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

*1)* *Solve the laminar boundary layer over a flat plate, parallel flow with constant and uniform 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 of blasius.*

*2)* *Engine oil at $20^0C$ is forced one side over a $20cm$ square plate at a velocity of $1.2 m/s$. The plate is heated to a uniform temperature of $60^0C$. Calculate the heat lost by the plate in $W$*

*3)* *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 liquid sodium flowing inside small diameter stainless steel tubes. Develop an expression for Nusselt number for this case with suitable assumptions.*

*Hint : Assume that the flow is steady and laminar and heat transfer is fully developed and use energy equation*

*4)* *Given that: $Pr$ = Prandtl number, $Nu$ = Nusselt number,
$Sh$ = Sherwood number, $Re$ = Reynolds 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:
Sh = molecular mass transport resistance/convective mass transport resistance
$$Sh= \frac{hl}{D}$$*

*where $D$ = Diffusivity of dissolved gas in liquid
$L$ = Characterstic length
$h$ = Convective mass transfer film coefficient*

*5)* A plate ($0.6 m$ x $0.6m$) heated by a $250 W$ heater is placed in an airflow at $27°C$, $1 atm$ with velocity= $5 m/s$. Calculate the average temperature of the plate and the local temperature of the plate at the trailing edge. *

*6)* *Water flow inside a cylindrical tube having dimension of $25 cm$ inner diamter and $20 m$ length, tube heated through uniform and constant heat flux along circumeference as well as axial. Water enters at mean temperature of $10°C$
and after heating it exits at mean temperature of $70°C$. Mass flow rate of water is taken as $720kg/h$. For steady flow, calculate Inner surface temperature at the tube exit.calculate stanton number, Peclet number, Prandlt number, calculate friction coefficient*

*7)* *A duct of cross-section $1*0.5$m is carrying air at the temperature of $20°C$ at the duct inlet position with velocity of $10m/s$. The duct is not insulated & exposed to ambient($1 atm$, $30°C$).
For laminar flow Nusselt number is $3.4$ for constant wall condition and for turbulent case $Nu=0.023*Re^{0.8}*Pr^{0.33}$
Calculate
a) Reynolds number for flow
b) Heat transer per meter length of duct in Watt Flowing fluid thermal thermal condutivity is $1W/mK$*

*8)* *Ratio of hydrodynamics boundary layer thickness to Thermal Boundary layer thickness of the flow two fluid A&B on a flat plate are $1/2$ & $2$ respectively. Reynolds number based on the plate length for both flow is $10^4$. Pr. & Nu. for fluid A is $1/8$ & $35$ then find the Pr.& Nu. for fluid B.*

*9)* *Calculate average heat transfer coefficient over heated plate surface is $100^0C$ plate temperature is uniform. Air at $20^0C$ is flowing over plate at the incident angle of $0^o$, Plate width is $1m$, air velocity is $10m/s$. Calculate heat transfer at the distance of $10cm$ from leading edge.*

*10)* *Calculate heat transfer coefficient for uniform heat flux and uniform wall temperature . Flowing fluid thermal thermal condutivity is $1W/mK$, flow is fully devloped with reynolds number of $1500$, pipe diameter $10cm$*

*11)* *A circular cylinder of $8 cm$ diameter and $10 cm$ length is exposed to a cross flow of air at a velocity of $2 m/s$. The temperature of the cylinder surface is maintained at $60°C$. Determine the convective heat transfer coefficient and the rate of heat transfer from the cylinder to the air, using the Sieder-Tate correlation for laminar flow over cylinders.*

*(Hint: The Sieder-Tate correlation for laminar flow over cylinders is given by:*

$$Nu_D = 4.36 Re_D^{1/2} Pr^{1/3}$$

*where
$Nu_D$ = Nusselt number based on the cylinder diameter
$Re_D$ = Reynolds number based on the cylinder diameter*)

*12)* *A bank of $4$ tubes of $2cm$ diameter and $1.5 m$ length is exposed to a cross flow of air at a velocity of $1.5 m/s$. The tubes are arranged in a staggered pattern with a pitch-to-diameter ratio of $1.25$. The temperature of the tube surface is maintained at $100°C$. Determine the average convective heat transfer coefficient and the rate of heat transfer from the tubes to the air, using the Gnielinski correlation for laminar flow over banks of tubes*

(*Hint : The correlation for the average Nusselt number for laminar flow over a bank of tubes is given by:*

$$Nu_D = 0.35 Pr^{0.36}(\frac{Pr}{Pr_w})^n Re_D^{0.6} $$

*$n = 0$ for gases
$n = 1/4$ for liquids*

*where
$Nu_D$ = Nusselt number based on the tube diameter
$Re_D$ = Reynolds number based on the tube diameter,
$Pr$ = Prandtl number of air at free stream temperature
$Pr_w$ = Prandtl number of air evaluated at uniform tube wall temperature*

*13)* *A flat plate of length $L = 1m$ is placed in a wind tunnel where air flows over it with a velocity of $U_\infty$ = $10 m/s$. The air temperature is maintained at a constant $T_\infty$ = $20°C$. plot the velocity profile and temperature profile along the length of the plate at a distance $y = 5mm$ from the plate surface, assuming laminar flow*

- *For properties of air refer [here](https://www.engineersedge.com/physics/viscosity_of_air_dynamic_and_kinematic_14483.htm)*
*(or) you can refer to Heat Transfer by Prof.P.S.Ghoshdastidar*
- *For properties of engine oil mentioned in Q2 refer [here](http://www.thermalfluidscentral.org/encyclopedia/index.php/Thermophysical_Properties:_Engine_Oil,_Unused)*