Analysis of Combined Power and Refrigeration Generation Using the Carbon Dioxide Thermodynamic Cycle to Recover the Waste Heat of an Internal Combustion Engine

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="689398.fig.005a" src="https://static.hindawi.com/articles/mpe/volume-2014/689398/figures/689398.fig.005a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Variation of the maximum net power output versus <svg height="18.75" id="M79" style="vertical-align:-5.04861pt" version="1.1" viewbox="0 0 20.887501 18.75" width="20.887501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.388,15.637)"><path d="M463 437l5 -8q-21 -38 -45 -51l-57 3q30 -35 30 -88q0 -76 -52.5 -118t-122.5 -42q-24 0 -51 5q-30 -21 -30 -42q0 -16 16 -27t47 -11q19 0 54 0.5t52 0.5q36 0 65.5 -8t53.5 -36t24 -74q0 -77 -75 -137.5t-174 -60.5q-79 0 -126 37.5t-48 84.5q0 32 24 56q21 21 83 70
q-49 15 -74 55q-13 20 -11 42q56 21 88 61q-37 16 -62.5 51t-25.5 83q0 78 56.5 122t122.5 44h1q51 0 96 -27q71 4 136 15zM219 418q-34 0 -58 -32t-24 -87q0 -59 26.5 -96.5t67.5 -37.5q35 1 59 32t24 87q0 59 -26 96.5t-69 37.5zM241 -11q-62 0 -87 -21q-46 -39 -46 -78
q0 -41 38 -68.5t94 -27.5q69 0 106.5 31t37.5 80q0 52 -45 71q-33 13 -98 13z" id="x67"></path></g><g transform="matrix(.012,-0,0,-.012,17.004,15.637)"><path d="M135 536q-20 0 -35 15.5t-15 35.5q0 22 15 37t36 15t35.5 -15t14.5 -37q0 -21 -15 -36t-36 -15zM252 0h-220v26q48 5 59 17t11 63v206q0 47 -9 58t-54 18v24q78 12 142 39v-345q0 -51 11.5 -63t59.5 -17v-26z" id="x69"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="689398.fig.005b" src="https://static.hindawi.com/articles/mpe/volume-2014/689398/figures/689398.fig.005b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Variation of the optimal value of <svg height="15.25" id="M80" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.275 15.25" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5
t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" id="x1D443"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg> versus <svg height="18.75" id="M81" style="vertical-align:-5.04861pt" version="1.1" viewbox="0 0 20.887501 18.75" width="20.887501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.388,15.637)"><path d="M463 437l5 -8q-21 -38 -45 -51l-57 3q30 -35 30 -88q0 -76 -52.5 -118t-122.5 -42q-24 0 -51 5q-30 -21 -30 -42q0 -16 16 -27t47 -11q19 0 54 0.5t52 0.5q36 0 65.5 -8t53.5 -36t24 -74q0 -77 -75 -137.5t-174 -60.5q-79 0 -126 37.5t-48 84.5q0 32 24 56q21 21 83 70
q-49 15 -74 55q-13 20 -11 42q56 21 88 61q-37 16 -62.5 51t-25.5 83q0 78 56.5 122t122.5 44h1q51 0 96 -27q71 4 136 15zM219 418q-34 0 -58 -32t-24 -87q0 -59 26.5 -96.5t67.5 -37.5q35 1 59 32t24 87q0 59 -26 96.5t-69 37.5zM241 -11q-62 0 -87 -21q-46 -39 -46 -78
q0 -41 38 -68.5t94 -27.5q69 0 106.5 31t37.5 80q0 52 -45 71q-33 13 -98 13z" id="x67"></path></g><g transform="matrix(.012,-0,0,-.012,17.004,15.637)"><path d="M135 536q-20 0 -35 15.5t-15 35.5q0 22 15 37t36 15t35.5 -15t14.5 -37q0 -21 -15 -36t-36 -15zM252 0h-220v26q48 5 59 17t11 63v206q0 47 -9 58t-54 18v24q78 12 142 39v-345q0 -51 11.5 -63t59.5 -17v-26z" id="x69"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="689398.fig.005c" src="https://static.hindawi.com/articles/mpe/volume-2014/689398/figures/689398.fig.005c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Variation of the optimal value of <svg height="15.25" id="M82" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.275 15.25" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5
t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" id="x1D443"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg> versus <svg height="18.75" id="M83" style="vertical-align:-5.04861pt" version="1.1" viewbox="0 0 20.887501 18.75" width="20.887501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.388,15.637)"><path d="M463 437l5 -8q-21 -38 -45 -51l-57 3q30 -35 30 -88q0 -76 -52.5 -118t-122.5 -42q-24 0 -51 5q-30 -21 -30 -42q0 -16 16 -27t47 -11q19 0 54 0.5t52 0.5q36 0 65.5 -8t53.5 -36t24 -74q0 -77 -75 -137.5t-174 -60.5q-79 0 -126 37.5t-48 84.5q0 32 24 56q21 21 83 70
q-49 15 -74 55q-13 20 -11 42q56 21 88 61q-37 16 -62.5 51t-25.5 83q0 78 56.5 122t122.5 44h1q51 0 96 -27q71 4 136 15zM219 418q-34 0 -58 -32t-24 -87q0 -59 26.5 -96.5t67.5 -37.5q35 1 59 32t24 87q0 59 -26 96.5t-69 37.5zM241 -11q-62 0 -87 -21q-46 -39 -46 -78
q0 -41 38 -68.5t94 -27.5q69 0 106.5 31t37.5 80q0 52 -45 71q-33 13 -98 13z" id="x67"></path></g><g transform="matrix(.012,-0,0,-.012,17.004,15.637)"><path d="M135 536q-20 0 -35 15.5t-15 35.5q0 22 15 37t36 15t35.5 -15t14.5 -37q0 -21 -15 -36t-36 -15zM252 0h-220v26q48 5 59 17t11 63v206q0 47 -9 58t-54 18v24q78 12 142 39v-345q0 -51 11.5 -63t59.5 -17v-26z" id="x69"></path></g>
</svg></td></tr></table></td></tr></table>

<table>Variation of the maximum net power output and the optimal value of parameters <svg height="15.25" id="M77" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.275 15.25" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5
t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" id="x1D443"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
</svg> and <svg height="15.25" id="M78" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.275 15.25" width="17.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5
t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" id="x1D443"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg> versus the exhaust temperature of ICE.</table>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Analysis of Combined Power and Refrigeration Generation Using the Carbon Dioxide Thermodynamic Cycle to Recover the Waste Heat of an Internal Combustion Engine 

Figure 5 | Analysis of Combined Power and Refrigeration Generation Using the Carbon Dioxide Thermodynamic Cycle to Recover the Waste Heat of an Internal Combustion Engine 