Monday, November 30, 2020

GATE Chemical Engineering Questions and Answers-Heat Transfer

Consider a solid block of unit thickness for which the thermal conductivity decreases with an increase in temperature. The opposite faces of the block are maintained at constant but different temperatures: T(x = 0) > T(x = 1). Heat transfer is by steady state conduction in x-direction only. There is no source or sink of heat inside the block. In the figure below, identify the correct temperature profile in the block.

GATE 2015

 

(A)             I

(B)              II

(C)              III

(D)             IV

                                                                                                            GATE 2015

 

Answer:          (C)

 

Air is flowing at a velocity of 3 m/s perpendicular to a long pipe as shown in the figure below. The outer diameter of the pipe is d = 6 cm and temperature at the outside surface of the pipe is maintained at 100°C. The temperature of the air far from the tube is 30°C.

Data for air: Kinematic viscosity, ν = 18×10-6 m2/s; thermal conductivity, k = 0.03 W/(m.K)

Using the Nusselt number correlation: Nu= hd/k = 0.024×Re0.8, the rate of heat loss per unit length (W/m) from the pipe to air (up to one decimal place) is _______________.

GATE 2015


                                                                                                                  GATE 2015

 

                Answer:    250 W/m

 

A heated solid copper sphere (of surface area A and volume V) is immersed in a large body of cold fluid. Assume the resistance to heat transfer inside the sphere to be negligible and heat transfer coefficient (h), density (ρ), heat capacity (C), and thermal conductivity (k) to be constant. Then, at time t, the temperature difference between the sphere and the fluid is proportional to:

GATE 2015

                                                                                                            GATE 2015

 

                Answer:    (A)

 

In the figure below, the temperature profiles of cold and hot fluids in counter current double pipe heat exchangers (in different modes of operation) are shown on the left. For each case, match the heat exchange process for the fluid represented by the bold curve with the options given on the right.

GATE 2015


(A)       I-P, II-Q, III-R, IV-S

(B)        I-P, II-Q, III-S, IV-R

(C)    I-Q, II-P, III-S, IV-R

(D)    I-Q, II-S, III-P, IV-R

                                                                                                                  GATE 2015

 

                Answer:    (C)

 

Two infinitely large parallel plates (I and II) are held at temperature TI and TII (TI > TII) respectively, and placed at a distance 2d apart in vacuum. An infinitely large flat radiation shield (III) is placed in parallel in between I and II. The emissivities of all the plates are equal. The ratio of the steady state radiative heat fluxes with and without the shield is:

GATE 2015


(A)             0.5

(B)              0.75

(C)              0.25

(D)             0

                                                                                                            GATE 2015

 

                Answer:    (A)

 

Match the dimensionless numbers in Group-1 with the ratios in Group-2

GATE 2016


(A)       P-II, Q-I, R-III

(B)       P-I, Q-III, R-II

(C)       P-III, Q-I, R-II

(D)       P-II, Q-III, R-I

                                                                                                                  GATE 2016

                Answer:    (D)

 

Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. The average Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 10°C and 55°C, respectively. Assume the physical properties of the fluid and steel to remain constant within the temperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1?

(A)             0.5

(B)              0.84

(C)              1.19

(D)             1.41

                                                                                                                  GATE 2016

 

                Answer:    (C)

 

A composite wall is made of four different materials of construction in the fashion shown below. The resistance (in K/W) of each of the sections of the wall is indicated in the diagram.

GATE 2016


The overall resistance (in K/W, rounded off to the first decimal place) of the composite wall, in the direction of heat flow, is _______.

 

                                                                                                                  GATE 2016

 

        Answer:          3.9 K/W

 

A jacketed stirred tank with a provision for heat removal is used to mix sulphuric acid and water ina steady state flow process. H2SO4 (l) enters at a rate of 4 kg/h at 25oC and H2O (l) enters at a rate of 6 kg/h at 10oC. The following data are available:

            Specific heat capacity of water = 4.2 kJ kg‒1K‒1.

Specific heat capacity of aqueous solution of 40 mass% H2SO4 = 2.8 kJ (kg solution)‒1 K‒1.

            Assume the specific heat capacities to be independent of temperature.

            Based on reference states of H2SO4 (l) and H2 O (l) at 25oC, the heat of mixing for aqueous                        solution of 40 mass% H2SO4 = ‒ 650 kJ (kg H2SO4)‒1.

            If the mixed stream leaves at 40oC, what is the rate of heat removal (in kJ/h)?

(A)             1802

(B)              2558

(C)              5702

(D)             6458

                                                                                                                  GATE 2016

 

                Answer:    (A)

 

The space between two hollow concentric spheres of radii 0.1 m and 0.2 m is under vacuum. Exchange of radiation (uniform in all directions) occurs only between the outer surface (S1) of the smaller sphere and the inner surface (S2) of the larger sphere. The fraction (rounded off to the second decimal place) of the radiation energy leaving S2, which reaches S1 is _______.

                                                                                                                        GATE 2016   

 

                Answer:    0.25

 

In an experimental setup, mineral oil is filled in between the narrow gap of two horizontal smooth plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these temperatures, ONLY the radiative heat flux is negligible. The thermal conductivity of the oil does not vary perceptibly in this temperature range. Consider four experiments at steady state under different experimental conditions, as shown in the figure below. The figure shows plate temperatures and the heat fluxes in the vertical direction.

GATE 2016


What is the steady state heat flux (in W m‒2) with the top plate at 70oC and the bottom plate at 40oC?

(A)  26

(B)  39

(C)  42

(D)  63

                                                                                                                        GATE 2016

 

            Answer:          (A)

 

In a 1- 1 pass shell and tube exchanger, steam is condensing in the shell side at a temperature (Ts) of 135oC and the cold fluid is heated from a temperature (T1) of 20oC to a temperature (T2) of 90oC. The energy balance equation for this heat exchanger is

GATE 2016


Where U is the overall heat transfer coefficient, A is the heat transfer area, m is the mass flow rate of the cold fluid and cp is its specific heat. Tube side fluid is in a turbulent flow and the heat transfer coefficient can be estimated from the following equation:

Nu = 0.023 (Re)0.8 (Pr)1/3

Where Nu is the Nusselt number, Re is the Reynolds number and Pr is the Prandtl number. The condensing heat transfer coefficient in the shell side is significantly higher than the tube side heat transfer coefficient. The resistance of the wall to heat transfer is negligible. If only the mass flow rate of the cold fluid is doubled, what is the outlet temperature (in oC) of the cold fluid at steady state?

(A)  80.2

(B)  84.2

(C)  87.4

(D)  88.6

                                                                                                                        GATE 2016

 

                   Answer:    (B)

 

The one dimensional unsteady heat conduction equation is

GATE 2017


Where T - Temperature, t - time, r - radial position, k - thermal conductivity, ρ-density, and Cp – specific heat.

For the cylindrical co-ordinate system, the value of n in the above equation is

(A)             0

(B)              1

(C)              2

(D)             3

GATE 2017

            Answer:          (B)

 

In a heat exchanger, the inner dimeter of a tube is 25 mm and its outer diameter is 30 mm. The overall heat transfer coefficient based on the inner area is 360 W/m2°C. Then, the overall heat transfer coefficient based on the outer area, rounded to the nearest integer, is ________ W/m2°C.

GATE 2017

Answer:          300

 

Let I be the spectral blackbody radiation intensity per unit wavelength about the wavelength λ. The black body radiation intensity emitted by a blackbody overall wavelength is

GATE 2017


GATE 2017

Answer:          (C)

 

A fluid flows over a heated horizontal plate maintained at temperature Tw. The bulk temperature of the fluid is T∞. The temperature profile in the thermal boundary layer is given by

GATE 2017

Here, y is the vertical distance from the plate, δt is the thickness of the thermal boundary layer and k is the thermal conductivity of the fluid. The local heat transfer coefficient is given by

(A) k/2 δt

(B)  k/δt

(C)  3k/2 δt

(D) 2k/ δt

                                                                                                      GATE 2017

Answer:    (C)

 

In nucleate boiling, the pressure inside a bubble is higher than the pressure of the surrounding liquid. Assuming that both the liquid and vapour are saturated, the temperature of the liquid will always be

(A) At 100°C

(B)  Lower than the temperature of the vapour

(C)  Equal to the temperature of the vapour

(D) Higher than the temperature of the vapour

                                                                                                GATE 2017

    Answer:          (B)


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