Page 1 of 3

Department of Mechanical Engineering

Indian Institute of Technology Bombay

ME415: Computational Fluid Dynamics & Heat Transfer

Assignment # 3: Unsteady Computational Heat Advection and Convection for Cartesian Geometry on a

Uniform Grid: Physics based Approach

Instructor: Prof. Atul Sharma,

Date Posted: 10/02/2015 Due Date: 17/02/15 ONLINE SUBMISSION THROUGH MOODLE ONLY (No late submission allowed): Create a

single zipped file consisting on (a) filled- in answer sheet of this doc file converted into a pdf file and (b) all the computer programs. The name of the zipped file should be rollnumber_A1

Note: Both problem and answer sheet are provided below. SCILAB or MATLAB should be used for programming as

well as generating graphical results.

1. 2D Computational Heat Advection (CHA):

Consider a 2D Cartesian (x,y) computational domain of size L=1m and H=1 m, for CHA of a fluid (=1000

kg/m3 and cp=4180 W/m.K) moving with a uniform velocity u=v=1 m/s and an initial temperature of 50

0C. The

left and top boundary of the domain is subjected to 1000C; and the bottom and right boundary to 0

0C

Using the physics based FVM as well as solution methodology, develop a computer program

A3_1_2DAdvection for the above problem, run the code for three different advection schemes: (a) FOU, (b)

SOU and (c) QUICK. Take the maximum number of grid points in x-and y-direction as imax=jmax=32 and

convergence criteria as 0.000001.

Report the results as

a) Plot and discuss the steady state temperature contours for the different advection schemes (3

figures).

b) Plot and discuss the temperature profile at the vertical centerline(x=0.5), T(y), for the different

advection schemes (3 figures).

2. 2D Computational Heat Convection (CHC):

Consider a 2D Cartesian computational x-y domain of size L=6 unit and H=1 unit, for CHC with a prescribed

velocity field. This corresponds to a slug flow (u=1, v=0) of a fluid in a channel; subjected to a non-dimensional

temperature of 1 at the inlet and 0 at the walls. At the outlet, fully developed Neumann BC is used. The initial

condition for non-dimensional temperature of the fluid is 0.

Using the physics based FVM as well as solution methodology, develop a computer program

A3_2_2DConvection for the above problem, run the code for two different advection schemes: (a) FOU and

(b) QUICK; at Re=10 and Pr=1 (you can take any value of thermo-physical properties to obtain the given Re

and Pr). Take the maximum number of grid points in x-and y-direction as imax=62 and jmax=22, respectively;

and convergence criteria as 0.000001.

Report the results as

a) Plot and discuss the steady state temperature contours for the different advection schemes (2

figures).

b) Plot and discuss the temperature profile, T(y), at different axial locations (x/L=0.2, 0.4, 0.6, 0.8 and

1), for the different advection schemes (2 figures).

BEST OF LUCK

Keep Playing with the Codes in Future also.

Page 2 of 3

Answer Sheet

Problem # 1: 2D Computational Heat Advection (CHA):

a) Plot and discuss the steady state temperature contours for the different advection schemes (3 figures).

b) Plot and discuss the temperature profile at the vertical centerline(x=0.5), T(y), for the different advection

schemes (3 figures).

(a1)

(b1)

(a2)

(b2)

(a3)

(b3)

Fig. 3.1: Steady state temperature contours using the (a1) FOU scheme (a2) SOU scheme (a3) QUICK

scheme. Temperature variation along the vertical centerline using the (b1) FOU scheme (b2) SOU scheme (b3) QUICK scheme The plots shown are Temperature vs y for x=0.5.

Fou scheme is the most deviating from the analytical solution, whereas quick and sou are closer approximations to the analytical solution. Quick and sou schemes nevertheless do not show a continous increasing trend like fou scheme. According to the analytical solution there is a abrupt

change in temperature at the diagonal of the plate.

Page 3 of 3

Problem # 2: 2D Computational Heat Convection (CHC):

a) Plot and discuss the steady state temperature contours for the different advection schemes (2

figures).

b) Plot and discuss the temperature profile, T(y), at different axial locations (x/L=0.2, 0.4, 0.6, 0.8 and

1), for the different advection schemes (2 figures).

Assuming Tinlet=100C and Twall=0. Ycoordinate vs temperature.

Legend used in graphs b1&b2: x/L=0.2(+), 0.4(o), 0.6(*), 0.8(.), 1(x)

(a1)

(b1)

(a2)

(b2)

Fig. 3.2: Steady state temperature contours using the (a1) FOU scheme and (a2) QUICK scheme.

Temperature variation at different axial locations using the (b1) FOU scheme and (b2) QUICK scheme.

The fou scheme gives higher values of steady state temperature for a given point compared to the quick scheme. The steady state temperature contour shows that the temperature keeps getting closer to the wall

temperature along the length.