$23\mathrm{.}12\mathrm{.}2023$

HEAT TRANSFER PROJECT WORK

Water is desired to be heated from $10C$ to $50C$ using a shell$-$and$-$tube heat exchanger. For this, hot water of mass flow rate $m_i=$dotsk$\frac{g}{s},$ flows through the pipes of the heat exchanger as temperature decreases to $t_1=$dots$C$ from $t_2=$dots$C.$ In the shell$-$side, the cold fluid needed to be heated, flows. The pipes are made of steel with a thermal conductivity of $k=$dots$\frac{W}{m^2}K.$ Tube diameters are $\frac{d_i}{d_o}=21mm/25$ mm and length of each pipe is $L=$dotsm. The heat exchanger is insulated against its environment. You are requested to design a counter$-$flow one$-$shell and one$-$tube pass heat exchanger. Hence, keep track of the path as follows:

a$)$ Find heat transfer rate between hot and cold fluids.

b$)$ Determine mass flow rate of the cold fluid.

c$)$ Find logarithmic mean temperature difference.

d$)$ By predicting the overall heat transfer coefficient between two fluids $(U_{\text{p}\text{r}\text{e}\text{d}}),$ find out number of tubes and diameter of the shell. According to this geometry, find out $h_i$ for fluid flow through tubes and $h_o$ for flow from the shell$-$side. Using those convection heat transfer coefficients, calculate overall heat transfer coefficient $(U_{\text{c}\text{a}\text{l}\text{c}}).$ Repeat calculations until $U_{\text{c}\text{a}\text{l}\text{c}}$ approximates $U_{\text{p}\text{r}\text{e}\text{d}}.$ The number of tubes andshell diameter have been acquired when this approximation is met.

e$)$ According to those results, technically draw this heat exchanger.

f$)$ Calculate pumping power requirements separately for both fluids.

Notes: $(1)$ In your calculations, select necessary equations and correlations, substitute values and reach results.

$\backslash$table$[[$Heat Transfer Project Work Data$],[L[m],k[\frac{W}{m}K],t_1[C],t_2[C],m_i[k\frac{g}{s}]$