Строительная теплофизика / 7
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<ha^mrguc j_`bf a^Zgby |
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<ha^mohijhgbpZ_fhklv h]jZ`^Zxsbo dhgkljmdpbc b __ \ebygb_ gZ \ha^mrgh |
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l_ieh\hc b \eZ`ghklguc j_`bfu ihf_s_gbc
Ijb jZaghklb J \ha^moZ k h^ghc b ^jm]hc klhjhgu HD q_j_a g__ fh`_l ijhgbdZlv \ha^mo \ gZijZ\e_gbb hl [hevr_]h J d f_gvr_fm Wlh y\e_gb_ gZau\Z_lky nbevljZpb_c ?keb nbevljZpby ijhbkoh^bl \ gZijZ\e_gbb hl gZjm`gh]h \ha^moZ \ ihf_s_gb_ lh hgZ gZau\Z_lky bgnbevljZpb_c ijb h[jZlghf gZijZ\e_gbb±wdknbevljZpb_c K\hckl\h HD beb fZl_jbZeZ ijhimkdZlv \ha^mo gZau\Z_lky \ha^mohijhgbpZ_fhklvx
JZaghklv J \ha^moZ gZ gZjm`ghc b \gmlj_gg_c ih\_joghklb HD \hagbdZ_l \ke_^kl\b_ jZaghklb ρ gZjm`gh]h b \gmlj_gg_]h \ha^moZ ]jZ\blZpbhggh_ ^Z\e_gb_ b ih^ \ebygb_f \_ljZ \_ljh\h_ ^Z\e_gb_
=jZ\blZpbhggh_ ^Z\e_gb_ < abfg__ \j_fy \ha^mo \ hlZieb\Z_fuo ihf_s_gbyo bf__l [hevrmx l_fi_jZlmjm q_f \ha^mo kgZjm`b Ijb wlhf gZjm`guc \ha^mo [m^_l bf_lv [hevrmx ρ q_f \ha^mo \ ihf_s_gbb JZaghklv ρ \ha^moZ b kha^Z_l jZaghklv _]h J GZ jbk ko_fZlbqgh bah[jZ`_gh ihi_j_qgh_ k_q_gb_ hlZieb\Z_fh]h ihf_s_gby k ^\mfy gZjm`gufb kl_gZfb
Jbk Ko_fZ jZkiheh`_gby g_cljZevghc iehkdhklb ijb gZebqbb ]jZ\blZpbhggh]h ^Z\e_gby
?keb \ lZdhf a^Zgbb ihe b ihlhehd [m^ml \ha^mohijhgbpZ_fufb lh q_j_a gb`gxx iheh\bgm gZjm`guo kl_g \ha^mo [m^_l ijhgbdZlv \gmljv a^Zgby Z q_j_a \_jogxx iheh\bgm±moh^blv ba g_]h GZ k_j_^bg_ \ukhlu ihf_s_gby ∆ J \ha^moZ [m^_l jZ\gh
g_cljZevgZy iehkdhklvPD[<_ebqbgZ ∆ J [m^_l m iheZ b ih^ ihlhedhf < g_dhlhjhf k_q_gbb Z Z hlklhys_c hl g_cljZevghc iehkdhklb gZ jZkklhygbbK\_ebqbgZ ∆ J khklZ\bl
∆ 3 = K ρ g − ρ \
]^_ ρ g ρ \ khhl\_lkl\_ggh iehlghklv gZjm`gh]h b \gmlj_gg_]h \ha^moZ d] f
>ey ihf_s_gby k_q_gb_ dhlhjh]h ihdZaZgh gZ jbk fZdkbfZevgZy \_ebqbgZ ]jZ\blZpbb J hij_^_ebl ih nhjfme_
∆ 3 = + ρ g − ρ \
]^_ G±\ukhlZ ihf_s_gby F <_ljh\h_ ^Z\e_gb_ Ih^ ^_ckl\b_f \_ljZ gZ gZ\_lj_gghc ih\_joghklb a^Zgby jbk
\hagbdZ_l ba[ulhqgh_ J Z gZ aZ\_lj_gghc ih\_joghklb±jZajy`_gb_ <_ebqbgZ ba[ulhqgh]h klZlbq_kdh]h ^Z\e_gby ∆ Jkl \_ljh\h]h ^Z\e_gby jZ\gZ
∆3kl = N − N ρ :+
=^_ D b D ±Zwjh^bgZfbq_kdb_ dhwnnbpb_glu khijhlb\e_gby k gZ\_lj_gghc b aZ\_lj_gghc klhjhg a^Zgby ρ :+ ^bgZfbq_kdh_ ^Z\e_gb_ gZ[_]Zxs_]h gZ a^Zgb_ ihlhdZ \ha^moZ Ijb kh\f_klghf ^_ckl\bb gZ a^Zgb_ ]jZ\blZpbhggh]h b \_ljh\h]h J \_ebqbgZ J \ ex[hc lhqd_ gZ ih\_joghklb a^Zgby jZ\gZ
3 = + ρ g − ρ \ + |
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<ha^mohijhgbpZ_fhklv HD hp_gb\Z_lky \h \_ebqbg_ khijhlb\e_gby \ha^mohijhgbpZgbx
>ey kiehrguo keh_\ fZl_jbZeh\ khijhlb\e_gb_ \ha^mohijhgbpZgbx5+ hij_^_ey_lky ih nhjfme_
5g = δ L
]^_ δ lhesbgZ kehy FLdhwnnbpb_gl \ha^mohijhgbpZ_fhklb fZl_jbZeZ d] f q IZ
oZjZdl_jbamxsbc dhebq_kl\h \ha^moZ \ d] dhlhjh_ ijhoh^bl q_j_a f HD aZ qZk ijb
∆ J IZ
NbevljZpby gZjm`gh]h \ha^moZ q_j_a HD \ oheh^guc i_jbh^ ]h^Z \uau\Z_l ^hihegbl_evgu_ ihl_jb l_iehlu ihf_s_gby Z lZd`_ hoeZ`^_gb_ \gmlj_gg_c ih\_joghklb HD hkh[_ggh \ kh\j_f_gguo fgh]hwlZ`guo a^Zgbyo Ihwlhfm KGbI,, ©Kljhbl_evgZy l_iehl_ogbdZªh]jZgbqb\Zxl \ha^mohijhgbpZ_fhklv HD
Khijhlb\e_gb_ \ha^mohijhgbpZ_fhklb5G""""g_ f_g__ lj_[m_fZy ih KGbI,,i
aZ bkdexq_gb_f""""k\_lh\uo ijh_fh\ hdhg [Zedhgguo ^\_j_c b nhgZj_c5+lj f q IZ d]
5G ≥ 5+lj = ∆Ρ * +
]^_*+ ghjfZlb\ \ha^mohijhgbpZgby HD
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H]jZ`^Zxsb_ dhgkljmdpbb |
GhjfZlb\ |
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\ha^mohijhgbpZ_fhklb |
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*+ d] f q |
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GZjm`gu_ kl_gu i_j_djulby b ihdjulby |
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`beuo h[s_kl\_gguo \kihfh]Zl_evguo |
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a^Zgbc |
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Lh `_ ijhba\h^kl\_gguo a^Zgbc |
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<oh^gu_ ^\_jb \ d\Zjlbju |
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HdgZ [Zedhggu_ ^\_jb b \hjhlZ |
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ijhba\h^kl\_gguo a^Zgbc \ jZchgZo kh |
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kj_^g_c l_fi_jZlmjhc gZb[he__ oheh^ghc |
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iylb^g_\db Wg = − b gb`_ |
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Lh `_ k Wg = − b \ur_ |
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Kludb f_`^m iZg_eyfb gZjm`guo HD |
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`beuo a^Zgbc g_ [he__ |
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>ey ijZdlbq_kdbo jZkq_lh\ ∆ J IZ nhjfZ aZibkb \ \b^_
∆ 3 = J+ ρ G − ρ \ + ρ g Z
]^_ G±\ukhlZ a^Zgby hl ih\_joghklb a_feb ^h \_joZ dZjgbaZ F ρ g ρ \ khhl\_lkl\_ggh iehlghklv gZjm`gh]h b \gmlj_gg_]h \ha^moZ
ρ = + W\g WgZj WgZb[he__ oheh^ghc iylb^g_\db h[_ki_q
Kdhjhklv \_ljZ ih jmf[Zf aZ yg\Zjv ih\lhjy_fhklv dhlhjh]h khklZ\ey_l b [he__ ijbf_f ih KgbI©Kljhbl_evgZy debfZlheh]by b ]_hnbabdZª>ey lbih\uo ijh_dlh\ ijbf_f jZ\ghc f k Z \ debfZlbq_kdbc ih^jZchg ; b = jZ\ghc f k Khijhlb\e_gb_ \ha^mohijhgbpZ_fhklb fgh]hkehcghc HD 5g f q IZ d] hij_^_ebf ih nhjfme_ 5QL = 5Q + 5Q + + 5LQ
]^_ 5Q 5Q 5LQ khijhlb\e_gb_ \ha^mohijhgbpZ_fhklb hl^_evguo keh_\ h]jZ`^_gby ijb\_^_g \ ijbeh`_gbb KGbI,,kf lZ[e
Khijhlb\e_gb_ \ha^mohijhgbpZ_fhklb fZl_jbZeh\ b dhgkljmdpbc
LZ[ebpZ
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FZl_jbZeu b HD |
LhesbgZ kehy ff |
Khijhlb\e_gb_ |
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\ha^mohijhgbpZ_fhklb |
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;_lhg kiehrghc [_a r\h\ |
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DZjlhg kljhbl_evguc [_a r\h\ |
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DbjibqgZy deZ^dZ ba kbebdZlgh]h |
b [he__ |
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dbjibqZ gZ p_f_glgh i_kqZghf |
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jZkl\hj_ |
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Khijhlb\e_gb_ \ha^mohijhgbpZ_fhklb hdhg b [Zedhgguo ^\_j_c `beuo b h[s_kl\_gguo a^Zgbc Z lZd`_ hdhg b nhgZj_c ijhba\h^kl\_gguo a^Zgbc 5Q ^he`gh [ulv g_ f_g__ lj_[m_fh]h khijhlb\e_gby \ha^mohijhgbpZ_fhklb 5Q lj b hij_^_ey_lky ih nhjfme_
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∆ 3 |
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lj |
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5Q |
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∆ 3 |
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]^_ ∆ 3 = jZaghklv J \ha^moZ ijb dhlhjhf hij_^_e_gh khijhlb\e_gb_ \ha^mohijhgbpZ_fhklb 5Q b J±kf n
<ebygb_ nbevljZpbb \ha^moZ gZ l_iehi_j_^Zqm
< fgh]hwlZ`guo a^Zgbyo ba djmighjZaf_jguo we_f_glh\ \ha^mohijhgbpZ_fhklv kms_kl\_ggh \eby_l gZ l_ieh\hc j_`bf ihf_s_gbc b ihl_jb l_iehlu q_j_a hl^_evgu_ HD <ebygb_ \ha^mohijhgbpZ_fhklb gZ l_iehhl^Zqm ^ey jZaebqguo we_f_glh\ HD hdZau\Z_lky ih jZaghfm BgnbevljZpby gZjm`gh]h \ha^moZ q_j_a hdgZ dhlhju_ bf_xl gZb[hevrmx \ha^mohijhgbpZ_fhklv k\yaZgu k m\_ebq_gb_f l_iehihl_jv bgnbevljZpby q_j_a fZkkb\ HD b kludb \ hkgh\ghf \uau\Z_l kgb`_gb_ l_fi_jZlmju \gmlj_gg_c ih\_joghklb HD Ijb nbevljZpbb \ha^moZ l_fi_jZlmjgh_ ihe_ b l_iehh[f_g gZ ih\_joghklb HD baf_gy_lky \ j_amevlZl_ l_iehi_j_ghkZ ihlhdhf \ha^moZ
L_fi_jZlmjZ gZ \gmlj_gg_c ih\_joghklb ihjbklh]h HD ijb bgnbevljZpbb gZjm`gh]h \ha^moZ
τ \ |
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− Wg |
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H&% M 5 −5% − |
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H&% M5 |
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]^_ K< l_ieh_fdhklv \ha^moZ 5 khijhlb\e_gb_ l_iehi_j_^Zq_ HD 5% = |
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Ijb wdknbevljZpbb jZkoh^ \gmlj_gg_]h \ha^moZ \ nhjfme_ [_j_lky«kh agZdhf © ªGZjm`guc \ha^mo ijhoh^y q_j_a HD gZ\klj_qm dhg^mdlb\ghfm aZ kq_l l_iehijh\h^ghklb HD ihlhdm l_jy_fhc ihf_s_gb_f l_iehlu gZ]j_\Z_lky b ihklmiZ_l \ ihf_s_gb_ k [hevr_c l_fi_jZlmjhc q_f _]h gZqZevgZy Ijhbkoh^bl k\h_h[jZagZy j_dmi_jZpby qZklbqguc \ha\jZl \ ihf_s_gb_ l_iehlu dhlhjZy ihlj_[h\ZeZkv [u gZ
ih^h]j_\ gZjm`gh]h \ha^moZ Ijb fZeuo jZkoh^Zo \ha^moZ ijb agZq_gbyo hlghkbl_evgh]h dhwnnbpb_glZ nbevljZpbhggZy l_iehh[f_gZ K< M5 < nbevljZpbx \ha^moZ fh`gh g_ mqblu\Zlv±l_iehihl_jb baf_g_gby f_gvr_ q_f gZ Ijb [hevrbo jZkoh^Zo \ha^moZ q_j_a ihjbklu_ HD dh]^Z K< M5 > ihl_jv l_iehlu nZdlbq_kdb g_ [m^_l l d ljZgkfbkkbbhgguc l_ieh\hc ihlhd ihqlb p_ebdhf [m^_l bkihevah\Zlvky gZ gZ]j_\ gZjm`gh]h \ha^moZ ihklmiZxs_]h \ ihf_s_gb_
< KGbI,,khijhlb\e_gb_ \ha^mohijhgbpZ_fhklb 5Q HD j_]eZf_glbjm_lky lj_[m_fhc _]h \_ebqbghc 5Q lj dhlhjZy ^he`gZ h[_ki_qblv ghjfZlb\gmx ijhgbpZ_fhklv \ha^moZ * g ^ey kl_g±^ey \oh^guo ^\_j_c±^ey hdhg± ± d]
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kf lZ[e ijb jZkq_l_ ∆ J \ha^moZ gZ gZjm`ghc b \gmlj_gg_c ih\_joghklyo gZjm`ghc HD
Mq_l \ha^mrgh]h j_`bfZ a^Zgby ijb jZkq_l_ hlhie_gby b \_glbeypbb
<ebygb_ abfg_]h \ha^mrgh l_ieh\h]h j_`bfZ ihf_s_gbc ijb jZkq_l_ kbkl_f hlhie_gby b \_glbeypbb jZkkfhlj_gh gZfb jZg__ \ e_dpbb
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E_lgbc l_ieh\hc j_`bf ihf_s_gby
JZkq_l fhsghklb kbkl_fu \_glbeypbb b dhg^bpbhgbjh\Zgby \ha^moZ ijb [hjv[_ k l_iehba[uldZfb
Hkh[_gghklvx e_lg_]h l_ieh\h]h j_`bfZ a^Zgbc y\ey_lky hij_^_e_gb_ l_iehihklmie_gby hl kheg_qghc jZ^bZpbb HgZ bf__l i_jbh^bqguc oZjZdl_j \ l_q_gb_ kmlhd qlh h[mkeZ\eb\Z_l lbibqgmx g_klZpbhgZjghklv ijhp_kkh\ l_iehh[f_gZ \ e_lgbc i_jbh^ < `Zjdb_ e_lgb_ f_kypu a^Zgby ih^\_j]Zxlky i_j_]j_\m qlh ijb\h^bl d kha^Zgbx ^bkdhfnhjlZ lhieb\guo mkeh\bc b dZd ke_^kl\b_ d kms_kl\_gguf i_j_gZijy`_gbyf kbkl_fu l_jfhj_]meypbb q_eh\_dZ
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4h]j + 4\_gl + 4l_og =
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MdZaZggu_ l_iehihklmie_gby y\eyxlky i_j_f_ggufb \h \j_f_gb \_ebqbgZfb <_ebqbgm4h]j hij_^_eyxl h[uqgh ^ey dZ`^h]h qZkZ jZkq_lguo e_lgbo kmlhd iml_f keh`_gby l_iehihklmie_gby q_j_a jZaebqgu_ \b^u fZkkb\guo g_ijhajZqguo HD kl_gu ihdjulby b emq_ijhajZqguo hdgZ nhgZjb HD jZaebqghc hjb_glZpbb
Ijb i_j_f_gguo l_ogheh]bq_kdbo l_ieh\u^_e_gbyo ih ^Zgguf l_ogheh]bq_kdh]h ijh_dlZ ^ey dZ`^h]h qZkZ jZkq_l kmlhd hij_^_ey_lky 4l_og KdeZ^u\Zy \_ebqbgu 4h]j b 4l_og ihemqZxl djb\mx jZkq_lgmx ihqZkh\h]h baf_g_gby l_iehihklmie_gby \ ihf_s_gb_4i Z
lZd`_ fZdkbfZevgh_ bo agZq_gb_
4Q PD[ = 4h]j + 4l_og PD[
AgZq_gb_ 4i bgh]^Z ijbgbfZxl dZd jZkq_l l_iehba[uldZ ^ey hij_^_e_gghc fhsghklb kbkl_f \_glbeypbb b KD< Ijb wlhf mklZgh\hqgZy fhsghklv KD< ihemqZ_lky \ur_ gZ
b [he__
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ihf_s_gby |
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hjb_glZpby ih klhjhgZf k\_lZ h[^m\ \_ljhf b l ^
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GZ ih^h]j_\ \ju\Zxs_]hky oheh^gh]h \ha^moZ >h[Z\dZ gZ ih^h]j_\ \ju\Zxs_]hky q_j_a gZjm`gu_ ^\_jb g_ h[hjm^h\Zggufb \ha^mrgufb beb \ha^mrgh lhieb\gufb aZ\_kZfb oheh^gh]h \ha^moZ ijb \ukhl_ a^Zgby G fh`_l ijbgbfZlvky \
jZaf_j_ β = G ^ey o ^\_j_c k ^\mfy lZf[mjZfb f_`^m gbfb β = G ±^ey o ^\_j_c k lZf[mjhf f_`^m gZfb β = G ^ey o ^\_j_c [_a lZf[mjZ b β = G ±^ey h^bgZjguo ^\_j_c >ey gZjm`guo \hjhl g_ h[hjm^h\Zgguo \ha^mrghc beb \ha^mrgh lhieb\ghc aZ\_khc β = ijb hlkmlkl\bb lZf[mjZ b β = ±ijb gZebqbb lZf[mjZ m \hjhl >ey e_lgbo b aZiZkguo gZjm`guo ^\_j_c b \hjhl ^h[Z\hqgu_ ihl_jb l_ieZ g_ mqblu\Zxlky
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4Q = ∑ |
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4′ = /ρ |
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