• Transport Phenomena Academy: Fluid Mechanics, Heat & Mass Transfer

  Biot and Nusselt Analogy and Difference in Heat Transfer Analysis

  Posted by Aliyar Javadi on July 6, 2024 at 6:27 pm

  Biot and Nusselt Analogy and Difference in Heat Transfer Analysis: Biot and Nusselt dimensionless numbers, both can be defined as hL/K , however with a big difference on K and L types:

  Thermal conductivity K (W/m·C):

  In Biot “K” is for solid, while “K” in Nu is for ambient fluid. Convective heat transfer coefficient “h” is a similar concept in both (h: W/m²·C).

  Characteristic length “L”:

  In Biot “L” is defined considering Volume/Surface of the solid body, in which we study heat conduction in its volume “V” with convective heat transfer to the ambient fluid via its surface “S”.

  “L” in Nusselt is the characteristic length for fluid flow such as diameter of the tube, in general concept we may define it like hydraulic diameter, D=4A/P, indicating ratio of cross-sectional area of the flow (A) to perimeter of the cross-section (P).

  Biot vs. Nusselt:

  “Biot=hL/K” indicates the ratio of “heat convection between solid body and ambient fluid” respect to the “heat conduction in solid body”, in which thermal conductivity “Kf” is related to the solid body.

  “Nusselt=hL/Kf” indicates the ratio of “heat convection between solid body and ambient fluid” respect to “heat conduction of the fluid (thin film) attached to solid surface”, in which thermal conductivity “Kf” is related to the ambient fluid (stagnant film attached to the solid surface, considering no slip boundary conditions, event for turbulent flows over a solid surface).

  Biot History and Application:

  The Biot number is named after Jean-Baptiste Biot (1774-1862), a French physicist and mathematician. The concept of the Biot number was developed to simplify the analysis of heat conduction problems where internal temperature gradients are minimal. It became a standard dimensionless group in heat transfer analysis during the 20th century.

  Biot Application:

  Bi≪1: Lumped system analysis is valid; internal temperature gradients are negligible, and the entire object can be assumed to have a uniform temperature.

  Bi≫1: Significant internal temperature gradients exist; detailed analysis is required.

  Nusselt History and application:

  Nusselt number is named after Wilhelm Nusselt (1882-1957), a German engineer who made pioneering contributions to the study of convective heat transfer. Nusselt’s work in the early 20th century laid the foundation for modern convective heat transfer theory. His dimensionless number became a fundamental tool for analyzing and designing heat exchangers and other systems involving convective heat transfer.

  Nusselt Application: The importance of Nusselt is developing empirical functions Nu=f (Re, Pr) by which we can estimate heat transfer coefficient “h” considering averaged Reynolds Number which is fluid+flow properties, and Pr= (μ/ρ)/(K/ρ*C) which is fluid properties. Indeed the required “h” for Biot can be found via Nusselt.

  We will discussed this in details during our upcoming Course on “Heat Transfer and Thermal Engineering”, starting 23 August (Registration Link https://lnkd.in/eRvHhdFW , Supervised-Live Online Course )

  Reference: Transport Phenomena Academy: Fluid Mechanics, Heat & Mass Transfer https://lnkd.in/ePErpz8R , World-Academies.Com

  Aliyar Javadi replied 3 months ago 1 Member · 0 Replies
• 0 Replies

Log In to Reply