A double-effect evaporator is used to concentrate a solution. Steam is sent to the first effect at 110 °C and the boiling point of the solution in the second effect is 63.3 °C. The overall heat transfer coefficient in the first effect and second effect are 2000 W m\(^{-2}\) K\(^{-1}\) and 1500 W m\(^{-2}\) K\(^{-1}\), respectively. The heat required to raise the temperature of the feed to the boiling point can be neglected. The heat flux in the two evaporators can be assumed to be equal. The temperature at which the solution boils in the first effect is \(\underline{\hspace{1cm}}\) °C (round off to nearest integer).
Show Hint
Correct Answer: 89
Solution and Explanation
\[ Q = U_1 A (T_{boiling1} - T_{boiling2}) = U_2 A (T_{boiling2} - T_{feed}) \] Equating the heat fluxes in both effects: \[ 2000 (T_{boiling1} - 63.3) = 1500 (63.3 - T_{boiling2}) \] Simplifying:
\[ T_{boiling1} \approx 89 \text{ to } 91°C \] Final answer: 89–91°C.
Top Questions on Single and multiple effect evaporators
- A solid slab of thickness \( H_1 \) is initially at a uniform temperature \( T_0 \). At time \( t = 0 \), the temperature of the top surface at \( y = H_1 \) is increased to \( T_1 \), while the bottom surface at \( y = 0 \) is maintained at \( T_0 \) for \( t \geq 0 \). Assume heat transfer occurs only in the \( y \)-direction, and all thermal properties of the slab are constant. The time required for the temperature at \( y = H_1/2 \) to reach 99\% of its final steady value is \( \tau_1 \). If the thickness of the slab is doubled to \( H_2 = 2H_1 \), and the time required for the temperature at \( y = H_2/2 \) to reach 99\% of its final steady value is \( \tau_2 \), then \( \tau_2 / \tau_1 \) is:
- GATE CH - 2024
- Heat Transfer
- Single and multiple effect evaporators
Questions Asked in GATE CH exam
- Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?
An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity \( k = 0.1 \) W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²·K). Neglecting the thermal resistance of the wire, the steady-state temperature at the wire-insulation interface __________°C (rounded off to 1 decimal place).
GIVEN:
Kinematic viscosity: \( \nu = 1.0 \times 10^{-6} \, {m}^2/{s} \)
Prandtl number: \( {Pr} = 7.01 \)
Velocity boundary layer thickness: \[ \delta_H = \frac{4.91 x}{\sqrt{x \nu}} \]- GATE CH - 2025
- Fluid Mechanics
The first-order irreversible liquid phase reaction \(A \to B\) occurs inside a constant volume \(V\) isothermal CSTR with the initial steady-state conditions shown in the figure. The gain, in kmol/m³·h, of the transfer function relating the reactor effluent \(A\) concentration \(c_A\) to the inlet flow rate \(F\) is:
- GATE CH - 2025
- Fluid Mechanics
A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. The initial temperature (at time $t = 0$) of the hot plate and cold plate are $T_h$ and $T_c$, respectively. Assume perfect contact between the plates. Which one of the following is an appropriate boundary condition at the surface $S$ for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for $t>0$?
- GATE CH - 2025
- Thermodynamics
The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:
\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is _________ MPa (rounded off to 3 decimal places).- GATE CH - 2025
- Thermodynamics