Mathematical Modeling of Double-Skin  Facade in Northern Area of China

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">External structure type</td><td align="center">Concrete-perlites-85</td><td align="center">Low-e hollow glass curtain wall</td><td align="center">The DSF</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">Total annual heat load <svg height="15.375" id="M40" style="vertical-align:-2.52519pt" version="1.1" viewbox="0 0 52.387501 15.375" width="52.387501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.425)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,46.437,12.425)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g><g transform="matrix(.017,-0,0,-.017,5.95,12.163)"><path d="M513 0l-137 -2q-16 18 -164 198q-19 22 -31 22q-7 0 -16 -3v-111q0 -49 11.5 -61t60.5 -17v-26h-223v26q50 4 61.5 17t11.5 61v472q0 50 -10 61.5t-56 15.5v24q57 6 144 35v-471q37 7 63 35q31 31 71 88q16 23 10.5 31.5t-40.5 12.5v26l204 9v-25q-51 -8 -75 -19.5
t-54 -39.5q-31 -31 -86 -95q13 -21 70 -87.5t85 -95.5q48 -52 100 -55v-26z" id="x6B"></path></g><g transform="matrix(.017,-0,0,-.017,14.296,12.163)"><path d="M696 437v-26q-37 -5 -50.5 -18.5t-28.5 -55.5q-36 -96 -120 -348h-29l-69.5 178.5l-52.5 132.5l-54.5 -141l-64.5 -170h-28q-71 229 -116 357q-13 39 -25.5 49.5t-48.5 15.5v26h207v-26q-45 -7 -53.5 -17t2.5 -44l74 -232h2l116 314h26q39 -111 120 -318h2q50 156 69 231
q10 38 0.5 48.5t-58.5 17.5v26h180z" id="x77"></path></g><g transform="matrix(.017,-0,0,-.017,29.697,12.163)"><path d="M170 255q0 -25 -16 -41t-40 -16t-40 16t-16 41t16 41.5t40 16.5t40 -16.5t16 -41.5z" id="x22C5"></path></g><g transform="matrix(.017,-0,0,-.017,37.364,12.163)"><path d="M513 0h-211v26q44 5 55 17t11 60v166q0 123 -98 123q-59 0 -104 -51v-238q0 -48 10 -60.5t55 -16.5v-26h-213l1 26q46 4 57 16t11 61v477q0 48 -9.5 58.5t-58.5 14.5v24q63 9 147 35v-336q73 73 143 73q64 0 101 -42t37 -129v-175q0 -49 11 -61t55 -16v-26z" id="x68"></path></g>
</svg></td><td align="center">411844.3</td><td align="center">514763</td><td align="center">439217.6</td></tr><tr><td align="left">Total annual cooling <svg height="15.375" id="M41" style="vertical-align:-2.52519pt" version="1.1" viewbox="0 0 52.387501 15.375" width="52.387501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.425)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,46.437,12.425)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g><g transform="matrix(.017,-0,0,-.017,5.95,12.163)"><path d="M513 0l-137 -2q-16 18 -164 198q-19 22 -31 22q-7 0 -16 -3v-111q0 -49 11.5 -61t60.5 -17v-26h-223v26q50 4 61.5 17t11.5 61v472q0 50 -10 61.5t-56 15.5v24q57 6 144 35v-471q37 7 63 35q31 31 71 88q16 23 10.5 31.5t-40.5 12.5v26l204 9v-25q-51 -8 -75 -19.5
t-54 -39.5q-31 -31 -86 -95q13 -21 70 -87.5t85 -95.5q48 -52 100 -55v-26z" id="x6B"></path></g><g transform="matrix(.017,-0,0,-.017,14.296,12.163)"><path d="M696 437v-26q-37 -5 -50.5 -18.5t-28.5 -55.5q-36 -96 -120 -348h-29l-69.5 178.5l-52.5 132.5l-54.5 -141l-64.5 -170h-28q-71 229 -116 357q-13 39 -25.5 49.5t-48.5 15.5v26h207v-26q-45 -7 -53.5 -17t2.5 -44l74 -232h2l116 314h26q39 -111 120 -318h2q50 156 69 231
q10 38 0.5 48.5t-58.5 17.5v26h180z" id="x77"></path></g><g transform="matrix(.017,-0,0,-.017,29.697,12.163)"><path d="M170 255q0 -25 -16 -41t-40 -16t-40 16t-16 41t16 41.5t40 16.5t40 -16.5t16 -41.5z" id="x22C5"></path></g><g transform="matrix(.017,-0,0,-.017,37.364,12.163)"><path d="M513 0h-211v26q44 5 55 17t11 60v166q0 123 -98 123q-59 0 -104 -51v-238q0 -48 10 -60.5t55 -16.5v-26h-213l1 26q46 4 57 16t11 61v477q0 48 -9.5 58.5t-58.5 14.5v24q63 9 147 35v-336q73 73 143 73q64 0 101 -42t37 -129v-175q0 -49 11 -61t55 -16v-26z" id="x68"></path></g>
</svg></td><td align="center">183457.6</td><td align="center">409413.4</td><td align="center">369627.6</td></tr><tr><td align="left">Total annual load statistics <svg height="15.375" id="M42" style="vertical-align:-2.52519pt" version="1.1" viewbox="0 0 52.387501 15.375" width="52.387501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.425)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,46.437,12.425)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g><g transform="matrix(.017,-0,0,-.017,5.95,12.163)"><path d="M513 0l-137 -2q-16 18 -164 198q-19 22 -31 22q-7 0 -16 -3v-111q0 -49 11.5 -61t60.5 -17v-26h-223v26q50 4 61.5 17t11.5 61v472q0 50 -10 61.5t-56 15.5v24q57 6 144 35v-471q37 7 63 35q31 31 71 88q16 23 10.5 31.5t-40.5 12.5v26l204 9v-25q-51 -8 -75 -19.5
t-54 -39.5q-31 -31 -86 -95q13 -21 70 -87.5t85 -95.5q48 -52 100 -55v-26z" id="x6B"></path></g><g transform="matrix(.017,-0,0,-.017,14.296,12.163)"><path d="M696 437v-26q-37 -5 -50.5 -18.5t-28.5 -55.5q-36 -96 -120 -348h-29l-69.5 178.5l-52.5 132.5l-54.5 -141l-64.5 -170h-28q-71 229 -116 357q-13 39 -25.5 49.5t-48.5 15.5v26h207v-26q-45 -7 -53.5 -17t2.5 -44l74 -232h2l116 314h26q39 -111 120 -318h2q50 156 69 231
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</svg></td><td align="center">595301.9</td><td align="center">924176.4</td><td align="center">808845.2</td></tr><tr><td align="left">Heating season heat load indicators <svg height="23.3125" id="M43" style="vertical-align:-5.82849pt" version="1.1" viewbox="0 0 54.087502 23.3125" width="54.087502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,16.262)"><path d="M378 -385l-22 -26q-139 111 -208 287.5t-69 394.5v1q0 215 69 391.5t208 289.5l22 -26q-104 -98 -162 -274t-58 -382q0 -205 58.5 -381.5t161.5 -274.5z" id="xF6022"></path></g><g transform="matrix(.017,-0,0,-.017,7.587,15.988)"><path d="M696 437v-26q-37 -5 -50.5 -18.5t-28.5 -55.5q-36 -96 -120 -348h-29l-69.5 178.5l-52.5 132.5l-54.5 -141l-64.5 -170h-28q-71 229 -116 357q-13 39 -25.5 49.5t-48.5 15.5v26h207v-26q-45 -7 -53.5 -17t2.5 -44l74 -232h2l116 314h26q39 -111 120 -318h2q50 156 69 231
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t-52 18.5v23q79 14 139 41v-81q3 2 29 20.5t44 29.5q45 28 81 28t66 -22t46 -61q25 20 83 57q39 26 76 26q59 0 93 -40t34 -113v-193q0 -49 10.5 -60.5t54.5 -16.5v-26z" id="x6D"></path></g>
<g transform="matrix(.012,-0,0,-.012,40.162,7.825)"><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>
<g transform="matrix(.017,-0,0,-.017,46.5,16.262)"><path d="M364 271q0 -218 -69 -394.5t-208 -287.5l-22 26q103 98 161.5 274.5t58.5 381.5q0 206 -58 382t-162 274l22 26q139 -113 208 -289.5t69 -391.5v-1z" id="xF6032"></path></g>
</svg></td><td align="center">27.5</td><td align="center">34.3</td><td align="center">29.3</td></tr><tr><td align="left">Air conditioning season's cold load indicators <svg height="23.3125" id="M44" style="vertical-align:-5.82849pt" version="1.1" viewbox="0 0 54.087502 23.3125" width="54.087502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,16.262)"><path d="M378 -385l-22 -26q-139 111 -208 287.5t-69 394.5v1q0 215 69 391.5t208 289.5l22 -26q-104 -98 -162 -274t-58 -382q0 -205 58.5 -381.5t161.5 -274.5z" id="xF6022"></path></g><g transform="matrix(.017,-0,0,-.017,7.587,15.988)"><path d="M696 437v-26q-37 -5 -50.5 -18.5t-28.5 -55.5q-36 -96 -120 -348h-29l-69.5 178.5l-52.5 132.5l-54.5 -141l-64.5 -170h-28q-71 229 -116 357q-13 39 -25.5 49.5t-48.5 15.5v26h207v-26q-45 -7 -53.5 -17t2.5 -44l74 -232h2l116 314h26q39 -111 120 -318h2q50 156 69 231
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t-52 18.5v23q79 14 139 41v-81q3 2 29 20.5t44 29.5q45 28 81 28t66 -22t46 -61q25 20 83 57q39 26 76 26q59 0 93 -40t34 -113v-193q0 -49 10.5 -60.5t54.5 -16.5v-26z" id="x6D"></path></g>
<g transform="matrix(.012,-0,0,-.012,40.162,7.825)"><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>
<g transform="matrix(.017,-0,0,-.017,46.5,16.262)"><path d="M364 271q0 -218 -69 -394.5t-208 -287.5l-22 26q103 98 161.5 274.5t58.5 381.5q0 206 -58 382t-162 274l22 26q139 -113 208 -289.5t69 -391.5v-1z" id="xF6032"></path></g>
</svg></td><td align="center">17.65</td><td align="center">31.4</td><td align="center">24.6</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Building energy consumption when the external wall is changed.

Mathematical Problems in Engineering

tab5

Table 5

Table 5: Mathematical Modeling of Double-Skin  Facade in Northern Area of China 