Combine multiple files into single file

General answer

Why not just use the Stream.CopyTo(Stream destination) method?

private static void CombineMultipleFilesIntoSingleFile(string inputDirectoryPath, string inputFileNamePattern, string outputFilePath)
{
    string[] inputFilePaths = Directory.GetFiles(inputDirectoryPath, inputFileNamePattern);
    Console.WriteLine("Number of files: {0}.", inputFilePaths.Length);
    using (var outputStream = File.Create(outputFilePath))
    {
        foreach (var inputFilePath in inputFilePaths)
        {
            using (var inputStream = File.OpenRead(inputFilePath))
            {
                // Buffer size can be passed as the second argument.
                inputStream.CopyTo(outputStream);
            }
            Console.WriteLine("The file {0} has been processed.", inputFilePath);
        }
    }
}

Buffer size adjustment

Please, note that the mentioned method is overloaded.

There are two method overloads:

1. CopyTo(Stream destination).
2. CopyTo(Stream destination, int bufferSize).

The second method overload provides the buffer size adjustment through the bufferSize parameter.

I would use a BlockingCollection to read so you can read and write concurrently.
Clearly should write to a separate physical disk to avoid hardware contention. This code will preserve order.
Read is going to be faster than write so no need for parallel read.
Again since read is going to be faster limit the size of the collection so read does not get farther ahead of write than it needs to.
A simple task to read the single next in parallel while writing the current has the problem of different file sizes - write a small file is faster than read a big.

I use this pattern to read and parse text on T1 and then insert to SQL on T2.

public void WriteFiles()
{
    using (BlockingCollection<string> bc = new BlockingCollection<string>(10))
    {
        // play with 10 if you have several small files then a big file
        // write can get ahead of read if not enough are queued

        TextWriter tw = new StreamWriter(@"c:\temp\alltext.text", true);
        // clearly you want to write to a different phyical disk 
        // ideally write to solid state even if you move the files to regular disk when done
        // Spin up a Task to populate the BlockingCollection
        using (Task t1 = Task.Factory.StartNew(() =>
        {
            string dir = @"c:\temp\";
            string fileText;      
            int minSize = 100000; // play with this
            StringBuilder sb = new StringBuilder(minSize);
            string[] fileAry = Directory.GetFiles(dir, @"*.txt");
            foreach (string fi in fileAry)
            {
                Debug.WriteLine("Add " + fi);
                fileText = File.ReadAllText(fi);
                //bc.Add(fi);  for testing just add filepath
                if (fileText.Length > minSize)
                {
                    if (sb.Length > 0)
                    { 
                       bc.Add(sb.ToString());
                       sb.Clear();
                    }
                    bc.Add(fileText);  // could be really big so don't hit sb
                }
                else
                {
                    sb.Append(fileText);
                    if (sb.Length > minSize)
                    {
                        bc.Add(sb.ToString());
                        sb.Clear();
                    }
                }
            }
            if (sb.Length > 0)
            {
                bc.Add(sb.ToString());
                sb.Clear();
            }
            bc.CompleteAdding();
        }))
        {

            // Spin up a Task to consume the BlockingCollection
            using (Task t2 = Task.Factory.StartNew(() =>
            {
                string text;
                try
                {
                    while (true)
                    {
                        text = bc.Take();
                        Debug.WriteLine("Take " + text);
                        tw.WriteLine(text);                  
                    }
                }
                catch (InvalidOperationException)
                {
                    // An InvalidOperationException means that Take() was called on a completed collection
                    Debug.WriteLine("That's All!");
                    tw.Close();
                    tw.Dispose();
                }
            }))

                Task.WaitAll(t1, t2);
        }
    }
}

BlockingCollection Class

One option is to utilize the copy command, and let it do what is does well.

Something like:

static void MultipleFilesToSingleFile(string dirPath, string filePattern, string destFile)
{
    var cmd = new ProcessStartInfo("cmd.exe", 
        String.Format("/c copy {0} {1}", filePattern, destFile));
    cmd.WorkingDirectory = dirPath;
    cmd.UseShellExecute = false;
    Process.Start(cmd);
}