VM271

VM271
Convection Treatment Problem for a Hollow Cylinder with Fluid Flow

Overview

Reference:

Vedat S.Arpaci, Ahmet Selamet, Shu-Hsin Kao, "Introduction to Heat Transfer", 2000, pg. 90-100.

Analysis Type(s):

Static analysis (ANTYPE = 0)

Element Type(s):

Coupled Thermal Fluid Pipe (FLUID116)

3D Thermal Surface Effect (SURF152)

3D Thermal Solid (SOLID70)

4-Node Thermal Shell (SHELL131)

3D Layered Thermal Solid (SOLID278)

4-Node Thermal Shell (SHELL294)

Input Listing:

vm271.dat

Test Case

A hollow cylinder is modeled with an inner radius of 0.01105m, an outer radius of 0.02m and a length of 0.1m. Fluid is made to flow through a hollow cylinder to simulate the convection problem. Surface effect elements with film coefficients are used in between the fluid and cylinder to include the convection loads. The inlet temperature of the fluid, mass flow rate of the fluid, and the bulk temperature at the outer cylinder surface are defined. A static analysis is performed on the model to determine the nodal temperature of the fluid elements.

Figure 471: Problem Sketch

Material Properties

Geometric Properties

Loading

Fluid:

Specific heat for fluid = 0.5474 J/kg°C

Thermal conductivity for fluid = 1.0e-16 W/m°C

Cylinder:

Thermal conductivity for cylinder = 1000 W/m°C

Inner radius (R1) = 0.01105 m

Outer radius (R2) = 0.02 m

Length (L) = 0.1 m

Inlet temperature of fluid (T_inlet) = 700 °C

Temperature at the outer cylinder (T_bulk) = 2000 °C

Film coefficients for surface element = 300 W/m²°C

Mass flow rate for fluid = 7.2 (kg/sec)

Analysis Assumptions and Modeling Notes

FLUID116 elements with temperature degrees of freedom only and with exponential upwind difference shape function are used to model the fluid flowing through the cylinder. The problem is solved for four cases with the hollow cylinder modeled using SOLID70 elements for case 1, SHELL131 elements for case 2, layered SOLID278 elements for case 3, and SHELL294 for case 4. SURF152 elements are used to model surface elements for specifying convection loads. The MSTOLE command is used to map the FLUID116 elements with SURF152 elements by adding two extra nodes from fluid to the surface elements. This is achieved by setting KEYOPT 5 =2 for SURF152 elements after the ESURF command and before issuing the MSTOLE command. The outer surface of the cylinder is held at a fixed temperature of 2000° C. The solid thermal conductivity is set very high so that the fluid experiences a bulk temperature of 2000° C. The inlet temperature and outer temperature of the cylinder are specified using the D command. The mass flow rate for the fluid element and film coefficient for surface element is defined using the SFE command. Static solve is performed for all three cases and nodal temperatures for FLUID116 elements are computed and compared with analytical solutions. The analytical solution is obtained using the equation below as defined in the reference book.

Where:

= main flow rate of the fluid

h = film coefficient

A = convection area

c_p = specific heat for fluid

Results Comparison

SOLID70	Node	Location (Z)	Temperatures
	Node	Location (Z)	Target	Mechanical APDL	Ratio
	1	0.000	700.000	700.000	1.000
	3	0.333	909.970	909.795	1.000
	4	0.667	1086.027	1085.734	1.000
	2	1.000	1233.647	1233.279	1.000
SHELL131	Node	Location (Z)	Temperatures
	Node	Location (Z)	Target	Mechanical APDL	Ratio
	1	0.000	700.000	700.000	1.000
	3	0.333	909.970	909.781	1.000
	4	0.667	1086.027	1085.710	1.000
	2	1.000	1233.647	1233.249	1.000
SOLID278	Node	Location (Z)	Temperatures
	Node	Location (Z)	Target	Mechanical APDL	Ratio
	1	0.000	700.000	700.000	1.000
	3	0.333	909.970	909.785	1.000
	4	0.667	1086.027	1085.715	1.000
	2	1.000	1233.647	1233.256	1.000
SHELL294	Node	Location (Z)	Temperatures
	Node	Location (Z)	Target	Mechanical APDL	Ratio
	1	0.000	700.000	700.000	1.000
	3	0.333	909.970	909.795	1.000
	4	0.667	1086.027	1085.734	1.000
	2	1.000	1233.647	1233.279	1.000