# CONVECTIVE HEAT AND MASS TRANSFER (ME-642A)
## ASSIGNMENT QUESTIONS

*1)* $Pr=1.3$ , $\rho=1000kg/m^3$ , $u_\infty=1m/s$ , $\mu=0.01pa-s$ , $k=3.23 W/m-k$ , $c_p=4200J/Kg-k$.
*The local nusselt number at a distance of $1m$ from the leading edge of the plate will be*

*2)* *Sphere of diameter $1m$ is maintained at temp $500K$ , surrounding air at temp $400K$ , moving with velocity $50m/s$, the average heat flux from the surface to the air is $40KW/m^2$. If second sphere of diameter $2m$ is maintained at same temperature $500K$ and placed in air at $400K$ . What is average convective heat transfer coefficient of second sphere of air velocity $25m/s$*

*3)* *The forced convective heat transfer coefficient of a plate depends on*

- gravity
- velocity of fluid
- conductivity of fluid
- condictivity of plate material

*4)* *The wall of a constant diameter pipe of length $1m$ is heated uniformly with flux $q"$by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all through the pipe. The bulk temperature of the fluid is equal to $0^0C$ at the inlet and $50^0C$ at the exit. The wall temperatures are measured at three locations $P,Q,R$ as shown in the figure .The flow thermally develops after some distance from the inlet. The following measurements are made:*

| Point | P | Q | R
| -------- | -------- | -------- | -------
| Wall temperature $^0c$ |50 | 80 | 90


*Among the locations P, Q and R, the flow is thermally developed at*

- P,Q,R
- P and Q only
- Q and R only
- R only

*5)* *Solve the laminar boundary layer for constant free-stream velocity, using the momentum integral equation and an assumption that the velocity profile may be approximated by*
$$\frac{u}{u_\infty} = sin{\frac{\pi y}{2\delta}}$$

*Evaluate the momentum thickness, displacement thickness, and friction coefficient, and compare with the exact solution.*

*6)* *Using von Karman 's integral analysis, show that for a liquid metal flowing over a flat plate maintained at constant temperature the local Nusselt number is related to the Reynolds number and the Prandtl number as*
$$Nu_x=0.53Re_x^{0.5}Pr^{0.5}$$

*7)* *Given that: $Pr$ = Prandtl number, $Nu$ = Nussett number,
$Sh$ = Shewood number, $Re$ = Reynold number,
$Sc$ = Schmidt number, $Gr$ = Grashoff number.
The functional relationship for forced convection mass and heat transfer is/are given as*

- $Nu = f(Gr,Pr)$
- $Sh = f(Sc,Gr)$
- $Nu = f(Re,Pr)$
- $Sh = f(Re,Sc)$

*Hint:
Shewood number $(Sh)$ = molecular mass transport resistance/convective mass transport resistance
$$Sh= \frac{k_cl}{D}$$*

*8)* *Power generation in a nuclear reactor is limited principally by the ability to transfer heat in a reactor: A solid fuel reactor is cooled by 1iquid sodium flowing inside small diameter stainless steel tubes. Develop an expression for Nusselt number for this case with suitable assumptions*

*9)* *A $1kW$ heater is constructed of a glass plate with an electrically conducting film that produces a constant heat flux. The plate is $60 cm$ by $60 cm$ and placed in an airstream at $27^0C$, $1 atm$ with $u_\infty = 5 m/s$. Calculate the average temperature difference along the plate and the temperature difference at the trailing edge.*

*10)* *Air at $1 atm$ and $300 K$ flows across a $20cm$ square plate at a free-stream velocity of $20 m/s$. The last half of the plate is heated to a constant temperature of $350 K$. Calculate the heat lost by the plate.*