(i = 1)^3)(((Subscript[x, i]) - (Subscript[x, i - 1]))/(Subscript[k, i - 1, i]))+(1/h3))^(-1)
",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]
];

txt18=Style["Comentarios",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt19=Style["Perfil de temperatura",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt20=Style["Es la ecuación que da la relación de la temperatura con la posición:
(Subscript[T, 0])-(Subscript[T, 1])=-(Subscript[q, 0])((((Subscript[x, 0]) - (Subscript[x, 1]))/(Subscript[k, 01])))

(Subscript[T, 1])-(Subscript[T, 2])=-(Subscript[q, 0])((((Subscript[x, 1]) - (Subscript[x, 2]))/(Subscript[k, 12])))

(Subscript[T, 2])-(Subscript[T, 3])=-(Subscript[q, 0])((((Subscript[x, 2]) - (Subscript[x, 3]))/(Subscript[k, 23])))
Es diferente en cada capa pero el flux es siempre el mismo",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt21=Style["Para cualquier punto entre (Subscript[X, 0]) y \!(Subscript[X, 1])",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt22=Style["
(Subscript[T, 0])-(Subscript[T, 1])=-(Subscript[q, 0])((((Subscript[x, 0]) - (Subscript[x, 1]))/(Subscript[k, 01])))

T=(Subscript[T, 0])-(((Subscript[q, 0]) (Subscript[x, 0]))/(Subscript[k, 01]))-((Subscript[q, 0])/(Subscript[k, 01]))x

T=-((Subscript[q, 0])/(Subscript[k, 01]))x+(((Subscript[k, 01]) (Subscript[T, 0]) + (Subscript[q, 0]) (Subscript[x, 0]))/(Subscript[k, 01]))


",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt23=Style["Interpretacion",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
img2=;
txt24=Style["
*Pendiente \!\(\*StyleBox[\"–\",FontSize->16]\)(Subscript[q, 0])\!\(\*StyleBox[\"/\",FontSize->16]\)(Subscript[k, 01])
* Ordenada al origen ((Subscript[k, 01]) (Subscript[T, 0]) + (Subscript[q, 0]) (Subscript[x, 0]))/(Subscript[k, 01])
*Para poderlo calcular es necesario antes conocer (Subscript[q, 0])
*En cada capa es una recta diferente.",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]]; 
txt25=Style["Flux",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt26=Style["
Es el mismo a través de todos los materiales

-(Subscript[k, 01])((Subscript[dT, 01])/dx)=(Subscript[q, 0])
-(Subscript[k, 12])((Subscript[dT, 12])/dx)=(Subscript[q, 0])

-(Subscript[k, 23])((Subscript[dT, 23])/dx)=(Subscript[q, 0])
Se calcula a partir de la suma:
(Subscript[q, 0])=(((Subscript[T, a]) - (Subscript[T, b]))/((1/(Subscript[h, 0])) + (∑_(i = 1)^3)(((Subscript[x, i]) - (Subscript[x, i - 1]))/(Subscript[k, i - 1, i])) + (1/h3)))
Siendo (Subscript[k, 01]), (Subscript[k, 12]) y (Subscript[k, 23]) constantes



",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];

txt27=Style["Mas Comentarios",FontFamily->"Times New Roman",24,FontColor->Darker[Gray]];
txt28=Style["Estas mismas ecuaciones pueden usarse para el caso límite de una sola capa de material a través de la cual ocurre la conducción, haciendo i =1

Un ejemplo interesante de la aplicación del cálculo del perfil de temperaturas es el estudio del flux que emite una aleta.  Ese análisis se presenta como tema suplementario en los recursos de esta semana.  
",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
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Op1=OpenerView[{txt18,Grid[{{txt19},{txt20},{txt21},{txt22},{txt23},{img2},{txt24},{txt25},{txt26}},Alignment->Left]}];
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txt29=Style["Actividades",FontFamily->"Times New Roman",24,FontColor->White];
txt30=Style["Usando el simulador resolver:
Un cuarto de almacenamiento refrigerado se construye con una plancha interna de 12 mm de pino, una plancha intermedia de 100 mm de corcho prensado y una plancha externa de 76  mm de concreto. La temperatura superficial de la pared interna es de 255 K y la exterior del concreto es de 297 K.
a)    Calculen la pérdida de calor en W para 1 m^2, así como la temperatura en la interfaz de la madera y el corcho. Los valores de conductividad, en unidades del SI, son de 0.151 para el pino; 0.0433 para el corcho prensado y 0.762 para el concreto. Consideren que no existe convección en las fronteras.

b)    Realicen un esquema que describa la situación
c)     Dibujen los perfiles de temperaturas

Usar el simulador para resolver el siguiente ejercicio:
Una casa tiene una pared compuesta de interior a exterior por 3 tres cm de aislante (k=0.045 W/mK), 10 cm de fibra de vidrio (k=0.082 W/mK) y 2 cm de yeso (k=0.17 W/mK). En los días fríos la temperatura del interior excede a la del exterior en 15° ¿Cuánto calor se pierde a lo largo de una pared de 5cm de ancho por cuatro metros de alto? Determina la caída de temperatura de cada pared y grafiquen su perfil.

",FontFamily->"Times New Roman",16,FontColor->White];
Framed[OpenerView[{Style[txt29,FontFamily->"Times New Roman",FontColor->Darker[Gray],24

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txt31="Paredes Compuestas Circulares";
img3=;
img4=;
img5=;

txt32="Balance de energia";
txt33=Style["Aplicando un balance a la seccion de volumen 2πrLΔr, se obtiene, para la conduccion del calor en la primera region:

(Subscript[q, r])(Subscript[\[VerticalSeparator], r])2πrL-(Subscript[q, r])(Subscript[\[VerticalSeparator], r + Δr])2π(r+Δr)L=0
Lo que lleva a 

(\[DifferentialD]/(\[DifferentialD]r))((Subscript[rq, r]))=0

Integrando se obtiene:
(Subscript[rq, r])=(Subscript[r, 0])\!\(\*SubscriptBox[\(q\), \(\(0\)\(\\n\)\)]\) 
y sabemos que tambien:

-(Subscript[K, 01])r(\[DifferentialD]/(\[DifferentialD]r))((Subscript[T, 01]))=(Subscript[r, 0])(Subscript[q, 0])

Analogamente:

-(Subscript[K, 12])r(\[DifferentialD]/(\[DifferentialD]r))((Subscript[T, 12]))=(Subscript[r, 0])\!\(\*SubscriptBox[\(q\), \(\(0\)\(\\n\)\(\\n\)\)]\)
y 
-(Subscript[K, 23])r(\[DifferentialD]/(\[DifferentialD]r))((Subscript[T, 23]))=(Subscript[r, 0])\!\(\*SubscriptBox[\(q\), \(\(0\)\(\\n\)\(\\n\)\)]\)
Integrando:
(Subscript[T, 0])-(Subscript[T, 1])=(Subscript[r, 0])(Subscript[q, 0])((Ln (((Subscript[r, 1])/(Subscript[r, 0]))))/(Subscript[K, 01]))

(Subscript[T, 1])-(Subscript[T, 2])=(Subscript[r, 0])(Subscript[q, 0])((Ln (((Subscript[r, 2])/(Subscript[r, 1]))))/(Subscript[K, 12]))

(Subscript[T, 2])-(Subscript[T, 3])=(Subscript[r, 0])(Subscript[q, 0])((Ln (((Subscript[r, 3])/(Subscript[r, 2]))))/(Subscript[K, 23]))
En las fronteras:

(Subscript[T, a])-(Subscript[T, 0])=(((Subscript[q, 0])/(Subscript[h, 0])))
(Subscript[T, 3])-(Subscript[T, b])=(((Subscript[q, 0])/(Subscript[h, 3])))=((Subscript[q, 0])/(Subscript[h, 3]))(((Subscript[r, 0])/(Subscript[r, 3])))

(Subscript[q, r])=cte

(Subscript[q, 0])(Subscript[r, 0])=(Subscript[q, 3])\!\(\*SubscriptBox[\(r\), \(\(3\)\(\\n\)\(\\n\)\)]\)

",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt34="Flujo total (Subscript[Q, 0])";
txt35=Style["(Subscript[Q, 0])=2(Subscript[πLr, 0])(Subscript[q, 0])=((2  πL ((Subscript[T, a]) - (Subscript[T, b])))/((1/((Subscript[r, 0]) (Subscript[h, 0]))) + ((ln ((Subscript[r, 1])/(Subscript[r, 0])))/(Subscript[k, 01])) + ((ln ((Subscript[r, 2])/(Subscript[r, 1])))/(Subscript[k, 12])) + ((ln ((Subscript[r, 3])/(Subscript[r, 2])))/(Subscript[k, 23])) + (1/((Subscript[r, 3]) (Subscript[h, 3])))))
comentario: Aplica la analogia con las resistencias electricas. Hay una reistencia equivalente o total que se calcula como suma de las resistencias individuales


",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt36="Sumando";
txt37=Style["(Subscript[Q, 0])=(Subscript[U, 0])(2(Subscript[πr, 0])L)((Subscript[T, a])-(Subscript[T, b]))


U=((Subscript[r, 0])^(-1))((1/((Subscript[r, 0]) (Subscript[h, 0])))+(∑_(i = 1)^3)((ln ((Subscript[r, i])/(Subscript[r, i - 1])))/(Subscript[k, i - 1, i]))+(1/((Subscript[r, 3]) h3)))^(-1)
",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
txt38="Perfil de temperaturas en coordenadas cilindricas";
txt39=Style["
(Subscript[T, 0])-(Subscript[T, 1])=(Subscript[r, 0])(Subscript[q, 0])(((ln ((Subscript[r, 1])/(Subscript[r, 0])))/(Subscript[k, 01])))
lleva a:
 T-(Subscript[T, 0])=-(Subscript[r, 0])(Subscript[q, 0 (])((Ln ((r/(Subscript[r, 0]))))/(Subscript[K, 01])))
",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];

grid1=Grid[
{
(*Primera fila*)
{
(*Primera columna*)
Text[Style["Balance macro",White]],
(*Segunda columna*)
Grid[{{"Cartesiana"},{"Cilindrica"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#30859d"]}}}],
(*Tercera columna*)Grid[{{"(Subscript[q, x01])(Subscript[|, x])WH - (Subscript[q, x01])(Subscript[|, x + ΔX])WH=0"},{"\!\(TraditionalForm\`\*SubscriptBox[\(q\), \(r\)]\*SubscriptBox[\(|\), \(r\)]2  π\\ rL\\  - \\ \*SubscriptBox[\(q\), \(r\)]\*SubscriptBox[\(|\), \(r + Δr\)]2 \( π(r + Δr)\) L = 0\)"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#ced5e4"]}}}]},


(*Segunda fila*)
{
(*Primera columna*)
Text[Style["Balance diferencial",White]],
(*Segunda columna*)
Grid[{{"Cartesiana"},{"Cilindrica"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#30859d"]}}}],
(*Tercera columna*)Grid[{{"\!\(\*FractionBox[\(\(d\)\(\\ \)\), \(dx\)]\)((Subscript[qx, 01]))=0"},{"\!\(TraditionalForm\`\*FractionBox[\(d\), \(dr\)] \((r\\ \*SubscriptBox[\(q\), \(r\)])\) = 0\)"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#ced5e4"]}}}]},
(*Tercera fila*)
{
(*Primera columna*)
Text[Style["Integracion",White]],
(*Segunda columna*)
Grid[{{"Cartesiana"},{"Cilindrica"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#30859d"]}}}],
(*Tercera columna*)Grid[{{"(Subscript[q, 01])=(Subscript[q, 0])"},{"\!\(TraditionalForm\`r\\ \*SubscriptBox[\(q\), \(r\)] = \*SubscriptBox[\(r\), \(0\)] \*SubscriptBox[\(q\), \(0\)]\)"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#ced5e4"]}}}]},

(*Cuarta fila*)
{
(*Primera columna*)
Text[Style["Ecuacion",White]],
(*Segunda columna*)
Grid[{{"Cartesiana"},{"Cilindrica"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#30859d"]}}}],
(*Tercera columna*)Grid[{{"(Subscript[q, x01])=-(Subscript[k, 01])((Subscript[dT, 01])/dx)"},{"-(Subscript[k, 01]) r ((Subscript[dT, 01])/dr) = (Subscript[r, 0]) (Subscript[q, 0])"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#ced5e4"]}}}]},

(*quinta fila*)
{
(*Primera columna*)
Text[Style["Solución",White]],
(*Segunda columna*)
Grid[{{"Cartesiana"},{"Cilindrica"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#30859d"]}}}],
(*Tercera columna*)Grid[{{"(Subscript[T, 0])-(Subscript[T, 1])=-(Subscript[q, 0])((((Subscript[x, 0]) - (Subscript[x, 1]))/(Subscript[k, 01])))"},{"(Subscript[T, 0])-(Subscript[T, 1])=-(Subscript[r, 0])(Subscript[q, 0])((ln ((Subscript[r, 1])/(Subscript[r, 0])))/(Subscript[k, 01]))"}},Background->{None,{{RGBColor["#93cddd"],RGBColor["#ced5e4"]}}}]}
},Background->{{RGBColor["#16365e"]},None}
];

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s1=Panel[Column[{
TextCell[Text[Style["  Conducción de calor a través de paredes compuestas: Cooerdenadas rectangulares  ",Bold,18]]],
A:=Manipulate[
h:=1/h0;
h1:=1/h3;
ka:=1/k1;
kb:=1/k2;
kc:=1/k3;
q0:=(Ta-Tb)/(h+(x1max/k1)+((x2max-x1max)/k2)+((x3max-x2max)/k3)+h1);
T0:=(-q0*h)+Ta;
Q0:=q0*A;

Initialization->{
T1[x1_]:=(-q0*x1*ka)+T0;
T2[x2_]:=(-q0*(x2-x1max)*kb)+T1[x1max];
T3[x3_]:=(-q0*(x3-x2max)*kc)+T2[x2max];
};

G1=Plot[ 
T1[x1],
{x1,x1min,x1max},
PlotRange->{{x1min, x3max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Green},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];

G2=Plot[ 
T2[x2],
{x2,x1max, x2max},
PlotRange->{{x1max, x3max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Orange},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G3=Plot[ 
T3[x3],
{x3,x2max,x3max},
PlotRange->{{x1max, x3max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Blue},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];

Switch[ctrl, 

1,
Show[G1,G2,G3],

2,
TextCell[
Row[{"Flux q, [W/m^2] ",ExpressionCell[Evaluate[
q0],

CellAutoOverwrite-> False,
CellFrame->True]}]],
3,
TextCell[
Row[{"Flujo Q, [W] ",ExpressionCell[Evaluate[
Q0],

CellAutoOverwrite-> False,
CellFrame->True]}]]


],

{{ctrl,1," "},{1-> "Perfil de Temperatura",2-> "Flux", 3->"Flujo"}},
{{k1,200,"Conductividad térmica de la pared 1, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k2,20,"Conductividad térmica de la pared 2, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k3,3.5,"Conductividad térmica de la pared 3, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{Ta,500,"Temperatura del fluido del extremo izquierdo Ta, K"},400,900,Appearance-> "Labeled"},
{{Tb,273,"Temperatura del fluido del extremo derecho Tb, K"},250,500,Appearance-> "Labeled"},
{{h0,100,"Coeficiente de trasnferencia de calor ha, W/((m^2)*K)"},0.1,300,Appearance-> "Labeled"},
{{h3,100,"Coeficiente de trasnferencia de calor hb, W/((m^2)*K)"},0.1,300,Appearance-> "Labeled"},
{{A,0.1,"Área, (m^2)"},0.01,1,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Distancia X [m]",
{{x1min,0,"x1 Mínimo"},0,0.05,Appearance-> "Labeled"},
{{x1max,0.075,"x1 Máximo = x2 Mínimo"},0.050001,0.10,Appearance-> "Labeled"},
{{x2max,0.125,"x2 Máximo = x3 Mínimo"},0.100001,0.15,Appearance-> "Labeled"},
{{x3max,0.175,"x3 Máximo"},0.150001,0.2,Appearance-> "Labeled"},


" "," ","                                                      Control del eje Temperatura [K]  ",
{{Tmin,200,"Mínimo"},0,700,Appearance-> "Labeled"},
{{Tmax,700,"Máximo"},600,800,Appearance-> "Labeled"},
AppearanceElements->"ResetButton"
];
B:=Manipulate[
h:=1/h0;
h1:=1/h3;
ka:=1/k1;
kb:=1/k2;
kc:=1/k3;
kd:=1/k4;
q0:=(Ta-Tb)/(h+(x1max/k1)+((x2max-x1max)/k2)+((x3max-x2max)/k3)+((x4max-x3max)/k4)+h1);
T0:=(-q0*h)+Ta;
Q0:=q0*A;

Initialization->{
T1[x1_]:=(-q0*x1*ka)+T0;
T2[x2_]:=(-q0*(x2-x1max)*kb)+T1[x1max];
T3[x3_]:=(-q0*(x3-x2max)*kc)+T2[x2max];
T4[x4_]:=(-q0*(x4-x3max)*kd)+T3[x3max];
};

G1=Plot[ 
T1[x1],
{x1,x1min,x1max},
PlotRange->{{x1min, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Green},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}


];
G2=Plot[ 
T2[x2],
{x2,x1max, x2max},
PlotRange->{{x1max, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Orange},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G3=Plot[ 
T3[x3],
{x3,x2max,x3max},
PlotRange->{{x1max, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Blue},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G4=Plot[ 
T4[x4],
{x4,x3max,x4max},
PlotRange->{{x1max, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Red},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
Switch[ctrl, 

1,
Show[G1,G2,G3,G4],

2,
TextCell[
Row[{"Flux q, [W/m^2] ",ExpressionCell[Evaluate[
q0],

CellAutoOverwrite-> False,
CellFrame->True]}]],
3,
TextCell[
Row[{"Flujo Q, [W] ",ExpressionCell[Evaluate[
Q0],

CellAutoOverwrite-> False,
CellFrame->True]}]]


],

{{ctrl,1," "},{1-> "Perfil de Temperatura",2-> "Flux", 3->"Flujo"}},
{{k1,200,"Conductividad térmica de la pared 1, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k2,20,"Conductividad térmica de la pared 2, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k3,3.5,"Conductividad térmica de la pared 3, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k4,0.5,"Conductividad térmica de la pared 4, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{Ta,500,"Temperatura del fluido del extremo izquierdo Ta, K"},400,900,Appearance-> "Labeled"},
{{Tb,273,"Temperatura del fluido del extremo derecho Tb, K"},250,500,Appearance-> "Labeled"},
{{h0,100,"Coeficiente de trasnferencia de calor ha, W/((m^2)*K)"},0.1,300,Appearance-> "Labeled"},
{{h3,100,"Coeficiente de trasnferencia de calor hb, W/((m^2)*K)"},0.1,300,Appearance-> "Labeled"},
{{A,0.1,"Área, (m^2)"},0.01,1,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Distancia X [m]",
{{x1min,0,"x1 Mínimo"},0,0.05,Appearance-> "Labeled"},
{{x1max,0.075,"x1 Máximo = x2 Mínimo"},0.050001,0.10,Appearance-> "Labeled"},
{{x2max,0.125,"x2 Máximo = x3 Mínimo"},0.100001,0.15,Appearance-> "Labeled"},
{{x3max,0.175,"x3 Máximo = x4 Mínimo" },0.150001,0.2,Appearance-> "Labeled"},
{{x4max,0.225,"x4 Máximo"},0.20001,0.25,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Temperatura [K]  ",
{{Tmin,200,"Mínimo"},0,700,Appearance-> "Labeled"},
{{Tmax,700,"Máximo"},600,800,Appearance-> "Labeled"},
AppearanceElements->"ResetButton"
];
C1a:=Manipulate[
h:=1/h0;
h1:=1/h3;
ka:=1/k1;
kb:=1/k2;
kc:=1/k3;
kd:=1/k4;
ke:=1/k5;
q0:=(Ta-Tb)/(h+(x1max/k1)+((x2max-x1max)/k2)+((x3max-x2max)/k3)+((x4max-x3max)/k4)+((x5max-x4max)/k5)+h1);
T0:=(-q0*h)+Ta;
Q0:=q0*A;

Initialization->{
T1[x1_]:=(-q0*x1*ka)+T0;
T2[x2_]:=(-q0*(x2-x1max)*kb)+T1[x1max];
T3[x3_]:=(-q0*(x3-x2max)*kc)+T2[x2max];
T4[x4_]:=(-q0*(x4-x3max)*kd)+T3[x3max];
T5[x5_]:=(-q0*(x5-x4max)*ke)+T4[x4max];
};

G1=Plot[ 
T1[x1],
{x1,x1min,x1max},
PlotRange->{{x1min, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Green},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}


];
G2=Plot[ 
T2[x2],
{x2,x1max, x2max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Orange},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G3=Plot[ 
T3[x3],
{x3,x2max,x3max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Blue},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G4=Plot[ 
T4[x4],
{x4,x3max,x4max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Red},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G5=Plot[ 
T5[x5],
{x5,x4max,x5max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Brown},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
Switch[ctrl, 

1,
Show[G1,G2,G3,G4,G5],

2,
TextCell[
Row[{"Flux q, [W/m^2] ",ExpressionCell[Evaluate[
q0],

CellAutoOverwrite-> False,
CellFrame->True]}]],
3,
TextCell[
Row[{"Flujo Q, [W] ",ExpressionCell[Evaluate[
Q0],

CellAutoOverwrite-> False,
CellFrame->True]}]]


],

{{ctrl,1," "},{1-> "Perfil de Temperatura",2-> "Flux", 3->"Flujo"}},
{{k1,200,"Conductividad térmica de la pared 1, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k2,20,"Conductividad térmica de la pared 2, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k3,3.5,"Conductividad térmica de la pared 3, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k4,0.5,"Conductividad térmica de la pared 4, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k5,0.05,"Conductividad térmica de la pared 5, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{Ta,500,"Temperatura del fluido del extremo izquierdo Ta, K"},400,900,Appearance-> "Labeled"},
{{Tb,273,"Temperatura del fluido del extremo derecho Tb, K"},250,500,Appearance-> "Labeled"},
{{h0,100,"Coeficiente de trasnferencia de calor ha, W/((m^2)*K)"},0.1,300,Appearance-> "Labeled"},
{{h3,100,"Coeficiente de trasnferencia de calor hb, W/((m^2)*K)"},0.1,300,Appearance-> "Labeled"},
{{A,0.1,"Área, (m^2)"},0.01,1,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Distancia X [m]",
{{x1min,0,"x1 Mínimo"},0,0.05,Appearance-> "Labeled"},
{{x1max,0.075,"x1 Máximo = x2 Mínimo"},0.05001,0.10,Appearance-> "Labeled"},
{{x2max,0.125,"x2 Máximo = x3 Mínimo"},0.10001,0.15,Appearance-> "Labeled"},
{{x3max,0.175,"x3 Máximo = x4 Mínimo" },0.15001,0.2,Appearance-> "Labeled"},
{{x4max,0.225,"x4 Máximo = x5 Mínimo"},0.20001,0.25,Appearance-> "Labeled"},
{{x5max,0.275,"x5 Máximo"},0.25001,0.3,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Temperatura [K]  ",
{{Tmin,200,"Mínimo"},0,700,Appearance-> "Labeled"},
{{Tmax,700,"Máximo"},600,800,Appearance-> "Labeled"},
AppearanceElements->"ResetButton"
];
H:=Manipulate[
ka:=1/k1;
kb:=1/k2;
kc:=1/k3;
q0:=(Ta-Tb)/((x1max/k1)+((x2max-x1max)/k2)+((x3max-x2max)/k3));

Q0:=q0*A;

Initialization->{
T1[x1_]:=(-q0*x1*ka)+Ta;
T2[x2_]:=(-q0*(x2-x1max)*kb)+T1[x1max];
T3[x3_]:=(-q0*(x3-x2max)*kc)+T2[x2max];
};

G1=Plot[ 
T1[x1],
{x1,x1min,x1max},
PlotRange->{{x1min, x3max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Blue},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}


];
G2=Plot[ 
T2[x2],
{x2,x1max, x2max},
PlotRange->{{x1max, x3max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Orange},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G3=Plot[ 
T3[x3],
{x3,x2max,x3max},
PlotRange->{{x1max, x3max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Green},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];

Switch[ctrl, 

1,
Show[G1,G2,G3],

2,
TextCell[
Row[{"Flux q, [W/m^2] ",ExpressionCell[Evaluate[
q0],

CellAutoOverwrite-> False,
CellFrame->True]}]],
3,
TextCell[
Row[{"Flujo Q, [W] ",ExpressionCell[Evaluate[
Q0],

CellAutoOverwrite-> False,
CellFrame->True]}]]


],

{{ctrl,1," "},{1-> "Perfil de Temperatura",2-> "Flux", 3->"Flujo"}},
{{k1,200,"Conductividad térmica de la pared 1, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k2,20,"Conductividad térmica de la pared 2, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k3,3.5,"Conductividad térmica de la pared 3, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{Ta,500,"Temperatura del fluido del extremo izquierdo Ta, K"},400,900,Appearance-> "Labeled"},
{{Tb,273,"Temperatura del fluido del extremo derecho Tb, K"},250,500,Appearance-> "Labeled"},
{{A,0.1,"Área, (m^2)"},0.01,1,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Distancia X [m]",
{{x1min,0,"x1 Mínimo"},0,0.05,Appearance-> "Labeled"},
{{x1max,0.075,"x1 Máximo = x2 Mínimo"},0.050001,0.10,Appearance-> "Labeled"},
{{x2max,0.125,"x2 Máximo = x3 Mínimo"},0.100001,0.15,Appearance-> "Labeled"},
{{x3max,0.175,"x3 Máximo"},0.150001,0.2,Appearance-> "Labeled"},


" "," ","                                                      Control del eje Temperatura [K]  ",
{{Tmin,200,"Mínimo"},0,700,Appearance-> "Labeled"},
{{Tmax,700,"Máximo"},600,800,Appearance-> "Labeled"},
AppearanceElements->"ResetButton"
];
I1:=Manipulate[
ka:=1/k1;
kb:=1/k2;
kc:=1/k3;
kd:=1/k4;
q0:=(Ta-Tb)/((x1max/k1)+((x2max-x1max)/k2)+((x3max-x2max)/k3)+((x4max-x3max)/k4));
Q0:=q0*A;

Initialization->{
T1[x1_]:=(-q0*x1*ka)+Ta;
T2[x2_]:=(-q0*(x2-x1max)*kb)+T1[x1max];
T3[x3_]:=(-q0*(x3-x2max)*kc)+T2[x2max];
T4[x4_]:=(-q0*(x4-x3max)*kd)+T3[x3max];
};

G1=Plot[ 
T1[x1],
{x1,x1min,x1max},
PlotRange->{{x1min, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Green},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}


];
G2=Plot[ 
T2[x2],
{x2,x1max, x2max},
PlotRange->{{x1max, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Orange},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G3=Plot[ 
T3[x3],
{x3,x2max,x3max},
PlotRange->{{x1max, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Blue},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G4=Plot[ 
T4[x4],
{x4,x3max,x4max},
PlotRange->{{x1max, x4max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Red},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
Switch[ctrl, 

1,
Show[G1,G2,G3,G4],

2,
TextCell[
Row[{"Flux q, [W/m^2] ",ExpressionCell[Evaluate[
q0],

CellAutoOverwrite-> False,
CellFrame->True]}]],
3,
TextCell[
Row[{"Flujo Q, [W] ",ExpressionCell[Evaluate[
Q0],

CellAutoOverwrite-> False,
CellFrame->True]}]]


],

{{ctrl,1," "},{1-> "Perfil de Temperatura",2-> "Flux", 3->"Flujo"}},
{{k1,200,"Conductividad térmica de la pared 1, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k2,20,"Conductividad térmica de la pared 2, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k3,3.5,"Conductividad térmica de la pared 3, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k4,0.5,"Conductividad térmica de la pared 4, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{Ta,500,"Temperatura del fluido del extremo izquierdo Ta, K"},400,900,Appearance-> "Labeled"},
{{Tb,273,"Temperatura del fluido del extremo derecho Tb, K"},250,500,Appearance-> "Labeled"},
{{A,0.1,"Área, (m^2)"},0.01,1,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Distancia X [m]",
{{x1min,0,"x1 Mínimo"},0,0.05,Appearance-> "Labeled"},
{{x1max,0.075,"x1 Máximo = x2 Mínimo"},0.050001,0.10,Appearance-> "Labeled"},
{{x2max,0.125,"x2 Máximo = x3 Mínimo"},0.100001,0.15,Appearance-> "Labeled"},
{{x3max,0.175,"x3 Máximo = x4 Mínimo" },0.150001,0.2,Appearance-> "Labeled"},
{{x4max,0.225,"x4 Máximo"},0.20001,0.25,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Temperatura [K]  ",
{{Tmin,200,"Mínimo"},0,700,Appearance-> "Labeled"},
{{Tmax,700,"Máximo"},600,800,Appearance-> "Labeled"},
AppearanceElements->"ResetButton"
];
Jk:=Manipulate[
ka:=1/k1;
kb:=1/k2;
kc:=1/k3;
kd:=1/k4;
ke:=1/k5;
q0:=(Ta-Tb)/((x1max/k1)+((x2max-x1max)/k2)+((x3max-x2max)/k3)+((x4max-x3max)/k4)+((x5max-x4max)/k5));
Q0:=q0*A;

Initialization->{
T1[x1_]:=(-q0*x1*ka)+Ta;
T2[x2_]:=(-q0*(x2-x1max)*kb)+T1[x1max];
T3[x3_]:=(-q0*(x3-x2max)*kc)+T2[x2max];
T4[x4_]:=(-q0*(x4-x3max)*kd)+T3[x3max];
T5[x5_]:=(-q0*(x5-x4max)*ke)+T4[x4max];
};

G1=Plot[ 
T1[x1],
{x1,x1min,x1max},
PlotRange->{{x1min, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Green},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}


];
G2=Plot[ 
T2[x2],
{x2,x1max, x2max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Orange},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G3=Plot[ 
T3[x3],
{x3,x2max,x3max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Blue},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G4=Plot[ 
T4[x4],
{x4,x3max,x4max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Red},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
G5=Plot[ 
T5[x5],
{x5,x4max,x5max},
PlotRange->{{x1max, x5max},{Tmin, Tmax}},
Frame-> True,
ImageSize-> {500,300},
PlotStyle-> {Brown},
GridLines-> Automatic,
FrameLabel-> {Style["Distancia x [m]",Bold,15],Style["Temperatura [K]",Bold,15]}
];
Switch[ctrl, 

1,
Show[G1,G2,G3,G4,G5],

2,
TextCell[
Row[{"Flux q, [W/m^2] ",ExpressionCell[Evaluate[
q0],

CellAutoOverwrite-> False,
CellFrame->True]}]],
3,
TextCell[
Row[{"Flujo Q, [W] ",ExpressionCell[Evaluate[
Q0],

CellAutoOverwrite-> False,
CellFrame->True]}]]


],

{{ctrl,1," "},{1-> "Perfil de Temperatura",2-> "Flux", 3->"Flujo"}},
{{k1,200,"Conductividad térmica de la pared 1, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k2,20,"Conductividad térmica de la pared 2, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k3,3.5,"Conductividad térmica de la pared 3, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k4,0.5,"Conductividad térmica de la pared 4, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{k5,0.05,"Conductividad térmica de la pared 5, W/(m*K)"},0.01,500,Appearance-> "Labeled"},
{{Ta,500,"Temperatura del fluido del extremo izquierdo Ta, K"},400,900,Appearance-> "Labeled"},
{{Tb,273,"Temperatura del fluido del extremo derecho Tb, K"},250,500,Appearance-> "Labeled"},
{{A,0.1,"Área, (m^2)"},0.01,1,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Distancia X [m]",
{{x1min,0,"x1 Mínimo"},0,0.05,Appearance-> "Labeled"},
{{x1max,0.075,"x1 Máximo = x2 Mínimo"},0.05001,0.10,Appearance-> "Labeled"},
{{x2max,0.125,"x2 Máximo = x3 Mínimo"},0.10001,0.15,Appearance-> "Labeled"},
{{x3max,0.175,"x3 Máximo = x4 Mínimo" },0.15001,0.2,Appearance-> "Labeled"},
{{x4max,0.225,"x4 Máximo = x5 Mínimo"},0.20001,0.25,Appearance-> "Labeled"},
{{x5max,0.275,"x5 Máximo"},0.25001,0.3,Appearance-> "Labeled"},

" "," ","                                                      Control del eje Temperatura [K]  ",
{{Tmin,200,"Mínimo"},0,700,Appearance-> "Labeled"},
{{Tmax,700,"Máximo"},600,800,Appearance-> "Labeled"},
AppearanceElements->"ResetButton"
];
 MenuView[{"Condiciones a la frontera"->"","Sin convección"->F,"Con convección"->D1},1],
 D1:=MenuView[{"Selecciona el número de paredes"->"","3"->A,"4"->B,"5"->C1a},1];
 F:=MenuView[{"Selecciona el número de paredes"->"","3"->H,"4"->I1,"5"->Jk},1];
}]];

txt40=Style["Diferencias y semejanzas en el caso de la geometria cartesiana y cilindrica",FontFamily->"Times New Roman",24,FontColor->White];
txt41=Style["Semejanzas:
*En ambos casos se trata de un fenomenos de conduccion a traves de capas sucesivas.

*Se resuelve efectuando un balance de energía sin fuentes. 

*En el caso del cilindro, la superficie varia con la distancia. En el caso rectangular, no.

*Cada caso lleva a una ecuación diferencial diferente.

*En uno la resistencia térmica es constante.

*En el otro varía con el inverso de la distancia.

*La integral de 1/r es ln(r) ",FontFamily->"Times New Roman",16,FontColor->White];
Framed[OpenerView[{txt40,txt41}],RoundingRadius->5,FrameMargins->Large,Background->RGBColor["#1C3D6C"]]

txt42=Style["Resistencia de contacto.",FontFamily->"Times New Roman",FontColor->RGBColor["#1C3D6C"],24];
txt43="Datos para R";
img6=;
img7=;

txt44="Tipos de preguntas";
txt45=Style["Variables:
*El flux
*La resistencia (conductividad)
*La temperatura
Toma de decisiones:
*Condiciones de operacion
*Mayor economía",FontFamily->"Times New Roman",16,FontColor->RGBColor["#1C3D6C"]];
Framed[OpenerView[{txt42,Grid[{{txt43},{img6},{img7}},Alignment->Left]}],RoundingRadius->5,FrameMargins->Large]

txt46=Style["Ejemplo 1. Flux a travs de una pared compuesta circular",FontFamily->"Times New Roman",16,FontColor->White];
txt47=Style["Un tubo de acero de 4 pulgadas de diámetro interior y 4.5 de diámetro exterior, se aísla con una capa de ¾ de pulgada de fibra de vidrio. La superficie interior del tubo está a 400 °F y la superficie exterior de fibra de vidrio a 90 °F. Determina cuál es la tasa de transferencia de calor por unidad de longitud del tubo. Utiliza para la conductividad del acero el valor de k=30 BTU/hr-ft-°F y para la fibra de vidrio k=0.032 en las mismas unidades. ",FontFamily->"Times New Roman",16,FontColor->White];
txt48=Style["Solucion",FontFamily->"Times New Roman",16,FontColor->White];
txt49=Style["Utilizamos la ecuación:
(Subscript[Q, 0])=2(Subscript[πLr, 0])(Subscript[q, 0])=((2  πL ((Subscript[T, a]) - (Subscript[T, b])))/((1/((Subscript[r, 0]) (Subscript[h, 0]))) + ((ln ((Subscript[r, 1])/(Subscript[r, 0])))/(Subscript[k, 01])) + ((ln ((Subscript[r, 2])/(Subscript[r, 1])))/(Subscript[k, 12])) + ((ln ((Subscript[r, 3])/(Subscript[r, 2])))/(Subscript[k, 23])) + (1/((Subscript[r, 3]) (Subscript[h, 3])))))
Con las condiciones del problema:
Q/L=((2  π ((Subscript[T, 1]) - (Subscript[T, 3])))/(((ln ((Subscript[r, 2])/(Subscript[r, 1])))/(Subscript[k, 12])) + ((ln ((Subscript[r, 3])/(Subscript[r, 2])))/(Subscript[k, 23]))))
sustituyendo valores numericos:
=((2  π (400 - 90))/(((ln (2.25/2))/30) + ((ln (3/2.25))/0.032)))
=((2  π (310))/(0.00393 + 8.9901))=216.56 Btu/hr-ft",FontFamily->"Times New Roman",16,FontColor->White];
txt50=Style["Ejemplo 2. Limites de operacion termica.",FontFamily->"Times New Roman",16,FontColor->White];
txt51=Style["Un chip de silicio y su base de aluminio están separados por un pegamento epóxico de espesor 0.02mm. El chip y su base tienen 10 mm de largo y son enfriados por una corriente de aire a 25 oC Con un coeficiente de convección de 100 W/m2 oK
Si el chip disipa energía a una tasa de 104 W/m2 ¿Podrá operar correctamente, si el límite máximo de temperatura que tolera es de 85 oC? 

Nota: La conductividad el Aluminio a 350 K es de 239 W/m K
Referencia: Incropera, Fundamentals of heat and mass transfer",FontFamily->"Times New Roman",16,FontColor->White];
img8=;
txt52="Solucion:";
txt53=Style["El flujo total de calor qc tiene dos partes: q1 que es el calor cedido hacía arriba por convención: 
(((Subscript[T, c]) - (Subscript[T, ∞]))/(1/h))
\!\(TraditionalForm\`\*SubscriptBox[\(q\), \(2\)]\\ que\\ es\\ el\\ calor\\ cedido\\ hacía\\ abajo\\ por\\ contacto, \\ conducción\\ y\\ \(\(convección\)\(.\)\)\)
(((Subscript[T, c]) - (Subscript[T, ∞]))/((Subscript[R, t, c]) + (L/K) + (1/h)))
Con lo que:
(Subscript[q, c])=(((Subscript[T, c]) - (Subscript[T, ∞]))/(1/h))+(((Subscript[T, c]) - (Subscript[T, ∞]))/((Subscript[R, t, c]) + (L/K) + (1/h)))
(Subscript[T, c])=(Subscript[T, ∞])+(Subscript[q, c])(h+(((Subscript[T, c]) - (Subscript[T, ∞]))/((Subscript[R, t, c]) + (L/K) + (1/h))))^(-1)
(Subscript[T, c])=25°C+(10^4)W/(m^2)(100+(1/((0.9 + 0.33 + 100) (10^(-4)))))^(-1)(m^2)k/W=75.3°C",FontFamily->"Times New Roman",16,FontColor->White];
txt54=Style["Actividades",FontFamily->"Times New Roman",16,FontColor->White];
txt55=Style["1.	Calculen las pérdidas de energía cuando se transporta un fluido dentro de un tubo que se encuentra aislado con capas de dos diferentes aislantes. 
Realicen un esquema que describa la situación.
¿Qué parámetros son los datos de entrada del problema? 
¿Con cuál fórmula van a calcular la pérdida de energía? 
signen valores numéricos (inspirados en el problema que se resolvió en clase) y escríban una hoja de Excel para obtener valores numéricos de la pérdida de energía. 
Verifiquen sus resultados con el simulador de Mathematica. 

.	Resolver el siguiente problema:
Un tubo de acero de 2 pulgadas que transporta vapor sobrecalentado y está aislado con 1.25 pulgadas de aislante hecho con tierra de diatomáceas (k=0.062 kcal/hm°C). Ésta a su vez está cubierta con 2.5 pulgadas de asbesto (k=0.0624 kcal/hm°C). En una prueba la temperatura ambiente era de 30°C, la temperatura del vapor era de 480°C  y la temperatura de la superficie de 50°C. Considera un coeficiente de convección h de 40 W / m2 K (Sugerencia: antes de realizar los cálculos, hagan la conversión de unidades, usando el convertidor que se encuentra en la página del curso Moodle).
Calculen las pérdidas de calor expresadas en kcal/hm.
Calculen la temperatura de la interface entre las dos capas de aislante.
¿Cuál es la perdida de calor si aumentan la temperatura del gas y mantienen la de la superficie? 
3.    En clase se utilizó la fórmula: 
(Subscript[T, c])=(Subscript[T, ∞])+(Subscript[q, c])(h+(((Subscript[T, c]) - (Subscript[T, ∞]))/((Subscript[R, t, c]) + (L/K) + (1/h))))^(-1)
(Subscript[T, c])=25°C+(10^4)W/(m^2)(100+(1/((0.9 + 0.33 + 100) (10^(-4)))))^(-1)(m^2)k/W=75.3°C
Para resolver el problema de determinar la posibilidad de operar un chip en un intervalo dado de temperaturas.  Construye una hoja de Excel para variar los valores de los tres términos dentro del corchete cuadrado y proponer soluciones que permitan reducir la temperatura máxima del chip.  Comenta tus análisis para cada uno de los términos.  ",FontFamily->"Times New Roman",16,FontColor->White];
txt100=Style["Ejemplos",FontFamily->"Times New Roman",24,FontColor->White];
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txt56=Style["Referencias",FontFamily->"Times New Roman",24,FontColor->RGBColor["#1C3D6C"]];
txt57=Style["Bird. Transport Phenomena",FontFamily->"Times New Roman",16,FontColor->Black];
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