Log Mean Temperature Difference (LMTD) Method with Examples

Logarithmic Mean temperature Difference is used to measure the Heat transfer rate in double pipe heat exchanger. The rate of heat transfer is got from the formula -

Q = U.A.LMTD .

U= Heat Transfer Co-efficient
A= Heat Transfer Surface Area
LMTD=  Mean Temperature Difference

LMTD is the logarithmic temperature difference between the hot and cold fluids passing through the each ends of heat exchanger pipes.

Log Mean Temperature Difference Method

Formula for LMTD calculation - 

LMTD or Logarithmic Mean Temperature Difference  is calculated by keeping some factors in mind 

  • The type of the heat exchanger 
  • temperature of the fluids at the four end positions 
These are - 
  • Inlet temperature of the hot fluid 
  • Inlet temperature of the cold fluid 
  • Outlet temperature of the cold fluid
  • Outlet temperature of the hot fluid 
LMTD =  dT1 - dT2 /ln (dT1/dT2)  

For parallel flow - 

dT1 = Temperature of the hot fluid entering - Temperature of the cold fluid entering 
dT2 = Temperature of the hot fluid exit - Temperature of the cold fluid exit 

For counter flow - 

dT1 = Temperature of the hot fluid entering - Temperature of the cold fluid exiting
dT2 = Temperature of the hot fluid exit - Temperature of the cold fluid entering  

Mathematical Example : 

1. For a Parallel Flow Heat Exchanger,  Hot fluid entering at temperature 100 degree Celsius and exiting at 90 degree Celsius . Cold fluid Entering at 30 degree Celsius and exiting at 50 degree Celsius. Find the LMTD . 

For Parallel or co - current flow , 

According to the above mentioned formulas - 

LMTD = ((100 - 30)-(90-50)) / ln (100-30/90-50) = 53.6 degree Celsius . 

2. For a Counter Flow Heat Exchanger for same data calculate the LMTD . 

For Counter Current HE , 

LMTD = ((100-50)-(90-30))/ln(100-50/90-30) = 54.85 degree Celsius . 

So Heat transfer rate for Counter Flow is higher . 

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Stress Strain Graph for Mild Steel explained


When any object of certain material is subjected to tensile or compressive or shear force, there may be a chance that its dimension will be affected.
If the dimension of a material is changed due to application of forces we can say that the material is under stress or experiencing the state of stress.

Stress is defined as the Force per unit cross section area.
Stress = F/A

Stress is mainly of two types normal stress and shear stress.

Normal Stress:

When the force applied is perpendicular to the cross section of the object then the stress is known as normal stress. (The force can be tensile or compressive)

Shear Stress: 

When the force applied is parallel to the material cross section then the stress is known as shear stress.

Stress Strain Graph for Mild Steel (Ductile Material)

stress strain curve for mild steel.

If a relatively small force is applied to ductile material steel and it starts to deform (that means that the steel is in stress and we can measure the strain) then we will a curve which is initially a straight line. After plotting stress vs strain we will get the relation. 
In this stress strain graph of mild steel we will find a straight line , that is up to point A from the origin. From that experimental graph we can conclude that stress is proportional to strain. Up to point A is the limit of proportionality. Within the elastic limit the deformation of the steel will be temporary. After the withdrawal of the force the steel bar will return to its original shape. If the force is increased then steel bar will be deformed elastically up to point B. This is the elastic limit (Point B). Beyond that if the force is increased then the plastic deformation will start and we will have upper yield point C and lower yield point D. For further increase in the force material will experience fracture or breaking stress (Max. Ultimate Stress). From this graph we get Young's modulus of elasticity for steel which is 210 GPa. This graph also associates modulus of resilience as well as modulus of toughness. 

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Plastic Extrusion Process Principles


Extrusion Process Principles

Extrusion process is very common in the plastic industry. It is used for high volume plastic production. In extrusion process the color pigments along with other performance enhancing additives are combined with resin which is then pushed through the rotating screws. The heat and pressure generated within the barrels of screw is dispersed and melts the plastic elements. Thus a homogeneous mixture is produced. A cool die is usually placed at the end of the mixture. After passing through the die the mixture is ready to experience the finishing operation which may include pelletizing, calendaring or other processes. 
The arrangements shows a motor which runs the gear box. The speed is used by this gear reducer box. Which then moves the screw. The metal ingredients is poured through the hopper. The feeding of metal is done in the feeding zone. Then with the increased pressure and temperature of the screw melts the elements in the melting zone. The next part is the melt pumping zone which increases the pressure of the liquid. This pressurized liquid is then pushed through the filter. Then the molten metal flows through the die and cooled. The thermocouple is set at different points to measure the temperature. The figure of the whole process is shown below. Click on it to have a better view . 

Advantages of Plastic Extrusion Process

One of the main advantages of the extrusion process is it can produce pipes of any length. It is continuous. High production volumes with very low cost per pound. The melting is very efficient. The mixing of the ingredients is very good. Different types of raw materials can be used. It uses thermoplastics which can be reused.

Disadvantages of Plastic Extrusion Process

Highly complicated parts are very not suitable for production in extrusion process. It can only produce the parts which have uniform cross sections. 

Please Read : 

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Different Types of Plastics- Advantages and Disadvantages

Plastics can be classifies into two broad categories -
Thermosets and Thermoplasctics. A brief description of these two classes will be discussed here.

  • Thermosets are the kind of plastics which are not recyclable. They undergo a kind of chemical change at the time of heating. As a result  they can be shaped once because of this permanent chemical change. This process is known as heat hardening. They are also known as thermosetting plastics. Examples : Epoxy Resin, Melamine formaldehyde , polyester resin , Urea formaldehyde. 
  • Thermoplastics are the recyclable types. While heating they undergo a temporary chemical change. After the heat is removed they retain their original shape. The process is known as heat softening.  Examples : Polyamide (Nylon), Polymethyl methacrylate, polypropelene, polystyrene, Low density Polythene (LDPE), High density Polythene (HDPE). 
Different Types of Plastics

Different Manufacturing Processes for Plastics 

Different manufacturing process for plastics include 
  • extrusion
  • lamination 
  • foaming
  • thermal forming 
  • molding 
  • solid-phase forming
  • molding, 
  • spinning  
  • casting   
The molding process alone have five different procedures -

  • Compression
  • Transfer
  • Blow
  • Rotational 
  • Injection 

The injection molding, Blow molding, Extrusion as well as calendering uses thermoplastics for fabrication. High Pressure Lamination, Compression Molding and reaction injection method uses thermosets

Advantages and Disadvantages of using Plastics 


  • Plastic is very light in weight. 
  • It has high strength to weight ratio. 
  • Complex parts can be easily manufactured. 
  • Plastics can be of variety of colors or can be clear. 
  • It is free from corrosion. 
  • It can work as a electrical as well as thermal insulator. 
  • It can damp the vibration. 

  • Creeping can be problem. 
  • It cannot withstand extreme heat. So it is thermally unstable. 
  • It can be UV light sensitive. 
  • The stiffness is relatively low in comparison to other tough materials. 
  • It has a low strength.
  • Reworking or repairing of plastic is very tough. 
  • Recycling of plastic is a hard job.  

Please Read :
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Diferent Parts of Sand Mold- Features


Cope and drag in Sand Mold :

Cope and Drag are the two parts of the casting flask. Cope is the upper part and drag is the lower part. Even if the casting process is flaskless , the same terms are used for the upper ans lower parts. Generally the flask is made of wood or metal. It contains molding sand. When metal is poured into the mold cavity the flask supports the mold.

Gating system:

If the molten metal is poured directly from the ladle , it will erode the bottom of the mould cavity. So molten metal is poured from the ladle to the cavity through a gating system. The gating system in casting creates a series of channels through which molten metal reaches the cavity. Gating system has -

  • Pouring Basin : It receives the molten metal from the liquid metal container. 
  • Sprue : Pouring cup is attached to the sprue. It is vertical in shape . On the other part of the sprue there is part called runner. 
  • Sprue Base : Its the base of the sprue
  • Runner : It is the horizontal part of the gating system. It connects the spues with the gates. 
  •  The next part is the choke. 
  • Then comes the skim bob 
  • Gates and ingates : It controls the movement of the metal from the runners into the cavity. 
  • Riser 

sand mold features

different parts of sand mold


The risers are also known as feed heads. When the metal solidifies it starts to shrink. And then risers comes into play. These feeder supply metals to the cavity when shrinking of the metal starts. 

sand mold gating system for a horizontal plating mold

sectional view of a sand mold


Cores are required to create the castings with holes. It can be made of refractory materials. Most often core sand is used to make it. Metal cores are also available but less frequently used. 


Chaplets are the supports for the cores. These are needed particularly when the cores are very big. Usually metal pieces are used to support the core. Without chaplets the core can be displaced and the casting can be spoiled. These chaplets are set-up between the core and mold surface. Caution should be taken while placing chaplets. Clean, oil and moisture free pieces should be used as chaplets. 


These are huge metal pieces used to reduce the effect of shrinkage. These increases the thermal conductivity and heat capacity. It helps in speeding up the cooling process. So thick metal parts are cooled quickly. They can be used along with the risers. 

Please read : 

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Lost Wax or Investment Casting Method Steps

Investment or lost-wax castings:

The Lost-wax method, sometimes, also called simply as precision-investment casting has been used for many years by jewelers and dentists. Since world-war-II, the method has been adapted to the production of small and precise, industrial fasting. Basically, the method involves the use of expendable (heat disposable) pattern unrounded with a shell of refractory material to form the casting mould.  Example: Piston making.
Cast parts are formed by putting the molten metal in the cavity. The wax pattern is melted and it is not reusable because of that the method is named "lost - wax method".

Follow :

 The steps involved in this Lost Wax Method  method are explained below:
  • Wax injection
  • Assembly
  • Shell building
  • Dewax
  • Conventional casting
  • Knockout
  • Cut-off
  • Finished castings
   (a) Wax patterns are usually made by injection molding

   (b) Multiple Patterns are assembled in central wax sprue .

(c) The assembly is immersed in a liquid ceramic slurry. After that this structure is dipped into a bed of very fine sand. More than one layer of sand may be necessary.

(d) The ceramic becomes dry. The wax is then melted. To melt all the wax ceramic is fired.

(e) Simple gravity pouring is used for filling the mould. After solidification all the parts of the ceramic structure become casting. Hollow castings can be made by pouring out the extra metal before solidification.

(f) The metal cools to room temperature and after that the ceramic structure is broken off by water blasting or by applying vibration. 

(g) The parts are separated by the high speed friction saw. Minor finishing is given to the parts. 

Advantages of Investment Casting Method:
  1. Intricate details can be cast.
  2. Undercuts and other shapes, which would not allow the withdrawal of a normal pattern, are easily obtained.
  3. The surface is very smooth and there is no parting line.
  4. High accuracy can be obtained so that much of complicated and costly machining can be eliminated.
  5. Unmachinable alloys can be cast.
  6. More than one casting can be made at a time.
  7. It can be reused.
  8. Preferred for casting weight less
Limitations of Lost Wax Casting :
  1. It is involved and thus expensive
  2. It has limitations in use of and location of holes
  3. The parts are limited in size to a few kg
  1. Parts for aerospace industry
  2. Parts for computers
  3. Parts for food and beverage
  4. Costume jewellery
Please Read : 
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Die Casting Principles

Die casting process is very different from sand casting as the mould used here is permanent. The mould is not expandable and need not to be broken after the cooling and solidification. Here the mould is called the die. 

Please Read : 

Die Casting Principles

Gravity die casting:
When the molten is metal is poured under a gravity head into the permanent mould it is called gravity die casting. It is also known as permanent mould casting. 

Gravity Die Casting properties:
(a)    It uses permanent mould and cavity. 
(b)   Accurately machined. 
(c)    Decent thermal conductivity 

Applications of gravity die casting 
These are used to make precision aluminum precision casting parts, machine parts, motor parts, heavy metal parts. 

Pressure die casting:
When molten metal is injected into the permanent metallic mould by the means of the external pressure it is known as die casting or pressure die casting. In this process the liquid metal is forced into the permanent die. 

Applications of pressure die casting  
Cast parts obtained from pressure die casting are used in automobiles , electrical equipment, motors, machine parts, telecommunication equipment, building materials, auto ancillary and many other sectors. Home appliances and children's toys also use pressure die cast parts . 

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Sand Casting Process with Diagram

Sand casting:
In sand casting which is also known as sand molded casting, an object is produced by sand mold. The process involves pouring of the molten metal in to the mold cavity. The molten metal is then cooled to the room temperature. The metal is solidified. After cooling, the metal object is separated from the mold.  Sand casting process has its advantages and disadvantages. So care should be taken while making delicate products. 

The six  main steps in this process are - 
  • Pattern making and placing it the sand mold. 
  • Making a proper gating system in the mold. 
  • Removing the pattern. 
  • Pouring the molten metal in the mold cavity. 
  • Cooling the mold to the room temperature. 
  • Breaking the mold and getting the casting. 
Please read : A complete guide to steps involved in casting process 

Before making the mold the properties of the molding sand should be checked.  There are different types of molding sands. Each type of sand is used in molding according to the cast materials and application of the materials. Mainly Green or Natural and Synthetic Sands are used

Another important factor is the pattern. Different types of patterns are available . Before making patterns these thing should be kept in mind. 

sand casting process

sand casting process diagram

Production steps in sand castings:

steps in sand casting

Figure: Steps involved in sand casting. This production sequence involves casting operation and pattern and mold making. 

After removing the casting engineers should look for the casting defects. If the defects are there then it should be identified. 

Please read 

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A Complete Guide to Steps Involved in Casting Process

We know that casting is the process of pouring molten metal in a desired shaped cavity and allowing it to solidify. After the solidification we get the desired shaped object.

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Basic Operation of the casting process
  • First we have to make a pattern 
  • Then the we have to melt the metal by applying heat 
  • pouring the metal into the mold and confirming that the metal gets the desired shape. 

What is Pattern in Casting Process  

Pattern is the object used to make cavity in the mold. The molten metal is poured into this cavity.

Why a good Pattern is required in casting ? 

  • To obtain the desired shape and size. 
  • It is easy to design and manufacture. 
  • making a pattern is not expensive. 
  • It is of high strength. 
Pattern Materials 
  • Wood 
  • Cast Iron / Brass 
  • Aluminum or White metal 
  • Plastic gypsum 
For a complete knowledge of pattern materials go to this link

Pattern Allowances 

  • Shrinkage allowance (due to cooling)
  • Machining allowance (due to machining)
  • Shaking allowances (due to rapping)
  • Draft allowance (follow the link)
  • Distortion allowance (due to irregular shape) 
For a complete knowledge about the allowances in patterns follow this link
Different Types of Patterns used in Casting 

  • Split piece pattern 
  • Match plate pattern 
  • cope and drag patterns 
  • sweep patterns 
  • draw backs 
  • Loose piece pattern 
  • Gated pattern 

Preparing Mould for the Casting 

While preparing mould one should be very careful . Different types of sands and binders are used in mould preparation. These are 

Green sand mould: Natural sands , clay and water is used in making green sand mould. It is very cheap with acceptable errors.  

Dry Sand Mould: It is natural sand mould with cereal and pitch used binders. 

Other materials for mould preparation includes silica sand and binder with additives. 

Please Read : 

Different Properties of the moulding sand 

These are the desired properties of the moulding sand 
  • Refractoriness 
  • Cohesiveness 
  • Permeability 
  • Co-efficient of expansion 
  • Adhesiveness 
  • Collapsibility 
  • Plasticity 
For details of each of the properties follow this link : 

Tests for the different moulding sands 
  1. Moisture Content Test 
  2. Fineness Test 
  3. Testing Amount of Clay 
  4. Permeability Test 
  5. Mould hardness test 
  6. Strength or cohesiveness test 

Core Making 

What is Core ? 
It is a structure made of refractory material . It is prepared before pouring the molten metal on to the cavity. There is another term known as core print which is the projection on a pattern used to make spaces in the mould. It is also known as core seat. 

Criteria for selecting a furnace for casting 

  1. Capacity needed to hold the molten metal 
  2. Melting rate 
  3. Quality of the melt 
  4. Temperature needed 
  5. Method of pouring 
Operation in Cupola Furnace 

Cupola is the most popular furnace for casting non ferrous and ferrous materials . It is known as a shaft furnace. The shell of cupola furnace is made of steel of 8-10 mm thickness. The shell is supported by columns or legs. The inside of the furnace is lined with refractory material to save the furnace from over heating.  

Different types of casting processes 

  1. Sand Casting 
  2. Shell Mold Casting 
  3. Expandable Mold Casting 
  4. Plaster Mold 
  5. Ceramic Mold 
  6. Investment Mold or Lost Wax Casting  
  7. Permanent Mold 
  8. Die Casting 
  9. Centrifugal casting 
Casting Defects 

steps involved in casting process

And lastly comes the casting defects. These defects can occur for different reasons like air trapping in the sand mold, low quality sands, improper ramming , defecting sand mold etc. Go through this link for detailed knowledge of casting defects.

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Different Types of Pattern Allowances in Casting


Pattern allowances:

There are some allowances which are responsible for the difference in the dimensions of the casting and the pattern. These allowances are considered when a pattern is designed for casting. In this article we will discuss those allowances -

Different types of Pattern Allowances in casting process

1.     Shrinkage allowance:

After solidification of the metal from further cooling (room temp.) dimensions  of the patterns increases. So pattern size is bigger than that of the finished cast products. This is known as shrinkage allowance. 

It depends on:
a)      Dimensions of casting
b)      Design and intricacy of casting
c)       Resistance of mol to shrinkage
d)      Molding materials used
e)      Method of molding used
f)       Pouring temp of the molten metal

2.     Draft or taper allowance:

Pattern draft is the taper placed on the pattern surfaces that are parallel to the direction in which the pattern is withdrawn from the mould (that is perpendicular to the parting plane), to allow removal of the pattern without damaging the mould cavity.

It depends on:
a)      the method of molding
b)      the sand mixture used
c)       the design (shape and length of the vertical side of the pattern)
d)      economic restrictions imposed on the casting
e)      intricacy of the pattern

3.     Distortion allowance:

This allowance is taken into consideration when casting products of irregular shapes. When these are cooled they are distorted due to metal shrinkage.

4.     Finishing or machining allowance:

Machining allowance or finish allowance indicates how much larger the rough casting should be over the finished casting to allow sufficient material to insure that machining will "clean up" the surfaces.

This machining allowance is added to all surfaces that are to be machined. Machining allowance is larger for hand molding as compared to machine molding.

It depends on:
a)      Machining operation
b)      Characteristics of metal
c)       Methods of castings
d)      Size, shapes and volumes of castings
e)      Degree of finish required in castings
f)       configuration of the casting

5.     Shaking or rapping allowance:

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