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89 lines
3.8 KiB
89 lines
3.8 KiB
function findClosest(value,array) { |
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closestDiff = null; |
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closestPosition = null; |
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for (var i=0;i<array.length;i++) { |
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diff = Math.abs(value-array[i]) |
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if (diff<closestDiff || closestDiff == null) { |
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closestPosition=i; |
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closestDiff = diff; |
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} |
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} |
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return ([closestPosition,array[closestPosition]]) |
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} |
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function biotSphereCoefficients (Biot) { |
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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] |
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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] |
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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 ] |
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position = findClosest(Biot,Bi)[0] |
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return([lambdaOne[position], alphaOne[position]]) |
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} |
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function lumpedCapacitance (outerRadius,radiusInner,tempInitial,tempInfini,heatConvectionTerm,t) { |
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volume = (4/3)*Math.PI*Math.pow(outerRadius,3) - (4/3)*Math.PI*Math.pow(radiusInner,3); //3D Sphere |
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surfaceArea = 4*Math.PI*Math.pow(outerRadius,2); //3D Sphere |
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mass = density * volume; |
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charLength = volume/surfaceArea ; |
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biotNum = heatConvectionTerm * charLength/thermalConduct |
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console.log("The Biot Value is " + biotNum) |
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b=(heatConvectionTerm)/(density*charLength*cp) |
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console.log("The time constant b is "+ b) |
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tempAtTime = Math.exp(-b*t)*(tempInitial-tempInfini)+tempInfini; |
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console.log("The Temperature at time " + t +" seconds is " + tempAtTime) |
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qDot = -1*heatConvectionTerm*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rate Useful for water Loss |
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console.log("The Heat Flux is " + qDot ) |
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return([tempAtTime,qDot]) |
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} |
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function transientSphereOneTerm (rPosition,rTotal,tempInitial,tempInfini,t) { |
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alpha = thermalConduct/(density*cp) |
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console.log("Alpha is " + alpha) |
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Fourier = (alpha*t)/Math.pow(rTotal,2) |
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console.log("Fourier is " + Fourier) |
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biotNum = heatConvection * rTotal/thermalConduct |
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console.log("The Biot Value is " + biotNum) |
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temp=biotSphereCoefficients(biotNum) |
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lambdaOne=temp[0]; |
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alphaOne=temp[1]; |
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console.log("lambda1 is " + lambdaOne) |
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console.log("A1 is " + alphaOne) |
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//This is only valid for Fourier greater than 0.2 |
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sinPortion= Math.sin(lambdaOne*rPosition/rTotal)/(lambdaOne*rPosition/rTotal); |
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expotentialPortion = alphaOne*(1/Math.exp(Math.pow(lambdaOne,2)*Fourier)) |
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tempAtTimeAndRadius=(sinPortion*expotentialPortion*(tempInitial-tempInfini))+tempInfini |
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console.log("The Temperature at radius " + rPosition + " m and time " + t + " seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F"); |
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} |
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function lumpedCapacitanceMethod (outerRadius,radiusInner,tempInitial,tempInfini, t) { |
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volume = (4/3)*Math.PI*Math.pow(outerRadius,3) - (4/3)*Math.PI*Math.pow(radiusInner,3); //3D Sphere |
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surfaceArea = 4*Math.PI*Math.pow(outerRadius,2); //3D Sphere |
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mass = density * volume; |
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charLength = volume/surfaceArea ; |
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biotNum = heatConvection * charLength/thermalConduct |
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console.log("The Biot Value is " + biotNum) |
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b=(heatConvection)/(density*charLength*cp) |
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console.log("The time constant b is "+ b) |
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tempAtTime = Math.exp(-b*t)*(tempInitial-tempInfini)+tempInfini; |
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console.log("The Temperature at time " + t +" seconds is " + tempAtTime) |
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Qdot = -1*heatConvection*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rate Useful for water Loss |
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console.log("The Heat Flux is " + Qdot ) |
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return(tempAtTime) |
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} |
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function findAllRoots (Biot) { |
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limit = 50; //Terms to Compute too |
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storage = []; |
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for (var k=0; k<=limit; k++) { |
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minK = (k+0.5)*Math.PI; |
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maxK = (k+1)*Math.PI; |
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answer = bisectionMethod(minK,maxK,Biot); |
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if (answer !=undefined) { |
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storage.push(answer); |
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} |
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} |
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//console.log(storage) |
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return(storage) |
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} |