TY - JOUR

T1 - Finite-Difference analysis of the generalized graetz problem with heat convection boundary condition

AU - Arıcı, Müslüm

AU - Macia, Yunesky Masip

AU - Campo, Antonio

N1 - Publisher Copyright:
© 2020 by Begell House, Inc.

PY - 2020

Y1 - 2020

N2 - The present study addresses forced convection heat transfer of an internal viscous fluid in a tube with fully developed laminar velocity and uniform entrance temperature. The internal viscous fluid exchanges heat with an external viscous fluid moving normally to the tube at a diﬀerent temperature. Specifically, the description corresponds to a generalized Graetz problem with heat convection boundary condition. Contrary to the tradition in vogue, the standard method of separation of variables and the ensuing Sturm-Liouville theory are not employed for solving the generalized Graetz problem in the present study. Rather, the goal of the study is to implement an approximate finite diﬀerence methodology with an explicit scheme. The primary thermal quantity of interest in the study is the mean bulk temperature of the internal viscous fluid accounting for the entire range of modified Biot numbers (0 < Bi < ∞). Subsequently, the other thermal quantities of secondary interest in the study are the wall temperature and the total heat transfer. The agreement of the approximate numerical results with the counterpart exact analytical results is excellent for all values of Bi ranging from 0 to 100 in practice. The exact analytical results expressed in terms of the generalized Graetz series are considered as the baseline solutions in the heat convection literature.

AB - The present study addresses forced convection heat transfer of an internal viscous fluid in a tube with fully developed laminar velocity and uniform entrance temperature. The internal viscous fluid exchanges heat with an external viscous fluid moving normally to the tube at a diﬀerent temperature. Specifically, the description corresponds to a generalized Graetz problem with heat convection boundary condition. Contrary to the tradition in vogue, the standard method of separation of variables and the ensuing Sturm-Liouville theory are not employed for solving the generalized Graetz problem in the present study. Rather, the goal of the study is to implement an approximate finite diﬀerence methodology with an explicit scheme. The primary thermal quantity of interest in the study is the mean bulk temperature of the internal viscous fluid accounting for the entire range of modified Biot numbers (0 < Bi < ∞). Subsequently, the other thermal quantities of secondary interest in the study are the wall temperature and the total heat transfer. The agreement of the approximate numerical results with the counterpart exact analytical results is excellent for all values of Bi ranging from 0 to 100 in practice. The exact analytical results expressed in terms of the generalized Graetz series are considered as the baseline solutions in the heat convection literature.

KW - Finite diﬀerence method

KW - Fully developed laminar velocity

KW - Heat convection boundary condition

KW - Numerical temperature field

KW - Total heat transfer

KW - Two-dimensional energy equation

KW - Uniform entrance temperature

UR - http://www.scopus.com/inward/record.url?scp=85088289777&partnerID=8YFLogxK

U2 - 10.1615/HEATTRANSRES.2020031877

DO - 10.1615/HEATTRANSRES.2020031877

M3 - Article

AN - SCOPUS:85088289777

SN - 1064-2285

VL - 51

SP - 797

EP - 806

JO - Heat Transfer Research

JF - Heat Transfer Research

IS - 8

ER -