The overall heat transfer coefficient is a parameter that depends on the fluid velocity, material, etc., and is given by<\/p>\r\n\r\n\r\n\r\n\r\n\r\n
$$U=\\frac{1}{\\frac{1}{h_{o}}+r_{o}+\\frac{x_{l}}{k}+r_{i}+\\frac{1}{h_{i}}}\u30fb\u30fb\u30fb(2)$$<\/p>\r\n
where ho<\/sub><\/em> is the outer heat transfer coefficient, ro<\/sub><\/em> is the outer fouling factor, xl <\/sub><\/em>is the thickness of material, k<\/em> is the thermal conductivity of heat transfer tube, ri <\/sub><\/em>is the inner fouling factor, hi<\/sub><\/em> is the inner heat transfer coefficient.<\/span><\/p>\r\n\r\n\r\n\r\n\r\n\r\n Consider the heat transfer around a heat transfer tube as shown in the above figure.\u00a0<\/p>\r\n As an example, assume that a high-temperature fluid is flowing outside and a low-temperature fluid is flowing inside, and that the surface of the heat transfer tube is covered with a thin layer of dirt.\u00a0<\/p>\r\n We will consider the heat transfer from the high temperature fluid to the low temperature fluid in this case.\u00a0<\/p>\r\n In order not to have to think strictly about the length direction of the heat transfer tube, we will consider a section of small length dx of the heat transfer tube.\u00a0<\/p>\r\n First, we consider the heat transfer from the hot fluid to the surface of the dirt layer.\u00a0<\/p>\r\n Since Newton’s cooling law of convective heat transfer holds,\u00a0<\/p>\r\n\r\n\r\n\r\n $$dQ=h_{o}\u03c0D_{o}dx(T_{h}-t_{wo})\u30fb\u30fb\u30fb(3)$$<\/p>\r\n where dQ<\/em> is the heat duty in a small section, Do<\/sub><\/em> is the the outer diameter of heat transfer tube, Th<\/sub><\/em> is the bulk temperature of high temperature fluid, two<\/sub><\/em> is the surface temperature of dirt adhering to the outer surface of the heat transfer tube.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n \u00a0\u03c0Do<\/sub>dx<\/em> means the heat transfer area.<\/p>\r\n Next, we consider the dirty layer on the outer surface of the heat transfer tube.\u00a0<\/p>\r\n In the dirty layer, the inverse of the dirty coefficient r<\/em> is the heat transfer coefficient, and the heat transfer to the outer surface of the heat transfer tube is given by\u00a0<\/p>\r\n\r\n\r\n\r\n $$dQ=\\frac{1}{r_{o}}\u03c0D_{o}dx(t_{wo}-t_{1})\u30fb\u30fb\u30fb(4)$$<\/p>\r\n where ro<\/sub><\/em> is the fouling factor<\/span> of outer surface of heat transfer tube, t1<\/sub><\/em> is the outer surface temperature of heat transfer tube.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n \u00a0Since the thickness of the dirty layer is very thin, the diameter of the dirty layer is considered to be the outer diameter of the heat transfer tube Do<\/sub><\/em>. \u00a0<\/p>\r\n Next, we consider the heat transfer from the outer surface of the heat transfer tube to the inner surface.\u00a0<\/p>\r\n Since the Fourier’s law of conduction heat transfer holds for the inside of the heat transfer tube\u00a0<\/p>\r\n\r\n\r\n\r\n $$dQ=\\frac{k}{x_{l}}\u03c0D_{m}dx(t_{1}-t_{2})\u30fb\u30fb\u30fb(5)$$<\/p>\r\n where Dm<\/sub><\/em> is the mean diameter of heat transfer tube, t2<\/sub><\/em> is the Inner surface temperature of heat transfer tube.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n The average diameter of the heat transfer tube Dm<\/sub><\/em> is given by\u00a0<\/p>\r\n\r\n\r\n\r\n $$D_{m}=\\frac{D_{o}-D_{i}}{ln(D_{o}\/D_{i})}\u30fb\u30fb\u30fb(6)$$<\/p>\r\n Next, we consider the dirty layer on the inner surface of the heat transfer tube.<\/p>\r\n\r\n\r\n\r\n Since it can be considered as the same as the outer surface, the equation is given by\u00a0<\/p>\r\n\r\n\r\n\r\n $$dQ=\\frac{1}{r_{i}}\u03c0D_{i}dx(t_{2}-t_{wi})\u30fb\u30fb\u30fb(7)$$<\/p>\r\n where Di<\/sub><\/em> is the inner diameter ot heat transfer tube, twi<\/sub><\/em> is the surface temperature of the dirt adhering to the inner surface of the heat transfer tube.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n \u00a0Similarly, since the thickness of the dirt layer is thin, the diameter of the dirt layer is considered to be the inner diameter of the heat transfer tube Di<\/sub><\/em>.<\/p>\r\n Finally, we consider the heat transfer from the surface of the dirty layer to the low-temperature fluid.<\/p>\r\n Similarly, since Newton’s cooling law for convective heat transfer holds\u00a0<\/p>\r\n\r\n\r\n\r\n $$dQ=h_{i}\u03c0D_{i}dx(t_{wi}-T_{c})\u30fb\u30fb\u30fb(8)$$<\/p>\r\n where Tc<\/sub><\/em> is the bulk temperature of low temperature fluid.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n The point is that the heat duty in each section is constant at dQ<\/em> for all steady state conditions.\u00a0<\/p>\r\n Next, Eq. (4)\uff5e(8) are transformed so that the right-hand side contains only the term for the temperature difference.\u00a0<\/p>\r\n\r\n\r\n\r\n $$\\frac{dQ}{h_{i}\u03c0D_{o}dx}=T_{h}-t_{wo}$$ $$\\frac{dQ}{\\frac{1}{r_{o}}\u03c0D_{o}dx}=t_{wo}-t_{1}$$ $$\\frac{dQ}{\\frac{k}{x_{l}}\u03c0D_{m}dx}=t_{1}-t_{2}$$ $$\\frac{dQ}{\\frac{1}{r_{i}}\u03c0D_{i}dx}=t_{2}-t_{wi}$$ $$\\frac{dQ}{h_{i}\u03c0D_{i}dx}=t_{wi}-T_{c}$$<\/p>\r\n Transform the equation in this way and add the five equations together side by side.<\/p>\r\n\r\n\r\n\r\n Then two<\/sub><\/em>, t1<\/sub><\/em>, t2<\/sub><\/em>, and twi<\/sub><\/em> on the right side disappear cleanly.\u00a0<\/p>\r\n\r\n\r\n\r\n $$dQ\\frac{1}{h_{o}\u03c0D_{o}dx+\\frac{1}{r_{o}}\u03c0D_{o}dx+\\frac{k}{x_{l}}\u03c0D_{m}dx+\\frac{1}{r_{i}}\u03c0D_{i}dx+h_{i}\u03c0D_{i}dx}=T_{h}-T_{c}\u30fb\u30fb\u30fb(9)$$<\/p>\r\n There are two ways to summarize the heat transfer tubes: based on the outer diameter or based on the inner diameter.<\/p>\r\n\r\n\r\n\r\n Either can be used, but we will use the outer diameter standard here.\u00a0<\/p>\r\n If the area of the outer surface of the heat transfer tube is Ao<\/sub><\/em>, dAo<\/sub><\/em> is expressed by Eq. (10).\u00a0<\/p>\r\n\r\n\r\n\r\n $$dA_{o}=\u03c0D_{o}dx\u30fb\u30fb\u30fb(10)$$<\/p>\r\n\r\n\r\n\r\n Transforming the left-hand side into the equation,\u00a0<\/p>\r\n\r\n\r\n\r\n $$\\frac{dQ}{\u03c0D_{o}dx}[\\frac{1}{h_{o}}+r_{o}+\\frac{x_{l}}{k}(\\frac{D_{o}}{D_{m}})+r_{i}(\\frac{D_{o}}{D_{i}})+\\frac{1}{h_{i}}(\\frac{D_{o}}{D_{i}})]=T_{h}-T_{c}$$<\/p>\r\n\r\n\r\n\r\n $$\\frac{dQ}{dA_{o}}[\\frac{1}{h_{o}}+r_{o}+\\frac{x_{l}}{k}(\\frac{D_{o}}{D_{m}})+r_{i}(\\frac{D_{o}}{D_{i}})+\\frac{1}{h_{i}}(\\frac{D_{o}}{D_{i}})]=T_{h}-T_{c}$$<\/p>\r\n The term in [ ] is transferred to the right-hand side, and is called the overall heat transfer coefficient based on the outer diameter Uo<\/sub><\/em>.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n $$U_{o}=\\frac{1}{\\frac{1}{h_{o}}+r_{o}+\\frac{x_{l}}{k}(\\frac{D_{o}}{D_{m}})+r_{i}(\\frac{D_{o}}{D_{i}})+\\frac{1}{h_{i}}(\\frac{D_{o}}{D_{i}})}\u30fb\u30fb\u30fb(11)$$<\/p>\r\n\r\n\r\n\r\n In summary, we can derive Eq. (12).<\/p>\r\n\r\n\r\n\r\n $$dQ=U_{o}dA(T_{h}-T_{c})$$<\/p>\r\n\r\n\r\n\r\n $$Q=U_{o}A\u0394T\u30fb\u30fb\u30fb(12)$$<\/p>\r\n\r\n\r\n\r\n The overall heat transfer coefficient of the inside diameter standard Ui<\/sub><\/em> can be organized in the same way by using Eq. (13).\u00a0<\/p>\r\n\r\n\r\n\r\n $$dA_{i}=\u03c0D_{i}dx\u30fb\u30fb\u30fb(13)$$<\/p>\r\n\r\n\r\n\r\n When the thickness of the heat transfer tube is thin and the outer and inner diameters are almost the same, the equation may be simplified to Do<\/em>\u2248Di<\/em>\u2248Dm<\/em>.\u00a0<\/p>\r\n\r\n\r\n\r\n $$U=\\frac{1}{\\frac{1}{h_{o}}+r_{o}+\\frac{x_{l}}{k}+r_{i}+\\frac{1}{h_{i}}}\u30fb\u30fb\u30fb(14)$$<\/p>\r\n\r\n\r\n\r\n The overall heat transfer coefficient is an important index in the design of heat exchangers, and its value is empirically known depending on the fluid being handled.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n Overall heat transfer<\/p>\r\n coefficient U<\/em> [W\/(m2<\/sup>K)]<\/p>\r\n<\/td>\r\n<\/tr>\r\n Water Methanol Ammonia<\/p>\r\n Aqueous solution<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity less than 0.5 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity 0.5 – 1.0 cp)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity more than 1.0 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity less than 0.5 cp<\/span>)<\/p>\r\n<\/td>\r\n Water Methanol Ammonia Aqueous solution<\/p>\r\n (viscosity less than 2.0 cp<\/span>)<\/p>\r\n<\/td>\r\n Aqueous solution<\/p>\r\n (viscosity more than 2.0 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity less than 0.5 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity 0.5 – 1.0 cp)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity more than 1.0 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity less than 0.5 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity less than 0.5 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity 0.5 – 1.0 cp)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity 0.5 – 1.0 cp)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity more than 1.0 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity more than 1.0 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity more than 1.0 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity less than 0.5 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity less than 0.5 cp<\/span>)<\/p>\r\n<\/td>\r\n Organic fluid<\/p>\r\n (viscosity more than 1.0 cp<\/span>)<\/p>\r\n<\/td>\r\n <\/p>\r\n The above table shows the overall heat transfer coefficients for typical fluid combinations.\u00a0<\/p>\r\n If you know the U<\/em>-value as a rough guide, you can roughly check whether the value you calculated is correct.\u00a0<\/p>\r\n This is useful for those times when there is an occasional shift of a digit or two due to a unit conversion error. However, if you deviate from the standard design specifications, you may not be able to rely on them.\u00a0<\/p>","protected":false},"excerpt":{"rendered":" The overall heat transfer coefficient is used to determine the heat duty and depends on the fluid velocity, material, etc.<\/p>\n","protected":false},"author":1,"featured_media":41,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-8","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-heat-transfer"],"_links":{"self":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts\/8","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":23,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts\/8\/revisions"}],"predecessor-version":[{"id":81,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/posts\/8\/revisions\/81"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/media\/41"}],"wp:attachment":[{"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/media?parent=8"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/categories?post=8"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/chemical-engineering-review.com\/en\/wp-json\/wp\/v2\/tags?post=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Derivation of overall heat transfer coefficient<\/h2>\r\n\r\n\r\n\r\n\r\n\r\n
![\"\"](\"https:\/\/chemical-engineering-review.com\/en\/wp-content\/uploads\/sites\/2\/2022\/01\/overall-heat-transfer-coefficient-1.png\"){kind=spacer}
<\/p>\r\nReference values for overall heat transfer coefficient<\/h2>\r\n
\r\n\r\n
\r\n High temperature fluid<\/td>\r\n Low temperature fluid<\/td>\r\n \r\n \r\n \r\n Water<\/td>\r\n 1400 – 2900<\/td>\r\n<\/tr>\r\n \r\n \r\n Water<\/td>\r\n 400 – 900<\/td>\r\n<\/tr>\r\n \r\n \r\n Water<\/td>\r\n 300 – 700<\/td>\r\n<\/tr>\r\n \r\n \r\n Water<\/td>\r\n 30 – 450<\/td>\r\n<\/tr>\r\n \r\n Gas<\/td>\r\n Water<\/td>\r\n 10 – 300<\/td>\r\n<\/tr>\r\n \r\n Water<\/td>\r\n Brine<\/td>\r\n 600 – 1150<\/td>\r\n<\/tr>\r\n \r\n \r\n Brine<\/td>\r\n 250 – 600<\/td>\r\n<\/tr>\r\n \r\n Steam<\/td>\r\n \r\n 1150 – 4050<\/td>\r\n<\/tr>\r\n \r\n Steam<\/td>\r\n \r\n 600 – 2900<\/td>\r\n<\/tr>\r\n \r\n Steam<\/td>\r\n \r\n 600 – 1150<\/td>\r\n<\/tr>\r\n \r\n Steam<\/td>\r\n \r\n 300 – 600<\/td>\r\n<\/tr>\r\n \r\n Steam<\/td>\r\n \r\n 35 – 350<\/td>\r\n<\/tr>\r\n \r\n Steam<\/td>\r\n Gas<\/td>\r\n 30 – 300<\/td>\r\n<\/tr>\r\n \r\n \r\n \r\n 250 – 450<\/td>\r\n<\/tr>\r\n \r\n \r\n \r\n 100 – 350<\/td>\r\n<\/tr>\r\n \r\n \r\n \r\n 50 – 250<\/td>\r\n<\/tr>\r\n \r\n \r\n \r\n 150 – 350<\/td>\r\n<\/tr>\r\n \r\n \r\n \r\n 50 – 250<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n