{"id":4139,"date":"2025-09-09T08:53:40","date_gmt":"2025-09-09T06:53:40","guid":{"rendered":"https:\/\/ghetool.eu\/?post_type=knowledgebase&#038;p=4139"},"modified":"2025-09-21T21:10:53","modified_gmt":"2025-09-21T19:10:53","slug":"flujo-de-modelizacion-y-sonda-vario","status":"publish","type":"knowledgebase","link":"https:\/\/ghetool.eu\/es_es\/knowledgebase\/modelling-flux-and-vario-probe\/","title":{"rendered":"Modelizaci\u00f3n de la sonda FLUX y VARIO"},"content":{"rendered":"<p>As of today, the GEROtherm\u00ae FLUX and VARIO probes are available in GHEtool Cloud. In this article, we will shed light on the mathematical model behind these conical probes and explain how it affects their hydraulic and thermal behaviour.<\/p>\n<p><iframe title=\"Modelling the VARIO and FLUX probe in GHEtool Cloud\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/vIkxKlQVuD0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<h2>GEROtherm\u00ae FLUX and VARIO probes<\/h2>\n<p>The GEROtherm\u00ae FLUX and VARIO probes are two innovative heat exchangers developed by HakaGerodur. They are designed to have the same pressure rating as a regular smooth geothermal probe, but with a lower pressure drop. To achieve this, the wall thickness of the probe is increased towards the end of the borehole, ensuring the required strength where the static pressure is highest. This design gives the VARIO and FLUX probes an overall larger inner diameter, which is beneficial for reducing pressure drop. A vertical cross-section of a FLUX probe is shown below.<\/p>\n<blockquote><p><span style=\"color: #3366ff;\"><strong>!Note<\/strong><\/span><br \/>\n<span style=\"color: #3366ff;\">From a modelling perspective, the GEROtherm\u00ae VARIO and GEROtherm\u00ae FLUX are both considered conical pipes. However, FLUX probes are designed for very deep boreholes (up to 500\u202fm), while VARIO probes are intended for shallower systems (up to 250\u202fm). For more information, you can visit HakaGerodur\u2019s website <a style=\"text-decoration: underline; color: #3366ff;\" href=\"https:\/\/www.hakagerodur.ch\/en\/gs-products\/\" target=\"_blank\" rel=\"noopener\">here<\/a>.<\/span><\/p><\/blockquote>\n<figure id=\"attachment_4140\" aria-describedby=\"caption-attachment-4140\" style=\"width: 829px\" class=\"wp-caption aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-4140 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/FLUX43-example.png\" alt=\"Vertical cross section of the GEROtherm\u00ae FLUX DN43 PN32 probe.\" width=\"829\" height=\"623\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/FLUX43-example.png 829w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/FLUX43-example-300x225.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/FLUX43-example-768x577.png 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/FLUX43-example-16x12.png 16w\" sizes=\"(max-width: 829px) 100vw, 829px\" \/><figcaption id=\"caption-attachment-4140\" class=\"wp-caption-text\">Vertical cross section of the GEROtherm\u00ae FLUX DN43 PN32 probe.<\/figcaption><\/figure>\n<h2>One pipe, three regions<\/h2>\n<p>When we take a closer look at the pipe, we can see it consists of three subsections. The first part of the probe is a regular smooth pipe with a constant wall thickness, for which the solution is already known. The last part of the probe is also a regular pipe with a constant, but different, wall thickness. The region in between, where the wall thickness increases, is where we need to develop a new model.<\/p>\n<blockquote><p><span style=\"color: #3366ff;\"><strong>!Note<\/strong><\/span><br \/>\n<span style=\"color: #3366ff;\">Some specific GEROtherm\u00ae VARIO probes end after the conical section and do not include a final, \u2018regular\u2019 section. This has no impact on the further development of the model.<\/span><\/p><\/blockquote>\n<figure id=\"attachment_4142\" aria-describedby=\"caption-attachment-4142\" style=\"width: 2560px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-4142 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-scaled.png\" alt=\"The three different models for the conical probe design.\" width=\"2560\" height=\"1258\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-scaled.png 2560w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-300x147.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-1024x503.png 1024w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-768x377.png 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-1536x755.png 1536w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-2048x1007.png 2048w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/three-regions-1-18x9.png 18w\" sizes=\"(max-width: 2560px) 100vw, 2560px\" \/><figcaption id=\"caption-attachment-4142\" class=\"wp-caption-text\">The three different sections of the conical probe design.<\/figcaption><\/figure>\n<p>A first idea might be to simply take an average value of the parameters we are interested in (such as the Reynolds number, friction factor, etc.) between the start and end of the conical section. However, since these parameters are not linear, this does not provide a good estimate. A more accurate approach is to use something called the <em data-start=\"377\" data-end=\"397\">mean value theorem<\/em>, which is briefly discussed in the next section.<\/p>\n<h2>Mean value theorem<\/h2>\n<div class=\"relative flex-col gap-1 md:gap-3\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"7fff3af0-e3d0-42be-a1e5-dba4cb264a39\" data-message-model-slug=\"gpt-4o\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light\">\n<p data-start=\"38\" data-end=\"332\" data-is-last-node=\"\" data-is-only-node=\"\">Typically, when we calculate an average value, we take two values and divide their sum by two. This inherently assumes a linear relationship between those two values. But what if the relationship is not linear\u2014more like the red curve in the graph below? How do we then calculate the mean value?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<figure id=\"attachment_4143\" aria-describedby=\"caption-attachment-4143\" style=\"width: 844px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-4143 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/mean-value-theorem.jpg\" alt=\"Graphical illustration of the mean value theorem.\" width=\"844\" height=\"646\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/mean-value-theorem.jpg 844w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/mean-value-theorem-300x230.jpg 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/mean-value-theorem-768x588.jpg 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/mean-value-theorem-16x12.jpg 16w\" sizes=\"(max-width: 844px) 100vw, 844px\" \/><figcaption id=\"caption-attachment-4143\" class=\"wp-caption-text\">Graphical illustration of the mean value theorem. (source: https:\/\/www.statisticshowto.com\/calculus-problem-solving\/intermediate-value-theorem\/mean-value-theorem)<\/figcaption><\/figure>\n<p>The mean value theorem can be described with the following formula:\u00a0$$f(c)=\\frac{1}{b-a} \\int_a^b{f(x)dx}$$<\/p>\n<p>where $a$ and $b$ are the boundary points between which we want to calculate the mean value of the function between points $a$ and $b$\u00a0(illustrated by the red squares in the figure above). The idea is to find a green rectangle with the same base width $b\u2212a$ and the same area. The height of this rectangle, $f(c)$, is the average value we are looking for.<\/p>\n<article class=\"text-token-text-primary w-full\" dir=\"auto\" data-testid=\"conversation-turn-34\" data-scroll-anchor=\"true\">\n<div class=\"text-base my-auto mx-auto py-5 [--thread-content-margin:--spacing(4)] @[37rem]:[--thread-content-margin:--spacing(6)] @[72rem]:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:32rem] @[34rem]:[--thread-content-max-width:40rem] @[64rem]:[--thread-content-max-width:48rem] mx-auto flex max-w-(--thread-content-max-width) flex-1 text-base gap-4 md:gap-5 lg:gap-6 group\/turn-messages focus-visible:outline-hidden\" tabindex=\"-1\">\n<div class=\"group\/conversation-turn relative flex w-full min-w-0 flex-col agent-turn\">\n<div class=\"relative flex-col gap-1 md:gap-3\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"bb061c55-2c57-4c3c-a97a-f78a8461a266\" data-message-model-slug=\"gpt-4o\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light\">\n<p data-start=\"671\" data-end=\"1189\" data-is-last-node=\"\" data-is-only-node=\"\">At first, this may seem overly complicated. However, if we look at the graph of the Reynolds number in the conical region of the probes, we see a clear difference. Since we are working with long probes (up to 500\u202fm for the GEROtherm\u00ae FLUX), this difference can have a significant impact\u2014especially in the laminar\u2013turbulent transition region. For the calculation of the Reynolds number, the friction factor, the pressure drop, and the effective borehole thermal resistance, this mean value theorem is therefore applied.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<figure id=\"attachment_4144\" aria-describedby=\"caption-attachment-4144\" style=\"width: 640px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4144 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Example-reynolds-number.png\" alt=\"Difference between using the average value and the mean value theorem for the Reynolds number in the conical part.\" width=\"640\" height=\"480\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Example-reynolds-number.png 640w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Example-reynolds-number-300x225.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Example-reynolds-number-16x12.png 16w\" sizes=\"(max-width: 640px) 100vw, 640px\" \/><figcaption id=\"caption-attachment-4144\" class=\"wp-caption-text\">Difference between using the average value and the mean value theorem for the Reynolds number in the conical part.<\/figcaption><\/figure>\n<blockquote><p><span style=\"color: #3366ff;\"><strong>!Note<\/strong><\/span><br \/>\n<span style=\"color: #3366ff;\">The equation above also allows for analytical solutions. Although a full mathematical derivation is outside the scope of this article, the equation for the Reynolds number in the conical region can be written as: $$\\overline{Re}(x)=\\frac{-1}{x}\\frac{4\\rho \\dot{V}}{\\pi \\mu}\\frac{1}{2a}\\left[ln(D_{in,start}-2ax)-ln(D_{in,start})\\right]$$ where $x$ is the position in the conical part of the probe [m] and $a$ is the rate of increase in wall thickness, $\\dot{V}$ the volume flow rate [m\u00b3\/s], $D_{in,start}$ the initial wall thickness at the start of the conical part [m] and the other parameters $\\rho$ and $\\mu$ are respectively the fluid density [kg\/m\u00b3] and the dynamic viscosity [Pa.s]. For more information on the Reynolds number, the reader is referred to <a style=\"text-decoration: underline;\" href=\"https:\/\/ghetool.eu\/knowledgebase\/what-is-the-reynolds-number\/\">this article<\/a>.<\/span><\/p><\/blockquote>\n<h2>Behavior of the conical probes<\/h2>\n<article class=\"text-token-text-primary w-full\" dir=\"auto\" data-testid=\"conversation-turn-38\" data-scroll-anchor=\"true\">\n<div class=\"text-base my-auto mx-auto py-5 [--thread-content-margin:--spacing(4)] @[37rem]:[--thread-content-margin:--spacing(6)] @[72rem]:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:32rem] @[34rem]:[--thread-content-max-width:40rem] @[64rem]:[--thread-content-max-width:48rem] mx-auto flex max-w-(--thread-content-max-width) flex-1 text-base gap-4 md:gap-5 lg:gap-6 group\/turn-messages focus-visible:outline-hidden\" tabindex=\"-1\">\n<div class=\"group\/conversation-turn relative flex w-full min-w-0 flex-col agent-turn\">\n<div class=\"relative flex-col gap-1 md:gap-3\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"1df49c77-63cf-4bab-a02d-4b5b1d371956\" data-message-model-slug=\"gpt-4o\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light\">\n<p data-start=\"38\" data-end=\"328\" data-is-last-node=\"\" data-is-only-node=\"\">Below is the graph showing the pressure drop of a GEROtherm\u00ae FLUX DN53 PN38 probe for different probe lengths. For comparison, the pressure drop of regular DN53 probes is also shown, using the starting wall thickness (pressure class PN14) and the final wall thickness (pressure class PN38).<\/p>\n<p data-start=\"38\" data-end=\"328\" data-is-last-node=\"\" data-is-only-node=\"\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4145 size-full aligncenter\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_depth.png\" alt=\"Pressure drop of a double GEROtherm\u00ae FLUX DN53 PN38 probe in function of depth for a 25% MEG mixture (@3\u00b0C) and 0.9 l\/s.\" width=\"638\" height=\"478\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_depth.png 638w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_depth-300x225.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_depth-16x12.png 16w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<p>Pressure drop of a double GEROtherm\u00ae FLUX DN53 PN38 probe in function of depth for a 25% MEG mixture @3\u00b0C and 0.9 l\/s.<\/p>\n<p data-start=\"38\" data-end=\"511\">Initially, the pressure drop of the FLUX probe follows the same trend as that of the regular PN14 probe, with the deviation starting at 140\u202fm\u2014where the conical section begins. Beyond this point, the pressure drop increases until it becomes more or less parallel to that of the regular PN38 probe. It is clear that for a system 500\u202fm deep, this difference in wall thickness has a significant impact on the overall pressure drop and, consequently, on pump energy consumption.<\/p>\n<p data-start=\"513\" data-end=\"820\">In the graph below, the depth is kept constant at 500\u202fm, while the flow rate is varied. Initially, the pressure drops are very similar due to the laminar flow regime. Around 0.4\u202fl\/s, the regular PN38 probe begins to transition into the turbulent zone, which is visible as a sudden increase in pressure drop.<\/p>\n<p data-start=\"822\" data-end=\"1218\" data-is-last-node=\"\" data-is-only-node=\"\">The same transition occurs at a higher flow rate for the PN14 probe. This is because its larger inner diameter results in a lower flow velocity, delaying the onset of turbulence. For the FLUX probe, the transition also begins around 0.4\u202fl\/s, but it is less pronounced\u2014since only part of the probe has the same PN38 wall thickness\u2014resulting in an overall lower pressure drop across all flow rates.<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_4147\" aria-describedby=\"caption-attachment-4147\" style=\"width: 638px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4147 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_volume.png\" alt=\"Pressure drop of a double GEROtherm\u00ae FLUX DN53 PN38 probe of 500m.\" width=\"638\" height=\"479\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_volume.png 638w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_volume-300x225.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_volume-16x12.png 16w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><figcaption id=\"caption-attachment-4147\" class=\"wp-caption-text\">Pressure drop of a double GEROtherm\u00ae FLUX DN53 PN38 probe of 500m.<\/figcaption><\/figure>\n<div class=\"relative flex-col gap-1 md:gap-3\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"f1c8147c-9fe9-4243-89d1-54f8744d9a37\" data-message-model-slug=\"gpt-4o\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light\">\n<p data-start=\"38\" data-end=\"181\" data-is-last-node=\"\" data-is-only-node=\"\">The final graph, which is of key importance for geothermal design, is of course the effective borehole thermal resistance. This is shown below.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<figure id=\"attachment_4146\" aria-describedby=\"caption-attachment-4146\" style=\"width: 638px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4146 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_rb.png\" alt=\"Effective borehole thermal resistance of a double GEROtherm\u00ae FLUX DN53 PN38 probe of 500m.\" width=\"638\" height=\"478\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_rb.png 638w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_rb-300x225.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/07\/Flux_rb-16x12.png 16w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><figcaption id=\"caption-attachment-4146\" class=\"wp-caption-text\">Effective borehole thermal resistance of a double GEROtherm\u00ae FLUX DN53 PN38 probe of 500m.<\/figcaption><\/figure>\n<p>For a probe of this length, the figure looks slightly different from the one we saw in <a style=\"text-decoration: underline;\" href=\"https:\/\/ghetool.eu\/knowledgebase\/borehole-thermal-resistance\/\">our previous article<\/a>, where the drop between the laminar and turbulent regimes was more pronounced. Here, since the probe is relatively long, this effect\u2014although still present\u2014is smaller. As you can see, the thermal performance of the conical FLUX probe is comparable to that of the other probes up to 0.5\u202fl\/s, but it starts to deviate beyond that point. Interestingly, the thermal performance is better than that of the regular PN38 pipe, due to its overall thinner wall thickness.<\/p>\n<blockquote><p><span style=\"color: #3366ff;\"><strong>!Note<\/strong><\/span><br \/>\n<span style=\"color: #3366ff;\">Due to its conical design, the heat transfer rate is not uniform along the depth of the probe, as turbulence and pipe resistance vary. However, since the g-functions are calculated using a boundary condition of uniform borehole wall temperature, this variation does not affect the accuracy of the model. More information on the g-function calculation can be found <a style=\"text-decoration: underline; color: #3366ff;\" href=\"https:\/\/ghetool.eu\/knowledgebase\/g-functions\/\">here<\/a>.<\/span><\/p><\/blockquote>\n<h2>GEROtherm\u00ae FLUX and VARIO probes in GHEtool Cloud<\/h2>\n<p>All the GEROtherm\u00ae FLUX and VARIO probes from HakaGerodur are now available in GHEtool Cloud in the drop-down list of all the heat exchangers.<\/p>\n<figure id=\"attachment_4261\" aria-describedby=\"caption-attachment-4261\" style=\"width: 806px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4261 size-full\" src=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/09\/GHEtool.png\" alt=\"Print screen of the Gerotherm FLUX and VARIO probes in GHEtool Cloud.\" width=\"806\" height=\"430\" srcset=\"https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/09\/GHEtool.png 806w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/09\/GHEtool-300x160.png 300w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/09\/GHEtool-768x410.png 768w, https:\/\/ghetool.eu\/wp-content\/uploads\/2025\/09\/GHEtool-18x10.png 18w\" sizes=\"(max-width: 806px) 100vw, 806px\" \/><figcaption id=\"caption-attachment-4261\" class=\"wp-caption-text\">Print screen of the Gerotherm FLUX and VARIO probes in GHEtool Cloud.<\/figcaption><\/figure>\n<h2>Conclusion<\/h2>\n<p data-start=\"1101\" data-end=\"1380\">This article described the mathematical model for the GEROtherm\u00ae FLUX and VARIO probes developed by HakaGerodur. It was shown that using a simple average to model the conical section is not sufficiently accurate, and that the mean value theorem provides a more reliable approach.<\/p>\n<p data-start=\"1382\" data-end=\"1758\" data-is-last-node=\"\" data-is-only-node=\"\">The results demonstrated that, especially at greater depths, the pressure drop is significantly reduced thanks to the conical design and its overall larger inner diameter. The thermal performance was similar to that of regular probes at lower flow rates, but at higher flow rates, a clear thermal improvement was observed compared to a regular pipe of the same pressure class.<\/p>\n<h2 id=\"reference\">References<\/h2>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li>Watch our video explanation over on our YouTube page by clicking <a style=\"text-decoration: underline;\" href=\"https:\/\/youtu.be\/vIkxKlQVuD0\" target=\"_blank\" rel=\"noopener\">here<\/a>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A partir de hoy, las sondas GEROtherm\u00ae FLUX y VARIO est\u00e1n disponibles en GHEtool Cloud. En este art\u00edculo, arrojaremos luz sobre el modelo matem\u00e1tico que hay detr\u00e1s de estas sondas c\u00f3nicas y explicaremos c\u00f3mo afecta a su comportamiento hidr\u00e1ulico y t\u00e9rmico.<\/p>","protected":false},"template":"","pdf-article":[97],"authors":[39],"knowledgebase-category":[67],"class_list":["post-4139","knowledgebase","type-knowledgebase","status-publish","hentry","pdf-article-flux-and-vario-probes","authors-wouter-peere","knowledgebase-category-physics"],"_links":{"self":[{"href":"https:\/\/ghetool.eu\/es_es\/wp-json\/wp\/v2\/knowledgebase\/4139","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ghetool.eu\/es_es\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ghetool.eu\/es_es\/wp-json\/wp\/v2\/types\/knowledgebase"}],"wp:attachment":[{"href":"https:\/\/ghetool.eu\/es_es\/wp-json\/wp\/v2\/media?parent=4139"}],"wp:term":[{"taxonomy":"pdf-article","embeddable":true,"href":"https:\/\/ghetool.eu\/es_es\/wp-json\/wp\/v2\/pdf-article?post=4139"},{"taxonomy":"authors","embeddable":true,"href":"https:\/\/ghetool.eu\/es_es\/wp-json\/wp\/v2\/authors?post=4139"},{"taxonomy":"knowledgebase-category","embeddable":true,"href":"https:\/\/ghetool.eu\/es_es\/wp-json\/wp\/v2\/knowledgebase-category?post=4139"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}