Investigation of That Heat Transfer during Laminar Fluid Flow in a Circular Tube

The problem of heat exchange during the flow of liquid in a circular tube has been studied in sufficient detail and is widely covered in the scientific literature. The solution of this type of thermophysical problems is obtained in the form of infinite series and is presented in detail in the monograph [2]. In this case, it is necessary to determine the eigenvalues and eigenfunctions depending on the number of Bio. The article examines the roots of the characteristic equation and suggests simple algebraic equations for their definition. Based on the formulas obtained for the eigenvalues μ, μ, μ rather narrow ranges of changes in their values are indicated depending on the value of the Bio number. The formulas obtained make it possible to determine the smallest and largest values of eigenvalues in a certain range of Bio numbers. The resulting numerical values of the eigenvalues have sufficient accuracy for engineering calculations.