From 40b26677795c5b49e811bd0ccf453874fbb55027 Mon Sep 17 00:00:00 2001
From: Scott Mobley <Zott820@yahoo.com>
Date: Fri, 15 Nov 2013 23:55:34 -0800
Subject: [PATCH] A 'working' transient model

Also, an AlternativeModels.js file contain some of the other models not used. Lumped sum, etc.
---
 js/AlternativeModels.js |  89 ++++++++++++++++++
 js/CookingFormula.js    | 203 ++++++++++++++--------------------------
 2 files changed, 160 insertions(+), 132 deletions(-)
 create mode 100644 js/AlternativeModels.js

diff --git a/js/AlternativeModels.js b/js/AlternativeModels.js
new file mode 100644
index 0000000..938c3ba
--- /dev/null
+++ b/js/AlternativeModels.js
@@ -0,0 +1,89 @@
+function findClosest(value,array) {
+closestDiff = null;
+closestPosition = null;
+	for (var i=0;i<array.length;i++) {
+		diff = Math.abs(value-array[i])
+		if (diff<closestDiff || closestDiff == null) {
+			closestPosition=i;
+			closestDiff = diff;
+		} 
+	}
+	return ([closestPosition,array[closestPosition]])
+}
+
+function biotSphereCoefficients (Biot) {
+Bi = [0.01, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100, 10000]
+lambdaOne = [0.1730, 0.2445, 0.3450, 0.4217, 0.4860, 0.5423, 0.7593, 0.9208, 1.0528, 1.1656, 1.2644, 1.3525, 1.4320, 1.5044, 1.5708, 2.0288, 2.2889, 2.4556, 2.5704, 2.6537, 2.7165, 2.7654, 2.8044, 2.8363, 2.9857, 3.3072, 3.0632, 3.0788, 3.1102, 3.1416]
+alphaOne = [ 1.0030, 1.0060, 1.0120, 1.0179, 1.0239, 1.0298, 1.0592, 1.0880, 1.1164, 1.1441, 1.1713, 1.1978, 1.2236, 1.2488, 1.2732, 1.4793, 1.6227, 1.7202, 1.7870, 1.8338, 1.8673, 1.8920, 1.9106, 1.9249, 1.9781, 1.9898, 1.9942, 1.9962, 1.9990, 2 ]
+position = findClosest(Biot,Bi)[0]
+return([lambdaOne[position], alphaOne[position]])
+}
+
+function lumpedCapacitance (outerRadius,radiusInner,tempInitial,tempInfini,heatConvectionTerm,t) {
+volume = (4/3)*Math.PI*Math.pow(outerRadius,3) - (4/3)*Math.PI*Math.pow(radiusInner,3); //3D Sphere
+surfaceArea = 4*Math.PI*Math.pow(outerRadius,2); //3D Sphere
+mass = density * volume;
+charLength = volume/surfaceArea ;
+biotNum = heatConvectionTerm * charLength/thermalConduct
+console.log("The Biot Value is " + biotNum)
+b=(heatConvectionTerm)/(density*charLength*cp)
+console.log("The time constant b is "+ b)
+tempAtTime = Math.exp(-b*t)*(tempInitial-tempInfini)+tempInfini;
+console.log("The Temperature at time " + t +" seconds is " + tempAtTime)
+qDot = -1*heatConvectionTerm*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rate Useful for water Loss
+console.log("The Heat Flux is " + qDot )
+return([tempAtTime,qDot])
+}
+
+function transientSphereOneTerm (rPosition,rTotal,tempInitial,tempInfini,t) {
+alpha = thermalConduct/(density*cp)
+console.log("Alpha is " + alpha)
+
+Fourier = (alpha*t)/Math.pow(rTotal,2)
+console.log("Fourier is " +  Fourier)
+biotNum = heatConvection * rTotal/thermalConduct
+console.log("The Biot Value is " + biotNum)
+temp=biotSphereCoefficients(biotNum)
+lambdaOne=temp[0];
+alphaOne=temp[1];
+console.log("lambda1 is " + lambdaOne)
+console.log("A1 is " + alphaOne)
+
+//This is only valid for Fourier greater than 0.2
+sinPortion= Math.sin(lambdaOne*rPosition/rTotal)/(lambdaOne*rPosition/rTotal);
+expotentialPortion = alphaOne*(1/Math.exp(Math.pow(lambdaOne,2)*Fourier))
+tempAtTimeAndRadius=(sinPortion*expotentialPortion*(tempInitial-tempInfini))+tempInfini
+console.log("The Temperature at radius " + rPosition + " m and time " + t + "  seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F");
+}
+
+function lumpedCapacitanceMethod (outerRadius,radiusInner,tempInitial,tempInfini, t) {
+volume = (4/3)*Math.PI*Math.pow(outerRadius,3) - (4/3)*Math.PI*Math.pow(radiusInner,3); //3D Sphere
+surfaceArea = 4*Math.PI*Math.pow(outerRadius,2); //3D Sphere
+mass = density * volume;
+charLength = volume/surfaceArea ;
+biotNum = heatConvection * charLength/thermalConduct
+console.log("The Biot Value is " + biotNum)
+b=(heatConvection)/(density*charLength*cp)
+console.log("The time constant b is "+ b)
+tempAtTime = Math.exp(-b*t)*(tempInitial-tempInfini)+tempInfini;
+console.log("The Temperature at time " + t +" seconds is " + tempAtTime)
+Qdot = -1*heatConvection*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rate Useful for water Loss
+console.log("The Heat Flux is " + Qdot )
+return(tempAtTime)
+}
+
+
+function findAllRoots (Biot) {
+limit = 50; //Terms to Compute too
+storage = [];
+	for (var k=0; k<=limit; k++) {
+		minK = (k+0.5)*Math.PI;
+		maxK = (k+1)*Math.PI;
+		answer = bisectionMethod(minK,maxK,Biot);
+		if (answer !=undefined) {
+		storage.push(answer);
+		}
+	}
+//console.log(storage)
+return(storage)
+}
\ No newline at end of file
diff --git a/js/CookingFormula.js b/js/CookingFormula.js
index 9386f49..0d08944 100644
--- a/js/CookingFormula.js
+++ b/js/CookingFormula.js
@@ -7,40 +7,24 @@
 density = 996; // kg/m3 Assuming Density of Water 1000 kg/m3
 cp = 2810 // J/kg K for Turkey
 heatConvection = 5; // W/m2 K Some Reasonable estimate for natural Convection. Change as needed. 5-25
-thermalConduct = 0.412 // W/m K
+thermalConduct = 0.412 // W/m K // Chicken
+globalTime = 1;
 
 function celsiusToFarenheit(celsius) {
 farenheit = (celsius*(9/5)) + 32;
 return(farenheit)
 }
 
+function farenheitToCelsius (farenheit) {
+celsius = (farenheit*(9/5)) + 32;
+return(celsius)
+}
+
 function poundsToKilograms(pounds) {
 kilograms = (pounds * 0.453592);
 return(kilograms)
 }
 
-function findClosest(value,array) {
-closestDiff = null;
-closestPosition = null;
-	for (var i=0;i<array.length;i++) {
-		diff = Math.abs(value-array[i])
-		if (diff<closestDiff || closestDiff == null) {
-			closestPosition=i;
-			closestDiff = diff;
-		} 
-	}
-	return ([closestPosition,array[closestPosition]])
-}
-
-function biotSphereCoefficients (Biot) {
-Bi = [0.01, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100, 10000]
-lambdaOne = [0.1730, 0.2445, 0.3450, 0.4217, 0.4860, 0.5423, 0.7593, 0.9208, 1.0528, 1.1656, 1.2644, 1.3525, 1.4320, 1.5044, 1.5708, 2.0288, 2.2889, 2.4556, 2.5704, 2.6537, 2.7165, 2.7654, 2.8044, 2.8363, 2.9857, 3.3072, 3.0632, 3.0788, 3.1102, 3.1416]
-alphaOne = [ 1.0030, 1.0060, 1.0120, 1.0179, 1.0239, 1.0298, 1.0592, 1.0880, 1.1164, 1.1441, 1.1713, 1.1978, 1.2236, 1.2488, 1.2732, 1.4793, 1.6227, 1.7202, 1.7870, 1.8338, 1.8673, 1.8920, 1.9106, 1.9249, 1.9781, 1.9898, 1.9942, 1.9962, 1.9990, 2 ]
-position = findClosest(Biot,Bi)[0]
-return([lambdaOne[position], alphaOne[position]])
-}
-
-
 function calculateRadius(weight) {
 //Using Ratios for a rectangular Box Turkey
 ratioLvG=1.4; //1.4, Turkey length vs shoulder girth
@@ -59,79 +43,8 @@ console.log("Complex Radius  " + complexRadius + " Meters")
 return(complexRadius)
 }
 
-function lumpedCapacitance (outerRadius,radiusInner,tempInitial,tempInfini,heatConvectionTerm,t) {
-volume = (4/3)*Math.PI*Math.pow(outerRadius,3) - (4/3)*Math.PI*Math.pow(radiusInner,3); //3D Sphere
-surfaceArea = 4*Math.PI*Math.pow(outerRadius,2); //3D Sphere
-mass = density * volume;
-charLength = volume/surfaceArea ;
-biotNum = heatConvectionTerm * charLength/thermalConduct
-console.log("The Biot Value is " + biotNum)
-b=(heatConvectionTerm)/(density*charLength*cp)
-console.log("The time constant b is "+ b)
-tempAtTime = Math.exp(-b*t)*(tempInitial-tempInfini)+tempInfini;
-console.log("The Temperature at time " + t +" seconds is " + tempAtTime)
-qDot = -1*heatConvectionTerm*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rate Useful for water Loss
-console.log("The Heat Flux is " + qDot )
-return([tempAtTime,qDot])
-}
-
-
-
-
-function lumpedCapacitanceMethod (outerRadius,radiusInner,tempInitial,tempInfini, t) {
-volume = (4/3)*Math.PI*Math.pow(outerRadius,3) - (4/3)*Math.PI*Math.pow(radiusInner,3); //3D Sphere
-surfaceArea = 4*Math.PI*Math.pow(outerRadius,2); //3D Sphere
-mass = density * volume;
-charLength = volume/surfaceArea ;
-biotNum = heatConvection * charLength/thermalConduct
-console.log("The Biot Value is " + biotNum)
-b=(heatConvection)/(density*charLength*cp)
-console.log("The time constant b is "+ b)
-tempAtTime = Math.exp(-b*t)*(tempInitial-tempInfini)+tempInfini;
-console.log("The Temperature at time " + t +" seconds is " + tempAtTime)
-Qdot = -1*heatConvection*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rate Useful for water Loss
-console.log("The Heat Flux is " + Qdot )
-return(tempAtTime)
-}
-
-
-function transientSphereOneTerm (rPosition,rTotal,tempInitial,tempInfini,t) {
-alpha = thermalConduct/(density*cp)
-console.log("Alpha is " + alpha)
-
-Fourier = (alpha*t)/Math.pow(rTotal,2)
-console.log("Fourier is " +  Fourier)
-biotNum = heatConvection * rTotal/thermalConduct
-console.log("The Biot Value is " + biotNum)
-temp=biotSphereCoefficients(biotNum)
-lambdaOne=temp[0];
-alphaOne=temp[1];
-console.log("lambda1 is " + lambdaOne)
-console.log("A1 is " + alphaOne)
-
-//This is only valid for Fourier greater than 0.2
-sinPortion= Math.sin(lambdaOne*rPosition/rTotal)/(lambdaOne*rPosition/rTotal);
-expotentialPortion = alphaOne*(1/Math.exp(Math.pow(lambdaOne,2)*Fourier))
-tempAtTimeAndRadius=(sinPortion*expotentialPortion*(tempInitial-tempInfini))+tempInfini
-console.log("The Temperature at radius " + rPosition + " m and time " + t + "  seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F");
-}
-
-function findAllRoots (Biot) {
-limit = 50; //Terms to Compute too
-storage = [];
-	for (var k=0; k<=limit; k++) {
-		minK = (k+0.5)*Math.PI;
-		maxK = (k+1)*Math.PI;
-		answer = bisectionMethod(minK,maxK,Biot);
-		if (answer !=undefined) {
-		storage.push(answer);
-		}
-	}
-//console.log(storage)
-return(storage)
-}
 
-function findAllRootsAlternative (min,max,splitsNum,Biot) {
+function findAllRoots(min,max,splitsNum,Biot) {
 var step = ( max - min ) / ( splitsNum - 1 );
 var storage = [];
 	for (var i = step; i < max; i=i+step ) {
@@ -186,10 +99,10 @@ return(result)
 }
 
 function oven() {
-this.tempInfini=0; //C
-this.setTemp = 0;
-var proportional = 0.01; // This value is arbitrary to how fast you want the temperatures to converge. (Or oscillate, which could be realistic as well)
-var errorTolerance = 1; //Stove is accurate to 1 degree Celcius Should hopefully oscillate below that value.
+this.tempInfini=20; //C
+this.setTemp = 20;
+var proportional = 0.1; // This value is arbitrary to how fast you want the temperatures to converge. (Or oscillate, which could be realistic as well)
+var errorTolerance = 5; //Stove is accurate to 1 degree Celcius Should hopefully oscillate below that value.
 
 	this.changeTemp = function(setTemp) {
 		this.setTemp = setTemp;
@@ -208,59 +121,85 @@ var errorTolerance = 1; //Stove is accurate to 1 degree Celcius Should hopefully
 		}
 	}
 }
-ovenObject = new oven ();
-
-function Turkey(weight,time) {
 
-totalRadius = calculateRadius(weight)
-	function Layer(name) {
-	this.name = name
-	this.temperature = 20;
-	this.waterContent =100;
+function layerModel(name,radiusPercent) {
+	this.name = name;
+	this.radiusPercent=radiusPercent;
+	this.initialTemp = 20;
+	this.waterContent =100000;
 	this.Qdot = 0;
-	}
-	
-skin= new Layer("Skin")
-body = new Layer("Body")
-core = new Layer("Core")
+	this.finalTemperature = 20;
+}
+ 
+
+function turkeyModel(weight) {
 
-skin.temperature = lumpedCapacitance(totalRadius,totalRadius*0.85,skin.temperature,ovenTemp,airConvection,time)[0]
-body.temperature = lumpedCapacitance(totalRadius*0.85,totalRadius*0.30,body.temperature,skin.temperature,airConvection*1000,time)[0]
-core.temperature = lumpedCapacitance(totalRadius*0.30,0,core.temperature,body.temperature,airConvection*1000,time)[0]
-} 
+this.totalRadius = calculateRadius(weight)
+this.skin = new layerModel("Skin",0.85)
+this.body = new layerModel("Body",0.45)
+this.core = new layerModel("Core",0.01)
 
+	this.updateLayerTemps = function() {
+		this.skin.finalTemperature = transientSphereSeries (this.skin.radiusPercent*this.totalRadius,this.totalRadius,this.skin.initialTemp,ovenObject.tempInfini,globalTime)
+		this.skin.initialTemp = this.skin.finalTemperature;
 
+		this.body.finalTemperature = transientSphereSeries (this.body.radiusPercent*this.totalRadius,this.totalRadius,this.body.initialTemp,ovenObject.tempInfini,globalTime)
+		this.body.initialTemp = this.body.finalTemperature;
+
+		this.core.finalTemperature = transientSphereSeries (this.core.radiusPercent*this.totalRadius,this.totalRadius,this.core.initialTemp,ovenObject.tempInfini,globalTime)
+		this.core.initialTemp = this.core.finalTemperature;
+	}
+}
+
+var oldBiot=null;
 function transientSphereSeries (rPosition,rTotal,tempInitial,tempInfini,t) {
+var min = 0;
+var max = 1000; // This are for setting Lambda boundries and nothing else
+
 var sum=0;
 var alpha = thermalConduct/(density*cp)
-console.log("Alpha is " + alpha)
+//console.log("Alpha is " + alpha)
 
 var Fourier = (alpha*t)/Math.pow(rTotal,2)
-console.log("Fourier is " +  Fourier)
+//console.log("Fourier is " +  Fourier)
+
 var biotNum = heatConvection * rTotal/thermalConduct
-console.log("The Biot Value is " + biotNum)
 
-var min = 0;
-var max = 1000;
+	if (biotNum != oldBiot) {
+		console.log("Recalculating Lambda Terms")
+		lambdaTerms = findAllRoots(min,max,max*Math.PI*10,biotNum)
+		oldBiot = biotNum;
+	}
 
-lambdaTerms=findAllRootsAlternative (min,max,max*Math.PI*10,biotNum)
-	for (var i = 0; i<lambdaTerms.length; i++) {
-		lambdaN = lambdaTerms[i]
+//console.log("The Biot Value is " + biotNum)
 
-		sinPortion= Math.sin(lambdaN*rPosition/rTotal)/(lambdaN*rPosition/rTotal);
-		exponentialPortion = (1/Math.exp(Math.pow(lambdaN,2)*Fourier))
-		frontCoefficientPortion = 4*(Math.sin(lambdaN)-(lambdaN*Math.cos(lambdaN)))/ (2*lambdaN-Math.sin(2*lambdaN))
-		sum = frontCoefficientPortion*exponentialPortion*sinPortion + sum
+for (var i = 0; i<lambdaTerms.length; i++) {
+	lambdaN = lambdaTerms[i]
+	sinPortion= Math.sin(lambdaN*rPosition/rTotal)/(lambdaN*rPosition/rTotal);
+	exponentialPortion = (1/Math.exp(Math.pow(lambdaN,2)*Fourier))
+	frontCoefficientPortion = 4*(Math.sin(lambdaN)-(lambdaN*Math.cos(lambdaN)))/ (2*lambdaN-Math.sin(2*lambdaN))
+	sum = frontCoefficientPortion*exponentialPortion*sinPortion + sum
 }
 tempAtTimeAndRadius=(sum*(tempInitial-tempInfini))+tempInfini
-console.log("The Temperature at radius " + rPosition + " m and time" + t + " seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F");
+
+console.log("The Temperature at radius " + rPosition + " m and time " + t + " seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F");
 return(tempAtTimeAndRadius)
 }
 
 
-setInterval(function(){time()},1000);
+//Running the Program Stuff
 
-function time() {
-ovenObject.equalizeTemp();
+ovenObject = new oven ();
+turkey = new turkeyModel(8);
+
+setInterval(function(){time()},20);
 
+function time() {
+	console.clear()
+	if (ovenObject.equalizeTemp() ) {
+		globalTime = 0; //Reset the model's time calculation if there are major changes in the tolerance of the temperature
+	}
+		else {globalTime = globalTime +60 }
+	console.log(ovenObject.tempInfini)
+	turkey.updateLayerTemps();
 }
\ No newline at end of file